generalized solution procedure for slope stability analysis using...

Generalized Solution Procedure for Slope Stability Analysis Using Genetic Algorithm 5

Generalized Solution Procedure for Slope Stability AnalysisUsing Genetic Algorithm

유전자 알고리즘을 이용한 사면안정해석의 일반화 해법

Shin, Eun-Chul1신 은 철

Chittaranjan R. Patra2시타라잔 파트라

R. Pradhan3프라드한

요 지

이 논문에서는 사면 안정 해석시 경사 절편법을 이용하여 안전율을 구하며 유전자 알고리즘방법을 이용하여

한계파괴면을결정하는이론을제안하였다 해석방법에서는한계전단파괴면과안전율을찾고비선형평형방정.식의해를구하기위해구속최적화문제로간주하여해석을수행하였다 유전자알고리즘방법의효율성을검증하.기 위하여 예제를 논문에 포함하였다 유전자 알고리즘 방법에 의하여 도출된 사면 안정 해석결과는 기존방법에.비하여 우수한 것으로 판명되었다.

Abstract

This paper pertains to the incorporation of a genetic algorithm methodology for determining the critical slip surfaceand the corresponding factor of safety of soil slopes using inclined slice method. The analysis is formulated asa constrained optimization problem to solve the nonlinear equilibrium equations and finding the factor of safetyand the critical slip surface. The sensitivity of GA optimization method is presented in terms of development offailure surface. Example problem is presented to demonstrate the efficiencies of the genetic algorithm approach.The results obtained by this method are compared with other traditional optimization technique.

Keywords : Consolidation, CRS test, Strain rate, Incremental loading test, Preconsolidation pressure

1 Member, Prof., Dept. of Civil & Environmental Engrg., Univ. of Incheon, [email protected], Corresponding Author2 Associate Prof., Dept. of Civil Engrg., National Institute of Technology, India3 Dept. of Civil Engrg., National Institute of Technology, India

1. Introduction

The stability of slopes has received wide attention due

to its practical importance in the design of excavations,

embankments, earth dams, and rock fill dams etc. Generally,

limit equilibrium techniques are commonly used to assess

the stability of slopes, as complex geological sub-soil

profiles, seepage, and external loads can be easily dealt

with. Most of these analytical approaches use either the

vertical method of slices or the multiple-wedge methods.

It has been recognized quite early that slope stability

analysis is essentially a problem of optimization (Basudhar,

1976; Baker and Garber, 1977) namely the determination

of the slip surface that yields the minimum factor of

safety. Many methods of factor of safety computations

for slopes using circular and noncircular slip surfaces

Jour. of the KGS, Vol. 24, No. 3. March 2008, pp. 5 11～

6 Jour. of the KGS, Vol. 24, No. 3, March 2008

have been developed over the years. Many slope stability

softwares using the limit equilibrium analysis have been

described in literature (Fredlund, 1984). Most of the

programs provided an automated version of the existing

methods of slope stability analysis. The need for auto-search

led to the use of sophisticated optimization algorithms

(Krugman and Krizek, 1973; Narayan and Ramamurthy,

1980). But such earlier attempts were based on the

assumption of circular slip surfaces. Successful use of

optimization techniques in slope stability analysis without

any a priori assumption regarding the shape of critical–surface has been reported (Martin, J. B., 1982; Arai, K.

and Tagyo, K., 1985; Bhattacharya, G. 1990). However,

these analyses have been made by considering slices to

be vertical and also traditional optimization algorithms

have been used for automated search of critical slip

surface and factor of safety.

The methods in use include a rectangular or trapezoidal

grid search and simplex optimization. For noncircular slip

surfaces, this is more complicated, as the number of

variables to be optimized can be substantially larger. The

traditional mathematical optimization methods that have

been used include dynamic programming, conjugate-gradient,

random search, and simplex optimization. The main short-

coming of these optimization techniques is the uncertainty

as to the robustness of the algorithms to locate the global

minimum factor of safety rather than the local minimum

factor of safety for complicated and non-homogeneous

geological subsoil conditions.

We proposed in this paper an alternative method of

determining the critical slip surface using a genetic-based

evolution technique called genetic algorithms (GAs). GAs

have been found wide spread application in variety of

problem domains because of their minimal requirement,

ease of operation, global perspective. The GA is becoming

increasingly popular in engineering optimization problems

because it has been shown to be suitably robust for a

wide variety of problems. The incorporation of genetic

algorithms in the slope stability analysis will be described.

Examples are presented to demonstrate the effectiveness

of the proposed approach. The critical acceleration Kc

required to bring the slope to a condition of limiting

equilibrium is given by

PEEeeeEAE

K nnnnc

1211 +−− −+=

K(1)

Where,

2311121 eeeaaeeaeaaAE nnnnnnnn KKLL −−−− ++++=(2)

2311121 eeeapeepeppPE nnnnnnnn KKLL −−−− ++++=(3)

( )( ) 111 seccos

cos

+++ ′−′+−′−′

=iiiii

iii

Wp

φδφαφαφ

(4)

( )( ) 111 seccos

seccos

+++ ′−′+−′′−′+−′

=iiiii

iiiiiie φδφαφ

φδφαφ(5)

( ) ( )( ) ( )( ) ( ) ( ) ( )11 sinsin

cossin

++ ⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−′⋅−−−′⋅+

′+−′Δ+Δ+=

iiiisiiiis

iiiiiqiivii

SS

RlqPWa

δαφδαφ

φαφ

( )11

1

coscos

++

+

−′+−′′

×iiii

i

δφαφφ

(6)

Where, iiiiii UbcR φα ′−′= tancos (7)

( ) ( ) iiwiiis PdcS φ′−′= tan (8)

( )iwP , ( ) 1+iwP are the water pressures on the inclined

inter slice faces.

Ui is the pore water pressure on the base of the slice.

The coefficient of critical acceleration (Kc) is calculated

by using the equation 1. If for a slope Kc is not equal

to zero, the static factor of safety is calculated by reducing

the shear strength simultaneously on all sliding surfaces

until the minimum Kc is obtained. This is achieved by

the following substitutions in equations 4 to 8.

LiLiLiLiii ffcffcFFc 11 tan,,tan,,tan, ++ ′′′′′′ φφφ

Where, fL = local factor of safety along inter slice faces.

fL = F = average factor of safety along the

surface, if F > 1.1; otherwise fL = 1.1, have been

adopted.

If there is no tension crack, then E1 = En+1 = 0. The

forces acting on the sides and base of each slide are found

by the progressive solution of the following equations,

starting from the known condition that E1 = 0.


iiciii eEKpaE +−=+1 (9)

( )( ) iiiiwii dcPEX ′+′−= +1tanφ (10)

( ) ( )iiiiiiiiii

iiiiiqiivii bcUEE

XXlqPWN

ααφδδ

δδ×⎟⎟⎠

⎞⎜⎜⎝

⎛

′−′++−

++Δ+Δ+=

++

++

tansintansinsin

coscos

11

11

( )ii

i

αφφ−′′

×cos

cos(11)

( ) iiiiiii bcUNS αφ sectan ′+′−= (12)

The normal stresses acting across the base and the sides

of a slice are calculated as

follows:

( ) ( ) iiiiib bUN ασ cos−=′ (13)

( ) ( )( ) iiwiis dPE −=′σ (14)

1.1 Design Variables, Objective Function and Con-

straints

After the stability equations are derived it is necessary

to identify the design variables and objective function,

which control the analysis and are to be estimated. For

this it is necessary to follow a set of iterative procedure

to find the minimum value of the objective function and

the corresponding values of the design variables at the

optimal point. However, the search for the optimal values

of the objective function and the corresponding design

vector cannot be made unrestrictedly. Some design restric-

tions called constraints are to be imposed so that the

obtained solution is physically meaningful. The design

variables, objective function and constraints that are relevant

to the present study are as follows:

1.2 Design Variables

The discretization model of the soil slope is shown in

Fig 1. Referring to the figure the identification of design

variables are made as follows:

The design vector D is,

( )TTsnnT zxxbbbFD ,,,,,,,,,,, 21121 KKKK −= ααα (15)

Where, F = average factor of safety along the slip

surface.bnbb ,,, 21 KK = width of nth slices.

121 ,,, −nααα KK = base inclination of the slices with

horizontal, positive in anti-clockwise direction.

121 ,,, −nδδδ KK = angle of inclination of inclined faces

with vertical, positive in clockwise direction.

sx = distance of starting point of the slip surface from

the bottom corner of the slope.

TT zx , = x and z coordinates of tension crack respec-

tively.

1.3 Objective Function

Once the design variables are identified, the function,

which is to be optimized, called objective function and

denoted by F (D) should be developed. In this case, by

taking only the force equilibrium, minimization of factor

of safety subjected to the condition that the value of Kc

should be zero is the objective. In this case the solution

is achieved by putting the value of Kc as a constraint.

Here, F (D) = F (16)

1.4 Design Constraints

To ensure that the obtained solution is physically

meaningful, the following design constraints need to be

imposed.

The critical surface should be concave when looked

from the top.

As the soil cannot take tension, the developed normal

stress at the base of the slice should be positive to avoid

generation of tension in the soil and inconsistent direction

Fig. 1. Discretization model for with inclined slices


of shear.

Normal stresses generated on the inclined inter slice

faces should be positive to avoid development of tension

there.

Since the value of Kc should be very small, the

following constraint has been put on Kc. Minimization of

the objective function should result in values of Kc tending

to zero.

The last point (b) of the critical slip surface should not

intersect the sloping portion.

2. Genetic Algorithm Tool

Genetic algorithm is a search technique based on the

principle and mechanism of natural selection and evaluation

where the stronger individuals are likely to survive in a

competing environment. The GA operates on an iterative

procedure on a set (population) of candidate solution of

the problem to be optimized. Each candidate (chromosome)

of this set is a concatenated version of the binary

substrings representing design variables of the problems

to be optimized. Initially these candidate solutions are

generated randomly which are then altered probabilistically

and carried forward for next iteration (or generation)

guided by three basic processes namely selection,

crossover and mutation. The fitness in a GA technology

is nothing but the value of objective function. Thus each

solution string is associated with a fitness value. (1)

selecting, according to the fitness value, some of the

solution strings of the present generation and also the

resulting combination and (2) rejecting others so as to

keep the population size constant form a new generation

of solution. While selection operation makes more copies

of better string, the crossover parameter controls over the

creation of new string by exchanging information among

the strings. In order to preserve some of the good strings

that are present in the population, selection of strings for

the crossover is done with a probability. Mutation operator

acts as a switch when the population becomes homogeneous

due to iterative use of cross over and mutation operations.

The actual optimization process requires the values of

some GA parameters such as string length of each decision

variable, population size, crossover parameters. Based on

the desired accuracy, the string length for each decision

variable is taken.

2.1 Methodology

In order to apply GA, the slope stability problem is

defined in terms of certain design variables. The function

to be optimized (objective function) and the guiding rules

(constraints) are expressed in terms of these design variables.

2.2 GA Based Problem Formulation

In the context of genetic algorithm, the present problem

has been put into the mathematical framework as follows:

Find (x1,x2, ..,x…… m) to minimize F(x) subject to gj(x)

0 for j = 1,2, m.≥ ………Where, x1,x2, ..,x…… m represents the design variables

corresponding to the base inclination of the slices, base

widths, locus of start point, and position of tension crack.

The terms gj(x) are set of j constraints. F(x) denotes either

objective function or the sum of objective function and

penalty term as discussed later.

The objective function is taken as the factor of safety

of the slope.

2.3 Fitness Function

Fitness of any string is the value returned to GA, based

on which GA operators modify the population. In present

problem Fit(x) is used as fitness function which denotes

the factor of safety with penalties after applying trans-

formation to convert maximization problem to the minimum

one. GA operators minimize F(X) which in turn reduces

the penalties and factor of safety of the given slope.

Transformation:

As GAs are basically maximization search techniques,

to convert the minimization problem to maximization one,

many types of transformations are available. In the present

formulation the following transformation is used.

( ) ( )xFxFit+

=1

1(17)


Where, Fit(x) is the Fitness function and F(x) is the

objective function.

2.4 Constraint Handling

Various physical and behavior constraints are used to

solve this class of problems. To take care of constraints,

the reproduction operator may be modified so that if the

solution is feasible (one or more constraints are violated),

the string is not copied to the mating pool. The problem

of finding a feasible solution is as difficult as the finding

of the optimal solution, especially when the number of

design variables and the design constraints are more. This

penalty terms are usually used to take care of these

constraints. So, in constrained optimization case, instead

of using the objective function as fitness, each constraint’s

violation is added to the objective function. As in the

present problem the constraints are taken in the normalized

form, and a single penalty coefficient is taken here. Hence

the composite function reduces to

( ) ( ) ( )xGrxFxFconn

jjkcomp ∑

=

+=1 (18)

Where, ( )xFcomp is the composite function, ( )xG j is the

constraint term applied to each variable, conn = total number

of constraints and kr is the penalty parameter.

3. Results

The present methodology is validated with the help of

a published example.

3.1 Example Problem

A problem (Spencer, 1967, Figure 2) is considered for

the validation of the optimization formulation of predicting

the minimum factor of safety and corresponding critical

slip surface. The same problem has been reanalyzed and

reported by Bhattacharya (1990) in order to validate his

proposed direct and indirect optimization formulation of

stability computations using vertical slices as reported in

literature. Here, by using the vertical slices, the same

problem has been reanalyzed and reported. The results

obtained are compared with that of Bhattacharya (1990)

and some other solutions reported in the literature.

This problem has been solved in conjunction with

genetic algorithms by considering the failed soil mass

bounded by the failure surface and the free ground surface

to be made up of a number of vertical slices. The

following GA parameters have been found suitable for

solution of this class of problem after successive numerical

experimentations as shown in Table 1.

In the present method by taking interslice faces vertical

and by taking 4, 6, 8, 10 and 12 number of slices, the

factor of safety and the critical slip surface is obtained.

In the present analysis no tension crack is taken and the

starting point of the slip surface is taken at the toe of

the slope.

The effect of number of slices on critical slip surface

and the factor of safety of the slope are critically examined

by using genetic algorithms. The results are shown in

Table 2, and Figure 3. The critical accelerations associated

with the critical slip surfaces corresponding to different

number of slices are also indicated in the Table 2. From

the Table 2 it is seen that with the increase in the number

of slices from 4 to 8, the obtained factor of safety

decreases. After 8 number of slices the factor of safety

increases. However the change in factor of safety with

the change in number of slices is marginal. Also, from

Figure 3, it is shown that the critical slip surfaces obtained

with 4, 6, 8, 10 and 12 number of slices fall in a narrow

Fig. 2. Spencer’s problem

Table 1. GA parameters

Population size 20

Probability of crossover (Pc) 0.8

Probability of mutation (Pm) 0.1

Total string length 16


zone which is also observed by Janbu (1979). The critical

accelerations obtained in all these cases are sufficiently

small to be taken to be zero as shown in Figure 3. Thus

it is prudent to take 8 numbers of slices if vertical slices

are considered in the analysis.

In Figure 4 the critical slip surface obtained by 8 number

of slices has been compared with the solution reported

by Bhattacharya (1990) using Janbu’s method with non-linear

programming and Patra et al. (2003) using Sarma’s method

with non-linear programming. From the figure it is seen

that the solutions obtained are in close agreement with

the known solutions reported in the literature. All these

critical surfaces fall in a zone rather than a well-defined

failure surface.

4. Concluding Remarks

It has been shown that the GA method that uses

probabilistic transition rules rather than deterministic rules

means that the search is normally not trapped in local

optima unlike other traditional methods. This method is

capable of obtaining the optimal solution starting from

broad range of domain of design variables.

The critical slip surfaces obtained through GAs crowd

over a zone instead of single well-defined surface. The

factor of safety obtained by this method is not very much

sensitive to the number of slices.

References

1. Arai, K. and Tagyo, K. (1985), “Determination of noncircular slipsurface giving the minimum factor of safety in slope stabilityanalysis”, Soils and Foundations, Vol.25, No.1, pp.43-51.

2. Baker and Garber, M. (1977), “Variational approach to slopestability”, Proceedings of 9th International Conference on SoilMechanics and Foundation Engineering, Tokyo 2, pp.9-12.

3. Basudhar, P. K. (1976), “Some application of mathematicalprogramming techniques to stability problems in GeotechnicalEngineering”, Ph.D. Thesis, Indian Institute of Technology, Kanpur,India.

4. Bhattacharya, G. (1990), “Sequential unconstrained minimizationtechnique in slope stability analysis”, Ph.D. Thesis, Indian Institute

Fig. 3. Effect of number of vertical slices on the critical slip surface

(problem 2)

Fig. 4. Comparison of critical slip surfaces by different methods

Table 2. Factor of safety and critical acceleration factor for different numbers of vertical slices

Surface Number of slices Factor of safety Critical acceleration factor (Kc)

1 4 1.06063 0.000072

2 6 1.04593 0.000049

3 8 1.03815 -0.000063

4 10 1.09061 -0.000048

5 12 1.10861 0.000903

Table 3. Comparison of Solutions with other investigators

Surface Investigator Factor of Safety

1 Patra et al. (2003) 1.04

2 Bhattacharya (1990) 1.00

3 Spencer (1967) 1.07

4 Present Method 1.04


of Technology, Kanpur, India.5. Fredlund, D. G. (1984), “Slope stability software usage in Canada”,proceedings of Speciality session in Computers in Soil Mechanics:Present and Future, IX International conference on Soil Mechanicsand Foundation Engineering, pp.289-302.

6. Janbu, N. (1973), “Slope stability computation”, In: R.C. Hirschfeldand S. J. Poulous (eds.), Embankment Dam Engineering, CasagrandeVolume, John Wiley and Sons, Newyork, pp.47-86.

7. Krugman, P. K. and Krizek, R. J. (1973), “Stability charts forinhomogeneous soil condition”, Geotechnical Engineering, Journalof South east-Asian Society of Civil Engineering, Vol.4, pp.1-13.

8. Marins J. B. (1982), “Embankments and slopes by mathematicalprogramming”, In: J. B. Martins (ed.), Numerical Methods inGeomechanics, D. Riedel Publishing Company, pp.305-334.

9. Narayan, C. G. P. and Ramamurthy, T. (1980), “Computer algorithmfor slip circle analysis”, Indian Geotechnical Journal, Vol.10, No.2,pp.238-250.

10. Patra, C. R. and Basudhar, P. K. (2003), “Generalized SolutionProcedure for Automated Slope Stability Analysis using InclinedSlices”, Geotechnical & Geological Engineering, Vol.21, pp.259-281.

11. Sarma, S. K. (1973), “Stability analysis of embankments andslopes”, Geotechnique 23, No.3, pp.423-433.

12. Sarma, S. K. (1979), “Stability analysis of embankments andslopes”, Journal of the Geotechnical Engineering Division, ASCE,105, No.GT5, pp.1511-1524.

13. Spencer, E. (1967), “The thrust line criterion in embankmentstability analysis”, Geotechnique, Vol.23, pp.85-101.

(received on Apr. 7, 2006, accepted on Mar. 25, 2008)

Estimation of Nonlinear Site Effects of Soil Profiles in Korea 13

Estimation of Nonlinear Site Effects of Soil Profiles in Korea

국내 지반에서의 비선형 부지효과 예측

Lee, Hong-Sung1이 홍 성 Yun, Se-Ung2

윤 세 웅

Park, Duhee3박 두 희 Kim, In-Tai4

김 인 태

요 지

시간영역에서 수행되는 비선형 지반응답해석에서 지반의 미소변형률 감쇠는 감쇠공식을 이용하여Rayleigh점성감쇠로서 모사된다 실제 지반의 미소변형률 감쇠는 주파수의 영향을 받지 않는 반면 시간영역해석에서의.점성감쇠는 주파수의 영향을 크게 받으며 이의영향정도는 감쇠공식에따라서결정된다 본연구에서는Rayleigh .국내 지반에 대한 비선형 지반응답해석시 감쇠공식의 영향을 평가하고자 일련의 해석을 수행하였다 해석결과.점성감쇠공식은계산된응답에매우큰영향을미치는것으로나타났다 널리사용되는 공식은. Simplified Rayleigh심도 이상의지반에서수치적으로발생하는인공감쇠로인하여고주파수에서의에너지소산을과대예측하는30m것으로나타난반면 공식을사용하며적절하게최적주파수를선정한경우 인공감쇠는크게감소하, Full Rayleigh ,는것으로나타났다 나아가해석결과를등가선형해석과비교한결과 미만의얕은심도지반에서도등가선형. 20m해석은 최대가속도를 과대예측할 수 있는 것으로 나타났다.

Abstract

In a nonlinear site response analysis which is performed in time domain, small strain damping is modeled asviscous damping through use of various forms of Rayleigh damping formulations. Small strain damping of soilis known to be independent of the loading frequency, but the viscous damping is greatly influenced by the loadingfrequency. The type of Rayleigh damping formulation has a pronounced influence on the dependence. This paperperforms a series of nonlinear analyses to evaluate the degree of influence of the viscous damping formulationon Korean soil profiles. Analyses highlight the strong influence of the viscous damping formulation for soil profilesexceeding 30 m in thickness, commonly used in simplified Rayleigh damping formulation overestimating energydissipation at high frequencies due to artificially introduced damping. When using the full Rayleigh dampingformulation and carefully selecting the optimum modes, the artificial damping is greatly reduced. Results are furthercompared to equivalent linear analyses. The equivalent linear analyses can overestimate the peak ground accelerationeven for shallow profiles less than 20 m in thickness.

Keywords : Equivalent linear, Nonlinear, Peak ground acceleration, Site response analysis, Viscous damping

1 Member, Hyundai Engrg. & Construction, Senior Researcher2 Graduate Student, Dept. of Civil Engrg., Hanyang Univ.3 Member, Full-time Lect., Dept. of Civil Engrg., Hanyang Univ., [email protected], Corresponding Author4 Full-time Lect., Dept. of Transportation Engrg., Myongji Univ.



1. Introduction

One-dimensional (1-D) site response analysis is widely

performed to estimate local site amplification effects

during an earthquake (Hashash and Park, 2001; Idriss,

1990; Roesset, 1977), in which ground motion propagation

is approximated as vertically propagating horizontal shear

waves through horizontally layered soil deposit. Solution

of wave propagation is performed in either frequency or

time domain.

Equivalent linear analysis, performed in frequency

domain, is dominantly used in practice due to its simplicity

and ease of use (Schnabel et al., 1972). The equivalent

linear method approximates nonlinear behavior by incor-

porating shear strain dependent shear modulus and damping

curves. However, a constant linear shear modulus and

damping at a representative level of strain are used

throughout the analysis.

In a nonlinear analysis, the dynamic equation of motion

is integrated in time domain and the nonlinear soil

behavior is accurately modeled. However, non-linear site

response analysis formulation contains the viscous damping

term to model damping at small strains that does not

always provide an accurate result. The influence of the

viscous damping formulation has been known to be

important for deep profiles thicker than 50 100 m–(Hashash and Park, 2002). The influence of the formulation

in shallower profiles has not yet been thoroughly studied.

A series of nonlinear site response analyses are performed

to investigate the influence of the viscous damping

formulation at selected sites in Korea, ranging in thickness

from 20 to 50 m. Results are further compared to

equivalent linear analyses.

2. Nonlinear Site Response Analysis

In a nonlinear site response analysis, the response of

a soil deposit is calculated by numerically integrating the

wave propagation equation. Each individual layer i is

represented by a corresponding mass, a spring, and a

dashpot for viscous damping. Lumping half the mass of

each of two consecutive layers at their common boundary

forms the mass matrix. The stiffness matrix is built from

the constitutive model and updated at each time step to

simulate the nonlinear soil behavior.

In a nonlinear analysis, the hysteretic damping is

modeled through the nonlinear soil model. Most nonlinear

soil models display linear behavior at small strains, while

the laboratory tests show that the soils damp the vibration

even at very low strains. The small strain damping, which

represent the damping ratio of the damping curve at the

lowest strain level, is modeled by the viscous damping

matrix [C]. Laboratory tests show that the small strain

damping of cohesionless soil is independent of the loading

frequency, while the cohesive soils are frequency dependent

to a limited extent (Kim et al., 1991). However, for

practical purposes, it is reasonable to assume that the small

strain damping is frequency independent. In a time domain

analysis, it is not possible to make the small strain

damping independent of loading frequency.

The type of the damping formulation determines the

degree of frequency dependence of the small strain

damping. In the original damping formulation proposed

by (Rayleigh and Lindsay, 1945), the [C] matrix is

assumed to be proportional to the mass and stiffness

matrix:

[ ] [ ] [ ]0 1C a M a K= + (1)

Scalar values of a0 and a1 can be computed using two

significant natural modes m and n using the following

equation:

0

1

1/11/4

m m

n n

f f af f a

ξξ π

⎧ ⎫⎡ ⎤⎡ ⎤= ⎨ ⎬⎢ ⎥⎢ ⎥

⎣ ⎦ ⎣ ⎦ ⎩ ⎭ (2)

where fm and fn are frequencies corresponding to selected

modes m and n.

The damping matrix is assumed in most nonlinear

seismic site response analysis codes to be only stiffness

proportional (Borja et al., 2002; Matasovic and Vucetic,

1995), since the value of a0[M] is small compared to

a1[K]. Small strain viscous damping effects are assumed

proportional only to the stiffness of the soil layers. Such

formulation will be termed simplified Rayleigh damping


formulation (SF) and the original formulation will be

termed full Rayleigh damping formulation (RF). Fig. 1

shows that SF results in a linear increase in damping with

increase in frequency, and thus will introduce high

numerical damping at frequencies higher than the natural

mode of the soil column. The dependence of the damping

on frequency is highly reduced using the RF.

The viscous damping formulation only matches the

target frequency independent damping at one frequency

for the SF and two frequencies for the RF. The formula-

tion will either underestimate or overestimate the damping

at other frequencies. The Rayleigh damping formulation

can be extended so that more than 2 frequencies/modes

can be specified, as shown in Fig. 1. However, incorporation

of additional modes is accompanied by significant increase

in computational cost, and the improvement in accuracy

of the solution is limited. It is thus recommended that

the full Rayleigh damping formulation be used in the

analyses (Park and Hashash, 2004).

The effect of the frequency dependent nature of the

viscous damping formulation is documented in Hashash

and Park (2002) and Park and Hashash (2004) using a

series of profiles up to 1000 m in thickness. It is concluded

that the viscous damping formulation will introduce

unacceptably high numerical damping for soil columns

thicker than 50 - 100 m.

3. Site Description

The measured shear wave velocity profiles used in the

analyses are shown in Fig. 2. The profiles are based on

extensive site investigations performed in Korea (Kim et

al., 2002; Sun et al., 2005; Yoon et al., 2006). Among

29 measured soil profiles selected in this study, 17, 15,

and 7 profiles are classified as Site Class C, D, and E,

respectively, according to the seismic design guideline

(Ministry of Construction and Transportation, 1997). Most

Extended Rayleigh

Simplified RayleighFull Ralyeigh

0

1

2

0 5 10 15 20 25 30 35Frequency (Hz)

Effe

ctiv

e da

mpi

ng ra

tio, ξ

(%)

Target damping ratio

fm

fn

fo

fp

Fig. 1. Frequency dependence of simplified (SF), full Rayleigh

damping formulation (RF), and extended Rayleigh damping

formulation (Park and Hashash, 2004)

Site Class C

0

10

20

30

40

50

60

0 250 500 750 1000

Vs (m/s)

Dep

th (m

)

Site Class D

0

10

20

30

40

50

60

0 250 500 750 1000

Vs (m/s)

Site Class E

0

10

20

30

40

50

60

0 250 500 750

Vs (m/s)

Fig. 2. Shear wave velocity profiles used in the site response analyses (Yoon, 2007)


inland profiles in Korea are classified as Site Class C or

D. Site Class E profiles are located mostly in the coastal

areas. Fig. 3 shows the site periods and thicknesses of

all selected profiles. Site Class C profiles show the

shortest site periods, ranging from 0.16 to 0.34 sec. Site

Class D profiles range from 0.2 to 0.54 sec. Site Class

E profiles show the longest site periods, ranging from 0.62

up to 1.1 sec.

The shear modulus reduction and damping curves

selected for the analyses are shown in Fig. 4. The

sedimentary soils and weathered soils used for the analyses

are based on the resonant column tests of reconstituted

samples of Gyeongju and undisturbed samples of Hongsong

(Kim et al., 2002; Sun et al., 2002). The curves developed

by Vucetic and Dobry (1991) for PI=30 soils are used

for clays.

4. One Dmensional Nonlinear Site Response

Analysis

A series of nonlinear site response analyses are

performed at the selected sites to characterize the effect

of the viscous damping formulation. Korean seismic code

only defines the seismic hazard in terms of peak ground

acceleration (PGA). Korea is divided into two seismic

zones based on probabilistic seismic hazard analysis,

termed zone I and II. The PGA of the seismic zone I

for earthquakes with return periods of 1000 years

(equivalent to 10% probability of exceedance in 10 years)

and 2400 years (equivalent to 10% probability of exceedance

in 250 years) are 0.154 g and 0.22 g, respectively. The

PGA of seismic zone II for return periods of 1000 years

and 2400 years are 0.1 g and 0.14 g, respectively. In this

study, all sites selected are assumed to be in seismic zone I.

Three motions are used in the analyses, as shown in

Fig. 5. The first motion is the recorded motion at Yerba

Buena Island during Loma Prieta earthquake (U.S., M=7.1,

PGA=0.067 g). The second motion is the recorded motion

at Ofunato during Miyugi-Oki earthquake (Japan, M=7.4,

PGA=0.23 g). The third motion is a synthetic motion

developed using SIMQKE (Gasparini and Vanmarcke,

1976), which is widely used to develop response spectrum

compatible ground motions in Korea. Each of the selected

motions has been scaled to match the PGA of seismic

zone I, with return periods of 1000 and 2400 years. Note

that the acceleration time histories and Fourier spectra of

the input motions shown in Fig. 5 are scaled to a PGA

of 0.154 g. Even though the motions are representative

of the ground motions at rock outcrop, the frequency

characteristics show distinct variation. The motion recorded

at Yerba Buena Island is rich in low frequency and

relatively low in high frequency. The recorded motion at

Ofunato (dominant frequency = 3 Hz) is rich in high

0

0.5

1

1.5

Site Class CSite Class DSite Class E

0 10 20 30 40 50 60

Site

per

iod

(sec

)

Depth (m)

Fig. 3. Site periods and depths of the soil profiles

0

10

20

30

40

0.0001 0.001 0.01 0.1 1

Dam

ping

(%)

Shear strain, γ (%)

Sedimentary Soil

W eath ered Soil (0~15m)



Clay (PI = 3 0)

0

0.2

0.4

0.6

0.8

1

G/G

max

Fig. 4. Dynamic curves obtained used in the analyses


frequency and very low at frequencies between 0.1 and

1 Hz. The energy of the synthetic motion is evenly

distributed along the full frequency spectrum. Fig. 6

shows the 5% damped acceleration response spectra of

the input motions. When comparing the response spectra

of the input motions with the design spectrum, the Ofunato

and synthetic motions match very well with design

spectrum, while the Yerba Buena motion is lower at short

periods and higher at long periods.

Six profiles are selected to be used in the analyses,

two for each Site Class. The selected profiles are shown

as thick lines in Fig. 2. Nonlinear analyses are performed

using the one dimensional site response analysis code

newly developed code GEOSHAKE. GEOSHAKE is built

upon DEEPSOIL (Hashash and Park, 2001), with various

additional features including rate dependent soil modeling

and frequency dependent equivalent linear algorithm.

However, such features are not used in the analysis. The

constitutive model used in GEOSHAKE is the modified

hyperbolic model (Matasovic, 1993), which is defined as

follows

1

mos

r

G γτγβγ

=⎛ ⎞

+ ⎜ ⎟⎝ ⎠ (3)

-0.2

-0.1

0

0.1

0.2

Yerba BuenaReturn period 1000 years

-0.2

-0.1

0

0.1

0.2OfunatoReturn period 1000 years

Acc

eler

atio

n (g

)

0

0.05

0.1Yerba BuenaReturn period 1000 years

0

0.05

0.1OfunatoReturn period 1000years

Four

ier A

mpl

itude

(g-s

ec)

-0.2

-0.1

0

0.1

0.2

0 10 20 30 40

Synthetic ground motionReturn period 1000 years

Time (sec)

0

0.05

0.1

0.1 1 10 100

Synthetic ground motionReturn period 1000 years

Frequency (Hz)

Fig. 5. Time histories and Fourier spectra of the input motions

0

0.1

0.2

0.3

0.4

0.5

0.6

Return Period 1000 yearsSite Class B Design SpectrumOfunatoYerba BuenaSynthetic ground motion

0.01 0.1 1 10

Spec

tral A

ccle

ratio

n (g

)

Period (sec)

Fig. 6. Response spectra of the scaled input motions and the

design response spectrum


where τ = shear stress, γ = shear strain, Gmo = maximum

shear modulus, γr = reference strain (γr = Gm0/τm0, τm0

= shear strength), β and s = curve fitting parameters that

adjust the shape of the backbone curve.

Fig. 7 compares the reference dynamic soils curves

(shear modulus reduction and damping curves) with the

curves derived from the nonlinear soil model. The shear

modulus reduction curves from the nonlinear model match

very well with the measured curves. The damping curves

match reasonably well the measured curves except for the

weathered soil, where the nonlinear model overestimates

damping at strains higher than 0.1%. The optimum modes

for the RF are selected based on the guidelines proposed

by Park and Hashash (2004). The predominant site

frequency is selected for the SF.

Fig. 8 compares the results of nonlinear analyses using

the SF and RF. For soil columns less than 30 m in

thickness, the responses using the SF and RF are within

tolerable range. However, for soil columns exceeding 30

m in thickness, the influence of the viscous damping

formulation is pronounced. The influence of the viscous

damping increases with increase in the thickness of the

soil column. If the thickness of the soil column increases,

the predominant site frequency decreases (fm in Fig. 1

Sedimentary SoilClay (PI = 30)Nonlinear Model

0

0.2

0.4

0.6

0.8

10.0001 0.001 0.01 0.1 1

G/G

max


Weathered Soil (0~15m)Weathered Soil (15~25m)Weathered Soil (25~50m)Nonlinear Model

0.0001 0.001 0.01 0.1 1Shear strain, γ (%)

0.0001 0.001 0.01 0.1 1Shear strain, γ (%)

0

10

20

30

40

0.0001 0.001 0.01 0.1 1

Dam

ping

(%)


Soil Type β s γr(%)

Sedimentary Soil 1 0.8 0.03

Clay 0.15 0.7 0.01

Weathered Soil (0-15m) 0.6 0.8 0.03

Weathered Soil (15-25m) 0.6 0.8 0.04

Weathered Soil (25-50m) 0.6 0.8 0.05

Fig. 7. Comparison of the measured data (shown as discrete points) and the shear modulus and damping curves derived from the nonlinear

constitutive model (shown as solid lines)


decreases). It will result in overestimating the damping

for all frequencies higher than fm. Therefore, SF results

in significantly lower response than the RF. The results

demonstrate that the use of the SF should not be permitted

for soil profiles thicker than 30 m.

Table 1 lists the selected optimum modes for the

nonlinear site response analyses. It is evident that the

modes are dependent on the frequency content of the

ground motion and the site period of the soil profile. The

selected modes for Ofunato motion is 1st and 3rd, 1st and

5th, and 1st and 8th. The selected higher mode increases

with increase in the thickness and site period of the soil

column. The selected modes for the Yerba Buena motion

are different from the modes selected for the Ofunato

motion, which are 1st and 3rd and 1st and 4th. The selected

higher mode is lower than when using the Ofunato motion

because the Yerba Buena motion has low energy content

at high frequencies. The selected modes are very similar

for the synthetic motion, ranging from 1st and 2nd to 1st

and 4th. Although there is a tendency for the selected

Site Class E - 52m

SFRF

0.01 0.1 1 10Period (sec)

0

0.4

0.8

1.2Site Class E - 37m

SFRF

0.01 0.1 1 10Period (sec)

Site Class D - 48m

SFRF

0

0.4

0.8

1.2Site Class D - 25m

SFRF

Spec

tral a

ccle

ratio

n (g

)

Site Class C - 50m

SFRF

0.01 0.1 1 10

0

0.4

0.8

1.2Site Class C - 20m

SFRF

0.01 0.1 1 10

Fig. 8. Computed 5% damped surface response spectra from nonlinear site response analyses and the design response spectrum

Table 1. Selected modes for the full Rayleigh damping formulation

Site Class Thickness (m) Natural Period (sec)Selected modes

Ofunato motion Yerba Buena motion Synthetic motion

C20 0.18 1

st& 3

rd1st& 3

rd1st& 2

nd

50 0.42 1st& 5

th1st& 4

th1st& 4

th

D25 0.32 1

st& 5

th1st& 3

rd1st& 3

rd

48 0.40 1st& 8

th1st& 4

th1st& 4

th

E37 0.74 1

st& 8

th1st& 4

th1st& 3

rd

52 1.13 1st& 8

th1st& 4

th1st& 3

rd


higher mode to increase with increase in the thickness

of the soil column, there is no clear rule in selecting the

modes and thus have to be selected by trial and error.

Fig. 9 compares the computed response spectra using

the synthetic motion scaled to PGA = 0.22 g. The selected

modes are identical to those selected for ground motion

scaled to PGA = 0.15 g. The discrepancy between SF

and RF is very similar to Fig. 8. For the profiles and

ground motions used in this study, the modes are

independent of the scaling of the ground motions.

5. Comparison of Nonlinear and Equivalent

Linear Analyses

The use of equivalent linear analysis in Korea has been

dominant, since the equivalent linear analysis is known

to be reliable when performing analyses at shallow soil

profiles and propagating weakly to moderate ground

motions (Kramer, 1996). A series of nonlinear and

equivalent linear analyses are performed using all soil

profiles shown in Fig. 2 to determine the degree of

discrepancy between the analysis methods. The equivalent

linear analyses are also performed using GEOSHAKE.

In performing an equivalent linear analysis, the dynamic

soil behavior is modeled using shear modulus reduction

and damping curves, whereas a constitutive model is used

in a nonlinear analysis. Current nonlinear constitutive

models cannot exactly simulate the measured soil behavior.

In addition, the curves used in practice are most often

representative curves developing often an array of

measurements. In such case, it is impossible to simulate

the curves by a constitutive model. The differences

between the representative curves and the curves derived

from the nonlinear analysis have been shown in Fig. 7.

Such approximation is acceptable for most purposes.

However, since this comparison is intended to characterize

Site Class E - 52mSFRF

0.01 0.1 1 10Period (sec)

0

0.5

1

1.5Site Class E - 37m

SFRF

0.01 0.1 1 10Period (sec)

Site Class D - 48m

SFRF

0

0.5

1

1.5Site Class D - 25m

SFRF

Spec

tral a

ccel

erat

ion

(g)

Site Class C - 50m

SFRF

0.01 0.1 1 10

0

0.5

1

1.5Site Class C - 20m

SFRF

0.01 0.1 1 10

Fig. 9. Computed 5% damped surface response spectra from nonlinear site response analyses and the design response spectrum


the difference originating from the analysis procedure

only, different characterization of the dynamic soil

behavior is a source of discrepancy between two analysis

methods and should not be allowed. Therefore, the

measured shear modulus reduction and damping curves,

Fig. 4, are not used in the equivalent linear analysis.

Instead, the shear modulus and damping curves derived

from the nonlinear constitutive model, Fig. 7, are used

in the equivalent linear analysis.

Fig. 10 compares the computed 5% damped surface

spectra between equivalent linear and nonlinear analyses

for the 48 m thick Site Class D profile. When using the

Ofunato motion, the calculated response spectra show

distinct discrepancy, the equivalent linear resulting in

higher estimation of the PGA and spectral acceleration

between 0.2 to 0.4 sec. The calculated response from the

equivalent linear analysis is also higher when using the

synthetic motion, but the difference is more subtle. For

both cases, the PGA calculated by the equivalent linear

analysis is higher than the nonlinear analysis results. The

reason for the overestimation of the PGA is due to the

intrinsic limitation of the equivalent linear procedure. It

is a common practice in performing an equivalent linear

analysis to use the secant shear modulus and damping at

65% of the maximum shear strain. In such case, the

simulated soil behavior becomes stiffer at maximum shear

strain (Yoshida and Iai, 1998). The PGA is most likely

be the highest at maximum shear strain. Since the soil

behavior at maximum shear strain is stiffer, the PGA

becomes larger than when modeling the true nonlinear

behavior.

Fig. 11 compares the computed PGA ratios, which is

defined as the ratio of the PGA from the equivalent linear

to that from the nonlinear analyses, as functions of the

site period. The range of calculated PGA ratio is from

unity up to 1.5. Very few analyses resulted in ratios below

unity, but even in such cases, the ratios are very close

0

0.25

0.5

0.75

1

Site C lass D - 48mSynthetic 100 0 years

0 .01 0.1 1 10

Spec

tral a

ccel

erat

ion

(g)

P er iod ( sec)

0

0 .2 5

0 .5

0 .7 5

1

S ite C lass D - 48mO fu nato 1000 years

Equ ivalent linearanalysisN on linear analysis

0 .01 0 .1 1 10

Spec

tral a

ccel

erat

ion

(g)

Fig. 10. Computed 5% surface spectra for 48 m thick Site Class

D profile using Ofunato and synthetic motions

0

0.5

1

1.5

2

Site period 1000yrSite period 2400yr

0 0.2 0.4 0.6 0.8 1 1.2 1.4

PGA

ratio

Site Class E

Natural period (sec)

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4 0.5 0.6

PGA

ratio

Site Class D

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4

PGA

ratio

Site Class C

Fig. 11. Computed ratios of PGA from equivalent linear to those

from nonlinear analyses


to unity. It can thus be concluded that the equivalent linear

analysis overestimates the PGA, while the degree of

overestimation is variable. A clear dependence of the ratio

on the input ground motion characteristics or the site

period is not observed, resulting in significant scatter in

the ratios. The ratio is, however, dependent on the

amplitude of the ground motion. The PGA ratios using

input motions scaled to a PGA of 0.22 g results are higher

than those using motions scaled to 0.154 g. It is evident

that the accuracy of the equivalent linear analysis decays

for stronger ground motions. Fig. 12 and Fig. 13 compare

the average spectral acceleration ratios between 0.1 to 0.5

sec and 0.4 to 2.0 sec. The average spectral acceleration

between the 0.1 to 0.5 and 0.4 to 2.0 has been used to

develop short-period and mid-period amplification factors

(termed Fa and Fv, as defined in NEHRP Provisions).

In contrast to the PGA, the equivalent linear analyses do

not always display higher estimates compared to the

nonlinear analyses. The comparisons demonstrate that the

type of analysis has a more pronounced influence on the

PGA than the average spectral accelerations.

6. Conclusions

A series of nonlinear site response analyses are performed

at various measured soil profiles in Korea. Three input

motions scaled to peak ground acceleration representative

of seismic hazard with return periods of 1000 years and

2400 years are used. Analyses results demonstrate that

the viscous damping formulation has pronounced influence

0

0.5

1

1.5

2


0 0.2 0.4 0.6 0.8 1 1.2 1.4

Site Class E


Ave

rage

(0.1

~0.5

sec)

Sp

ectra

l acc

eler

atio

n ra

tio

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4 0.5 0.6

Site Class D

Ave

rage

(0.1

~0.5

sec)

Sp

ectra

l acc

eler

atio

n ra

tio

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4

Ave

rage

(0.1

~0.5

sec

) Sp

ectra

l acc

eler

atio

n ra

tio

Site Class C

Fig. 12. Computed ratios of average spectral accelerations (0.1

0.5 sec) from equivalent linear to those from nonlinear–analyses

0

0.5

1

1.5

2


0 0.2 0.4 0.6 0.8 1 1.2 1.4

Site Class E


Ave

rage

(0.4

~2.0

sec)

Sp

ectra

l acc

eler

atio

n ra

tio

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4 0.5 0.6

Site Class D

Ave

rage

(0.4

~2.0

sec)

Sp

ectra

l acc

eler

atio

n ra

tio

0

0.5

1

1.5

2


0 0.1 0.2 0.3 0.4

Ave

rage

(0.4

~2.0

sec)

Sp

ectra

l acc

eler

atio

n ra

tio

Site Class C

Fig. 13. Computed ratios of average spectral accelerations (0.4

2.0 sec) from equivalent linear to those from nonlinear–analyses


on the propagated ground motion. The simplified Rayleigh

damping filters out important frequency components even

for soil profiles higher than 30 m in thickness. The effect

becomes more significant with increases in thickness and

decrease in stiffness of the soil profile. When using the

full Rayleigh damping formulation and carefully selecting

the optimum modes, the artificial damping introduced is

greatly reduced. Results confirm the importance of

controlling the viscous damping in a nonlinear analysis

and that the use of the full Rayleigh damping and selecting

optimum modes is not an option, but a prerequisite for

obtaining reliable results for profiles higher than 30 m

in thickness.

Results are further compared to equivalent linear analyses.

Comparisons show that the computed PGA is highly

dependent on the analysis type, the equivalent linear

analyses consistently overestimating the response even for

stiff and shallow soil columns.

Acknowledgements

This work was supported by the Korea Research

Foundation Grant funded by the Korean Government

(MOEHRD, Basic Research Promotion Fund) (KRF-2006-

003-D00579). Authors would also like to thank Dr.

Jong-Ku Yoon and Professor Dong-Su Kim for their

valuable data on shear wave velocity profiles and dynamic

soil curves. All opinions expressed in this paper are solely

those of the authors.

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(received on Oct. 25, 2006, accepted on Mar. 18, 2008)

Finite Element Analysis of Earth Retention System with Prestressed Wales 25

Finite Element Analysis of Earth Retention Systemwith Prestressed Wales

프리스트레스트 띠장을 적용한 흙막이 시스템의 유한요소해석

Park, Jong-Sik1박 종 식 Kim, Sung-Kyu2

김 성 규

Joo, Yong-Sun3주 용 선 Kim, Nak-Kyung4

김 낙 경

요 지

프리스트레스트 띠장을 적용한 새로운 흙막이 시스템에 대한 유한요소 해석이 수행되었다 본 연구에서는.프리스트레스트 띠장을 적용한 흙막이 시스템의 거동을 규명하기 위하여 차원 유한요소 모델이 적용되었다3 .새로운흙막이시스템에대한유한요소모델링절차와방법이제시되었다 지반 벽체 버팀보및프리스트레스트. , ,띠장시스템을구성하고있는띠장 받침대 강선에대한모델링과지반벽체그리고벽체띠장간의접촉면모델링, , - -이 제시되었다 벽체 횡방향 변위 버팀보 축력 프리스트레스트 띠장 시스템 부재인 띠장과 받침대 축력에 대한. , ,유한요소 해석결과가 현장 계측결과와 비교 검증되었다 검증된 차원 유한요소 모델을 이용하여 강선 인장력. 3변화에따른새로운프리스트레스트띠장의휨모멘트와변형거동이규명되었으며이에따른흙막이벽체배면에

서의 토압 거동이 규명되었다.

Abstract

A finite element analysis was performed for new earth retention system with prestressed wales. A 3D finiteelement model was adopted in this study to investigate the behavior of the earth retention system with prestressedwales. A procedure of the 3D finite element modeling of this earth retention system was presented. The procedureincluded the modeling of soil, wall, strut, and members of prestressed wale system which consists of wale, supportleg, and steel wires, and the interface modeling of soil-wall and wall-wale. The numerical predictions of lateralwall deflection, and axial load on the members of prestressed wale systems and struts were evaluated in comparisonwith the measurements obtained from field instruments. A sensitivity analysis was performed using the proposed3D finite element model to investigate the behavior of new earth retention system on a wide range of prestressload conditions of steel wires. The lateral deflection of the wall and wale, the bending moment of the wale, andthe lateral earth pressure distribution on the wall were computed. Implications of the results from this study werediscussed.

Keywords : Earth retention system, Excavation, Finite element analysis, Prestressed wale

1 Member, Senior Researcher, Hanwha Research Institute of Technology2 Member, Graduate Student, Dept. of Civil, Architect. Envir. System Engrg., Sungkyunkwan Univ.3 Member, Graduate Student, Dept. of Civil, Architect. Envir. System Engrg., Sungkyunkwan Univ.4 Member, Assoc. Prof., Dept. of Civil, Architectual and Envir. System Engrg., Sunkyunkwan Univ., [email protected], Corresponding Author



1. Introduction

A new earth retention system with prestressed wales

was developed and introduced as an alternative method

for conventional temporary earth support systems as

braced cuts and anchored walls (Han et al. 2003a; Kim

et al. 2004). A new wale system is a wale prestressed

by tensioning steel wires. The newly prestressed wale

system consists of wales, H-beam support legs, steel

wires, and hydraulic jacks, as shown in Fig. 1. The newly

prestressed wale system provides a highly flexural resistance

against a bending by lateral earth pressures. A new earth

retention system with prestressed wales provides the

spacing of supports drastically larger than those of

conventional temporary support systems. The new earth

retention system can reduce the quantity of steel beams

than conventional braced cuts. Therefore, large workspace

provides construction easiness. The prestressed wale system

has a preloading effect on the wall, and the preload

restricts the wall deformation due to ground excavation.

The new earth retention system with prestressed wales

in excavations for buildings, water lines, bridge piers,

subway structures performed successfully. There have

been studies on the new earth retention system with

prestressed wales by Han et al. (2003b), Kim et al.

(2005a), Kim et al. (2004, 2005b,c), Kim et al. (2005d),

and Park et al. (2003a,b, 2004). The basic principles and

design method of new earth retention system with

prestressed wales were investigated by Han et al. (2003b),

Kim et al. (2004), and Park et al. (2003a,b). The

applicability and safety of the new earth retention system

in a variety of field excavations were investigated and

discussed by Kim et al. (2004, 2005b,c). The stability of

the new prestressed wale system was evaluated by the

finite element approach by Kim et al. (2005a). The

structural behavior of this prestressed wale system applied

in the earth retention system in soft clay was studied by

Kim et al. (2005d). A modeling technique for this

prestressed wale system was proposed by Kim et al.

(2005a).

A numerical analysis of the new earth retention system

with prestressed wales was performed using the finite

element method. A 3D finite element model was adopted

to investigate the behavior of the wall and newly

prestressed wales in excavation. The modeling of soil,

wall, strut, and prestressed wale system members, and

the interface modeling of soil-wall and wall-wale were

presented in this paper. The numerical predictions of

lateral wall deflection, and axial load on the members of

prestressed wale systems and struts were evaluated

compared with the measured data from field monitoring.

In order to investigate the behavior of the new earth

retention system on the effect of prestress load conditions

of steel wires, a series of finite element analyses were

performed using the proposed 3D finite element model.

The lateral deflection of the wall and wale, the bending

moment of the wale, and the lateral earth pressure

distribution on the wall were computed. The implications

of the results were discussed.

2. New Earth Retention System with Prestressed

Wales in Urban Excavation

2.1 Site Conditions

The new earth retention system with prestressed wales

was selected for temporary earth support in apartment

complex building in Anyang area. The excavation was

48 meters wide, 44 meters long, and 11.9 meters deep.

The old houses and stores were located in the vicinity

of the site. The subsurface soil consists of fill, silty clay

with sand, weathered soil, and weathered rock. The

construction site map, geologic map, boring locations,

subsurface soil distribution, and SPT profiles of the

excavation site are reported by Kim et al. (2005b) in

detail.

hydraulic jack

wale support leg

strut

steel wires bracing

earth pressure

reaction on strut

Fig. 1. Components of new prestressed wale system


2.2 Excavation Support System

The CIP wall is internally braced with three levels of

prestressed wales and preloaded corner struts. LW

grouting was used to prevent the inflow of the ground

water. Details of the CIP wall, the prestressed wale

systems and corner struts used in the excavation and

conditions of the prestresses on steel wires of the wale

systems and the preloads of corner struts are reported by

Kim et al. (2005b). And the construction sequence and

field monitoring plan for the new earth retention system

with prestressed wales are presented by Kim et al.

(2005b). The new earth retention system with prestressed

wales in urban excavation performed successfully, as

shown in Fig. 2.

3. Three Dimensional Finite Element Analysis

of Earth Retention System with Prestressed

Wales

A three-dimensional finite element analysis was per-

formed for the new earth retention system with prestressed

wales. Details of the finite element modeling of this earth

retention system were presented. The numerical predictions

of the lateral wall deflection, and axial loads of the wale,

support leg, and strut were evaluated and compared with

the field measurements.

3.1 Finite Element Model

3.1.1 Mesh Boundary Condition

An idealized 3D mesh, which consists of 88,440 nodes

and 71,664 elements, was generated to minimize the effect

of mesh size effect on the finite element analysis, as

shown in Fig. 3. Based on studies proposed by Briaud

and Lim (1999), and Yoo (2001), and on a previous study

for boundary effect on this 3D finite element analysis,

the mesh boundaries were defined in Fig. 4. The finite

element mesh of the wall and prestressed wale systems

is shown in Fig. 5. The depth of excavation H was 12.0

m. The distance from the bottom of the excavation to the

hard layer Db was 1.2H. The 3D mesh extended laterally

to a distance of 4.0H from the vertical excavation surface.

Fig. 2. New Earth Retention System with Prestressed Wales in

Urban Excavation

10 meters

Fig. 3. 3D finite element mesh

H

Db

4H4H

Fig. 4. Definition of mesh boundaries

Fig. 5. Finite element mesh of wall and prestressed wale system


3.1.2 Soil and Rock Element Model

The soil and rock were simulated with 3D eight-noded

solid elements. The soil and rock were assumed to be

elasto-plastic material obeying the Drucker-Prager failure

criterion available in ABAQUS (ABAQUS 2004), a

commercial FE program. The strength parameters of soil

deposits are computed by using the Mohr-Coulomb strength

parameters of friction angle and cohesion c in con-

junction with the Drucker-Prager model parameters of

and d (ABAQUS 2004). The strength parameters of the

rock mass to perform the finite element analysis were

calculated by using the Hoek and Brown criterion (Hoek

and Brown 1988). The stiffness of the soil and rock was

calculated based on an empirical relationship reported by

Janbu (1963). The modeling of the groundwater was not

considered in the finite element analysis because the

groundwater was not encountered at the site during exca-

vation. The soil and rock material properties examined

in the finite element analysis are tabulated in Table 1.

3.1.3 Excavation Support System Model

The CIP wall was simulated with 3D eight-noded solid

elements. This solid model was treated as a linear elastic

material. The flexural stiffness for the simulated wall was

an EI value of the CIP wall in this case history (Kim

et al. 2005b). The strut was modeled with two-noded

spring elements. In the modeling of the prestressed wale

system consisting of wale, support leg, and steel wires,

the wale and support leg were modeled with two-noded

beam elements. The steel wires were modeled with

two-noded truss elements. The material properties of

members of the prestressed wale systems and struts are

tabulated in Table 2.

3.1.4 Wall-Soil and Wall-Wale Interface Model

The interface of wall-soil and wall-wale was modeled

with 2D zero thickness interface model available in

ABAQUS. The interface of wall-soil and wall-wale was

simulated by the Coulomb friction model provided in

ABAQUS. As can be seen in Fig. 6 (a), the proposed

Table 1. Soil and rock material properties examined in finite element analysis

Materialγ

(kN/m3)

ν E(kPa)

β(degrees)

Kψ

(degrees)

σc(kPa)

Fill 18.6 0.3 15,000 50.194 1.0 8.0 16.974

Silty clay with sand 17.6 0.3 25,000 48.065 1.0 6.0 48.930

Weathered soil 19.6 0.3 35,000 52.157 1.0 6.0 53.039

Weathered rock 21.6 0.3 1.78×106

54.814 1.0 6.0 112.954

Note: γ is unit weight. ν is Poisson’s ratio. E is modulus of elasticity. β is material angle of friction in the P-t plane. K is the ratio

of the flow stress in triaxial tension to the flow stress in triaxial compression. ψ is dilation angle in the P-t plane. σc is uniaxial compression

yield stress. Here, ψ values used in this analysis were referenced from the studies by Bolton (1986), Jewell (1989), and Perkins and

Madson (2000). The soil and rock material properties were calculated and based on the results of the field tests.

Table 2. Parameters of members of Earth Retention System for finite element analysis

Data Parameter Value

Wall

Thickness (m) 0.5

Height (m) 14.0

Flexural stiffness (kN m･ 2/m) 4.4×10

4

IPS wale No. 1, 3

Length (m) 28.0

1stfloor Flexural stiffness (kN m･ 2

) 5.27×106

2nd

and 3rd

floor Flexural stiffness (kN m･ 2) 8.15×10

6

IPS wale No. 2, 4

Length (m) 22.0

1st floor Flexural stiffness (kN m･ 2) 2.68×10

6

2nd

and 3rd

floor Flexural stiffness (kN m･ 2) 3.27×10

6

Corner strut1stfloor Axial stiffness (kN/m) 2.11×10

7

2nd

and 3rd

floor Axial stiffness (kN/m) 3.07×107


model defines the critical shear stress τcrit = pμ , where μ= constant friction coefficient, and p = contact pressure.

Constant friction coefficients of μ = 0.2 for the interface

between the soil and the wall and μ = 0.3 for the interface

between the wall and the wale were examined in the

analyses.

For modeling on the normal behavior of soil-wall and

wall-wale interface, as shown in Fig. 6 (b), a contact

model to define an exponential contact pressure-overclosure

relationship was used in the analyses. For the soil-wall

interface modeling, the soil confining pressure of σ3 was

used as the contact pressure p0. For the wall-wale interface

modeling, the pressure of vertical component in a tensioning

force of steel wires was used as the contact pressure p0.

The clearance c0 ranging between 10-2 and 10-4 m was

examined in the finite element analyses.

3.1.5 Simulation of Construction Sequence

The simulation sequence for construction activities are

shown in Fig. 7. The first step was to turn the gravity

stresses on the entire solid, which was 144 m in length,

140 m in width, and 26.4 m in depth. The second step

was to install the CIP walls and was to activate the solid

elements simulating the wall. The third step was to

excavate the soil mass to 3.5 m in depth. The fourth step

was to install and prestress the IPS wale systems at the

first row. This step consisted of activating the beam

elements simulating the IPS wale systems and simulating

nodal forces to the wales and support legs, respectively.

The fifth step was to install the corner struts at the first

row. This step consisted of activating the beam elements

simulating the corner struts. The sixth step was to excavate

the next soil mass to 5.5 m in depth. The seventh step

continued with repetitions of Step 4 to simulate the

prestressed wale system at the second row. Total run

required about 12 hr of processing on the personal

computer with 2GB RAM.

3.1.6 Calibration of Numerical Model

The calibration of 3D finite element model wasperformed to best match the measured and the calculated.The calibration process consisted of finding the model forwall, strut, and members of the prestressed wale systemthat led to the best match between the measured andcalculated wall deflection. The cast-in-place (CIP) wallwas modeled and replaced with rectangular type brickelement with equivalent stiffness (AE and EI). For theprestressed wale system modeling, the rectangular beamswith equivalent stiffness (AE and EI) were included withthe wales, the support legs, and the struts.

3.2 Comparison with Full Scale Experiment

3.2.1 Lateral Wall Deflection

The comparison between numerical predictions and

Equivalent shear stress , °

Contact pressure , p

Constant friction coefficient , °

Critical shear stress in model

Stick region

(a) Friction model

c0

p0

Contact pressure, p

Clearance , c

Exponential pressure ? overclosure relationship

(b) Contact pressure-overclosure relationship

Fig. 6. Interface model Fig. 7. Simulation of construction activities


measurements for lateral wall deflection are shown in Fig.

8. The lateral wall deflection profiles of HI 1 matched

well within 0-13% errors, as shown in Fig. 8 (a). The

predicted lateral wall deflections of HI 2 overestimated

the deflection 18% larger than the measurements, as

shown in Fig. 8 (b).

3.2.2 Axial Load of Wale

The numerical predictions for axial load of wale of the

prestressed wale system were compared with the measure-

ments, as shown in Fig. 9. The predictions of axial load

of the wale of the prestressed wale No. 1 at the first to

third level gave a correlation with the measurements

within 0-20% errors, as shown in Fig. 9.

3.2.3 Axial Load of Support Leg

The comparison between numerical predictions and

measurements for axial load of support leg are shown in

Fig. 10. The predictions of axial load of support legs of

the IPS wale No. 1 at the second level and No. 3 at the

third level overestimated the load 10.2-25.5% larger than

the measurements, as shown in Fig. 10.

3.2.4 Axial Load of Strut

The predicted axial loads of corner strut were compared

with the measured data, as shown in Fig. 11. The

predictions of corner struts at the first and the third level

gave a correlation with the measurement within 9-21%

errors, as shown in Fig. 11.

4. Sensitivity Analysis of New Earth Retention

System with Prestressed Wales

The sensitivity analysis was performed for the new

earth retention system with prestressed wales by the finite

element method. The prestress load on the new wale

system was examined in the finite element analysis to

Fig. 8. Comparison between predictions and measurements for

lateral wall deflection

40 60 80 100 120 140Period (Days)

0

200

400

600

800

1000

Loa

d (k

N)

IPS wale No. 1 (SWa1)MeasuredPredicted

(a) axial load of wale at the first level

40 60 80 100 120 140Period (Days)

0

500

1000

1500

2000

2500

3000

Load

(kN

)


(b) axial load of wale at the second level

60 80 100 120 140Period (Days)

0

500

1000

1500

2000

2500

3000

Load

(kN

)


(c) axial load of wale at the third level


axial load of wale


evaluate the influence on the lateral deflection of the wall

and wales, and the lateral earth pressure distribution on

the wall.

4.1 Parameter Examined in Analysis

The prestress load of steel wires was selected as the

parameter for the sensitivity analysis of the earth retention

system with prestressed wales. The value of the parameter

used for the finite element analysis of the earth retention

system with prestressed wales is as follows: 1) the value

of the prestress load of steel wires was selected as no

prestress load, and 50%, 75%, 100%, and 120% of the

design tension load of steel wires. The soil properties

shown in Section 3.1.2 were used for the sensitivity

analysis.

4.2 Sensitivity Analysis Results

4.2.1 Lateral Deflection of Wall and Wale

The lateral wall deflection profiles on the mid-span of

the prestressed wale systems at the final construction stage

are shown in Fig. 12. The prestress load varied from 0

to 120% of the design tension load of steel wires. As

can be seen in Fig. 12, the lateral wall deflection

decreased by increasing the prestress load. The wall at

the location of the prestressed wale systems significantly

deformed back the retained ground by increasing the

prestress load. The wall deflection max by applying

prestress load to 120% of the design tension load of steel

wires was 1.9% smaller than those of the design load.

The wall deflection max by applying prestress load to

50% and 75% of the design load was 15% and 45%,

respectively, larger than those of the design tension load

40 60 80 100 120 140Period (Days)

0

300

600

900

1200

1500L

oad

(kN

)IPS wale No. 1 (SBa2)

Measured by SBa2-2Measured by SBa2-3Predicted by SBa2-2Predicted by SBa2-3

40 60 80 100 120 140Period (Days)

0

200

400

600

800

Load

(kN

)

Corner 1 (SCa1)MeasuredPredicted

(a) axial load of support leg at the second level (a) axial load of corner strut at the first level

60 80 100 120 140Period (Days)

0

300

600

900

1200

1500

Load

(kN

)

IPS wale No. 3 (SBc3)Measured by SBc3-2Measured by SBc3-3Predicted by SBc3-2Predicted by SBc3-3

60 80 100 120 140Period (Days)

0

500

1000

1500

2000

Loa

d (k

N)

Corner 3 (SCc3)Measured by SCc3-1Measured by SCc3-2Measured by SCc3-3Predicted

(b) axial load of support leg at the third level (b) axial load of corner strut at the third level


axial load of support leg


axial load of corner strut


of steel wires.

The lateral deflections of the prestressed wale installed

at each level at the final construction stage are shown

in Fig. 13. The prestressed wale gradually moved toward

the retained ground by increasing the prestress load. The

wale at the location of support legs significantly deformed

back the retained ground by increasing prestress load. The

wale at the location of struts was not nearly deformed

by large axial stiffness of the strut. The wale prestressed

to 120% of the design load of steel wires moved back

the retained ground with the deflection of 44% smaller

than those of the design tension load of steel wires. The

wale prestressed to 50% and 75% of the design load

moved back the retained ground with the deflection of

16% and 33%, respectively, larger than those of the design

tension load of steel wires.

4.2.2 Bending Moment of Wale

The bending moments of the prestressed wale installed

at each level at the final construction stage are shown

in Fig. 14. As can be seen in this Figure, the bending

moment of the prestressed wale increased with increasing

the prestress load. The maximum bending moment of the

wale occurred at the location of the outer legs of the

prestressed wale system. The bending moment Mmax by

prestressing to 120% of the design tension load of steel

wires was 20.5% larger than those of the design tension

load. The bending moment Mmax by prestressing to 50%

and 75% of the design tension load was 25.6% and 51.3%,

respectively, smaller than those of the design tension load.

4.2.3 Lateral Earth Pressure on Wall

The lateral earth pressure distributions acting on the

wall along the prestressed wale installed at each level at

the final construction stage are shown in Fig. 15. As can

be seen in Fig. 15, the lateral earth pressure on the wall

increased with increasing the prestress load. The maximum

1st floor

2nd floor

3rd floor

16

14

12

10

8

6

4

2

0

Dep

th (m

)30 25 20 15 10 5 0 -5

Deflection (mm)

not prestressedprestressed to 50% of design tension loadprestressed to 75% of design tension loadprestressed to 100% of design tension loadprestressed to 120% of design tension load

Fill

Silty clay with sand

Weatheredsoil

Weatheredrock

N = 17-19

N = 7-11

N = 16-50

N = 50 blows/100 mm

Fig. 12. Variation of lateral deflection of wall

40

30

20

10

0

-10

-20

-30

-40

Def

lect

ion

(mm

)


Back

Front

(a) lateral deflection of the wale at the first level

Back

Front

40

30

20

10

0

-10

-20

-30

-40

Def

lect

ion

(mm

)


(b) lateral deflection of the wale at the second level

Back

Front40

30

20

10

0

-10

-20

-30

-40

Def

lect

ion

(mm

)


(c) lateral deflection of the wale at the third level

Fig. 13. Variation of lateral deflection of wale


lateral earth pressure occurred at the location of the outer

support legs of the prestressed wale system. The lateral

earth pressure on the wall at the location of the support

legs significantly increased by increasing the prestress

load. The maximum earth pressure pmax by prestressing

to 120% of the design tension load of steel wires was

20.2% larger than those of the design tension load of steel

wires. The maximum earth pressure pmax by prestressing

to 50% and 75% of the design load of steel wires was

24.6% and 47.8%, respectively, smaller than those of the

design tension load of steel wires.

5. Conclusions

A 3D finite element analysis was performed to investigate

the behavior of the new earth retention system with

prestressed wales. Details of the finite element modeling

of the earth retention system with prestressed wales were

presented. The numerical predictions on the members of

the new earth retention system were evaluated compared

with the measurements obtained from field instruments.

For sensitivity analysis, the prestress load on the new wale

system was examined in the finite element analysis to

evaluate the influence on the lateral deflection of the wall

Back

front900

600

300

0

-300

-600

-900

-1200

-1500

Bend

ing

Mom

ent (

kN .

m)


150

100

50

0

-50

-100

-150

-200

-250

-300

Pres

sure

(kN

/m2 )

prestressed to 50% of design tension loadprestressed to 75% of design tension loadprestressed to 100% of design tension loadprestressed to 120% of design tension load

(a) bending moment distribution of the wale at the first level (a) lateral earth pressure distribution on the wall at the first level

Back

front

900

600

300

0

-300

-600

-900

-1200

-1500

Bend

ing

Mom

ent (

kN .

m)


150

100

50

0

-50

-100

-150

-200

-250

-300

Pres

sure

(kN

/m2 )


(b) bending moment distribution of the wale at the second level (b) lateral earth pressure distribution on the wall at the second level

Back

front

900

600

300

0

-300

-600

-900

-1200

-1500

Bend

ing

Mom

ent (

kN .

m)


150

100

50

0

-50

-100

-150

-200

-250

-300

Pres

sure

(kN

/m2 )


(c) bending moment distribution of the wale at the third level (c) lateral earth pressure distribution on the wall at the third level

Fig. 14. Variation of bending moment distribution of wale Fig. 15. Variation of lateral earth pressure distribution on wall


and wale, the bending moment of the wale, and the lateral

earth pressure distribution on the wall. The following

conclusions can be drawn:

(1) The finite element method can be used to simulate

a behavior of the new earth retention system with

prestressed wales. The predicted and measured results

showed that the lateral wall deflections matched well

with 0-18% errors, that the axial loads of the wales

gave a correlation with the measured data within

0-20% errors, that the axial loads of the struts gave

a correlation with the measured data within 9-21%

errors, and that the axial loads of the support legs well

matched with the measured data within 10.2-25.5%

errors. The numerical error was due to simplifications

such as idealization of construction activities, unreal

numerical parameters, and excavation geometry.

(2) Based on the numerical results, the lateral deflection

and the bending moment of the wale, and the

distribution of lateral earth pressure acting on the wall

along the prestressed wales were investigated. It was

recognized that the behavior of lateral wale deflection

had a relationship with the lateral earth pressure

distribution on the wall.

(3) The behavior of the lateral deflection of the wall and

wale, the bending moment of the wale, and the lateral

earth pressure distribution on the wall on the effect

of the prestress load of steel wires was investigated.

From the sensitivity analysis results, it was notified

that the prestress load significantly had an influence

on the behavior of the wall and wale.

Acknowledgments

This work was supported by grant No. (R01-2003-000-

11630-0) from the Basic Research Program of the Korea

Science & Engineering Foundation.

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(received on Oct. 12, 2007, accepted on Jan. 23, 2008)

Development of Modified Disturbed State Concept Model for Liquefaction Analysis 35

Development of Modified Disturbed State Concept Modelfor Liquefaction Analysis

액상화 해석을 위한 수정교란상태개념 모델 개발

Park, Keun-Bo1박 근 보 Choi, Jae-Soon2

최 재 순

Park, Inn-Joon3박 인 준 Kim, Ki-Poong4

김 기 풍

Kim, Soo-Il5김 수 일

요 지

본논문에서는액상화해석에관한 모델을실험및해석적관점에서그적용성을평가하였다 포화사질토DSC .의동적거동을보다정확히예측하기위해 모델을유효응력경로와과잉간극수압발현에기초하여수정하였DSC다 액상화에대한동적거동및 모델에대한매개변수산정을위해정적배수삼축시험과반복비배수삼축시험. DSC을 상대밀도와 구속응력에 따라 수행하였다 유효응력 경로와 과잉간극수압의 항으로 액상화 상태를 분류하고.수정된 모델을적용시켜액상화해석을수행하였다 제안된방법을토대로 모델과제안된 모델에DSC . DSC DSC대한 액상화 해석을 상대밀도와 구속응력에 따라 비교하였다 비교 결과 수정 모델은 액상화 시작점 및 동적.거동을 보다 정밀하게 평가하였고 입력변수의 수가 감소하고 산정방법이 간편해졌다, .

Abstract

In this paper, the application of the DSC model to the analysis of liquefaction potential is examined throughexperimental and analytical investigations. For more realistic description of dynamic responses of saturated sands,the DSC model was modified based on the dynamic effective stress path and excess pore pressure development.Both static and cyclic undrained triaxial tests were performed for sands with different relative densities and confiningstresses. Based on test results, a classification of liquefaction phases in terms of the dynamic effective stress pathand the excess pore pressure development was proposed and adopted into the modified DSC model. The proposedmethods using the original and modified DSC models were compared with examples with different relative densitiesand confining stresses. Based on the comparisons between the predicted results using the original and modifiedDSC models and experimental data, the parameters required to define the model were simplified. It was also foundthat modified model more accurately simulate initial liquefaction and dynamic responses of soil under cyclic undrainedtriaxial tests.

Keywords : Disturbance, Disturbed state concept, Earthquakes, Excess pore pressure, Liquefaction

1 Member, Post Doc., School of Civil & Env. Eng., Yonsei Univ., [email protected], Corresponding Author2 Member, Instructor, Dept. of Civil Eng., Seokyeong Univ.3 Member, Associate Prof., Dept. of Civil Eng., Hanseo Univ.4 Graduate Student, School of Civil & Env. Eng., Yonsei Univ.5 Member, Prof., School of Civil & Env. Eng., Yonsei Univ.



1. Introduction

The excess pore pressure is an important consideration

for the behavior of saturated sands under seismic loading

conditions. When a dynamic force such as an earthquake

is applied to saturated sands, the excess pore pressure

builds up continuously with decreases of soil strength, and

sands are eventually liquefied. For the assessment of

liquefaction potential or susceptibility for sands, experimental

investigations are often used based on cyclic triaxial tests

or in-situ field tests such as SPT and CPT [Seed et al.,

1983; Youd et al., 2001]. Analytical investigations based

on numerical modeling and analysis have been limited to

those requiring accurate description of complex undrained

behaviors of saturated sands, including mobilization and

accumulation of the excess pore pressure and consequent

stress softening.

There have been several soil models for describing

undrained behaviors of fully saturated sands under dynamic

loading conditions [Finn et al., 1977; Iai et al., 1992; Desai

and Ma, 1992; Desai et al., 1998]. Representative examples

are those of Finn et al. [1977], Iai et al. [1992], and Desai

et al. [1998], all of which are based on the effective stress

concept. According to Finn et al. [1977], mobilized excess

pore pressures under undrained conditions can be determined

as a function of drained volumetric strains. In this approach,

different stress-strain relationships are considered for

initial loading and reloading stages for the calculation of

excess pore pressure development and dissipation.

For the analysis of liquefaction potential, Iai et al.

[1992] defined an initial liquefaction occurrence at the

liquefaction front state given by the phase change line

(e.g., phase transformation line). The phase change line

represents a boundary between contractive and dilative

behaviors observed in dynamic effective stress paths.

Disturbed state concept (DSC) was first introduced by

Desai [1980] to characterize work-hardening behaviors of

over-consolidated soils with reference to those of normally

consolidated soils. Further development was made for the

description of undrained behaviors for saturated sands

afterward [Desai et al., 1991; Desai and Ma, 1992; Katti

and Desai, 1994; Desai and Toth, 1996; Desai et al., 1997;

Desai and Rigby, 1997; Desai et al., 1998]. In the DSC

model [Desai and Ma, 1992; Desai et al., 1998], dynamic

responses of soils are defined as a function of the material

disturbance caused by an applied force and induced

deviatoric plastic strains. The material disturbance represents

changes in microstructures of a material due to an applied

force from the relative intact (RI) to the fully adjustment

(FA) states. Observed responses of the material are then

given by relative differences between RI and FA states,

which are quantified through the material disturbance.

While the DSC model has been successfully verified

for many geotechnical dynamic problems [Desai et al.,

1998; Desai and Toth, 1996; Desai et al., 1997; Desai

and Rigby, 1997; Pal and Wathugala, 1999], those have

been primarily for low excess pore water pressure and

small-strain conditions. For the application to liquefaction,

it has been limited to the determination of the initial

liquefaction occurrence, and not been fully implemented

for a whole process of liquefaction analysis, including the

determination of liquefaction potential.

In this paper, the application of the DSC model to the

analysis of liquefaction potential is examined through

experimental and analytical investigations. For more realistic

description of dynamic responses of saturated sands, the

DSC model is further modified based on experimental

results and soil phases observed in the dynamic effective

stress path. Both static and cyclic undrained triaxial tests

are performed for sands with different soil and stress

conditions. Based on test results, a classification of

liquefaction phases in terms of the dynamic effective

stress path and the excess pore pressure development is

proposed and adopted into the modified DSC model.

2. Disturbed State Concept

2.1 RI and FA States

According to the disturbed state concept (DSC) proposed

by Desai et al. [1998], external forces cause changes and

disturbances in the microstructure system of a material.

The stress-strain response of the material at a certain

loading condition is then determined from a degree of


the disturbance caused by the external force. There are

two reference states defined in the DSC model: relative

intact (RI) and fully adjusted (FA) states. A material in

the RI state upon loading modifies continuously through

a process of natural self-adjustment, and a part of it

approaches the FA state at randomly disturbed locations

in the material. As a result, observed or average responses

of the material can be determined from responses of RI

and FA states in terms of the disturbance D. This is

illustrated in Fig. 1. The RI state is defined with con-

tinuum soil models, such as the elastic-plastic stress-strain

models, while the FA state is defined as a response of

a material at the ultimate state. In the original DSC model

[Desai and Ma, 1992; Desai et al., 1998], the RI state

is determined by Hierarchical Single Surface (HiSS)

model [Desai et al., 1991] with the isotropic hardening

and associated flow rule whereas the FA state is given

by the critical state model [Roscoe et al., 1958].

From stress strain responses of RI, FA, and observed–states shown in Fig. 1, the disturbance D and effective

stresses in the DSC model are given by:

Fij

Rij

Oij

RijD

''

''

σσ

σσ

−

−=

(1)

Fij

Rij

Oij DD ''' )1( σσσ +−= (2)

where D = disturbance at a current observed state; and

σ'ijR, σ'ijF, and σ'ijO = effective stresses at RI, FA, and

observed states, respectively. Differentiating Eq. (2), the

incremental formulation of the observed stress is obtained

as follows [Desai, 1980]:

)()1( ''''' Rij

Fij

Fij

Rij

Oij dDDddDd σσσσσ −++−= (3)

where dσ'ijR, dσ'ijF, and dσ'ijO = stress increments at RI,

FA, and observed states, respectively.

2.2 Disturbance

Key parameter in the DSC model is the disturbance

D as it determines the stress-strain response and shear

resistance at a certain loading stage. According to Desai

et al. [1998], the disturbance D and deviatoric plastic

strain trajectory ξD are defined through the following

relationship:

)]exp(1[ ZDu ADD ξ−−= (4)

where Du, A, and Z = material constants obtained from

experimental test results; and ξD = deviatoric plastic strain

trajectory. The deviatoric plastic strain trajectory ξD in

(4) is defined as:

∫= pij

pijD dd εεξ (5)

where dεijp is an increment of the deviatoric plastic strain

tensor under undrained conditions. Eq. (5) represents that

the deviatoric plastic strain trajectory ξD is equal to

absolute amount of deviatoric plastic strains accumulated

from the initial to a given loading cycle in a dynamic

loading process.

Fig. 2 shows the calculation procedure of the deviatoric

plastic strain trajectory ξD from a cyclic stress-strain

response and typical disturbance curve in terms of D and

ξD for sands. As shown in the figure, values of D vary

from 0 to 1 through linear increase, non-linear increase,

and stabilization stages. Value of D equal to 0 represents

the initial RI state while D = 1 corresponds to the FA

state. From the disturbance curve in Fig. 2 (b), it is seen

that there is a point of the maximum curvature (i.e., point

A) before the stabilized D value equal to 1 is reached.

Value of D corresponding to this point is defined as theFig. 1. Stress-strain responses with disturbed state concept (after

Desai et al., 1998)


critical disturbance Dc. Importance and application of the

critical disturbance Dc to liquefaction will be discussed

later.

2.3 Stress-Stain Models for RI and FA States in DSC

In the DSC model by Desai and Ma [1992] and Desai

et al. [1998], the HiSS model [Desai et al., 1991] and

the well-known critical state model [Roscoe et al., 1958]

are used to define RI and FA states, respectively. The

yield surface in the HiSS model for the RI state is given

by:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ ++⎟⎟

⎠

⎞⎜⎜⎝

⎛ +−−=

2

11112

2

a

su

n

a

s

a

D

pJJ

pJJ

pJ

F γα(6)

where J1 = the first invariant of the stress tensor; J2D =

the second invariant of the deviatoric stress tensor; J1s =

shift of J1 axis for materials such as concretes which

possess tensile strength; pa = atmospheric pressure in the

same unit as the stress tensor; n and γu = model

parameters; and = hardening function. The hardening

function can be defined in terms of the deviatoric plastic

strain trajectory ξD for undrained conditions as follows

[Desai, 1980]:

2

1hD

hξ

α =(7)

where h1 and h2 = hardening function parameters; and

ξD = deviatoric plastic strain trajectory defined by (5).

Fig. 3 shows the yield surface given by the HiSS model.

In the HiSS model, as shown in Fig. 3, there are two

reference lines defined for states of soil responses: phase

change and ultimate state lines. The phase change line

represents a boundary under which soils are contractive

and a point where states of soil responses were changed.

Once a stress path meets the phase change line, a sand

becomes dilative with a stress path approaching to the

ultimate state line. The ultimate state line represents a state

of no volume change corresponding to the critical state

line in drained conditions.

(a) determination of ξD

(b) disturbance function

Fig. 2. Deviatoric plastic strain trajectory ξD and disturbance

function curve (after Desai et al., 1998)

Fig. 3. Yield surface in HiSS model (after Desai et al., 1991)


3. Experimental Investigation of Dynamic Soil

Responses

3.1 Cyclic and Static Triaxial Tests

In order to investigate detailed undrained behaviors and

dynamic responses of saturated sands, both cyclic and

static undrained triaxial tests were performed for different

soil conditions. The testing equipment was the automated

triaxial testing system manufactured by Soil Engineering

EquipmentⓇ, which allows application of both cyclic and

static loadings. Test soil was the Jumunjin sand, a standard

sand in Korea with properties given in Table 1. For static

tests, two different confining stresses (σ'c = 100 and 150

kPa) and two different relative densities (DR = 40 and

60%) were used. Also, two test conditions, σ'c = 150 kPa

with DR = 40% and σ'c = 100 kPa with DR = 60%, were

used for dynamic tests.

Fig. 4 shows loading mechanisms for cyclic and static

undrained triaxial tests adopted in the present study. For

cyclic triaxial tests in Fig. 4 (a), the sinusoidal type of

cyclic deviatoric stresses equal to 63 and 44 kPa were

applied while cyclic radial stresses were applied with a

magnitude equal to a half deviatoric stress at a phase angle

difference of 180°. This allows the constant mean total

stress of soil samples throughout the tests. In cyclic triaxial

tests, the stress-strain curve for the first compression stage

represents the RI state, whereas subsequent loading cycles

result in increases of the material disturbance with stress

softening behavior. Fig. 4 (b) shows the loading mechanism

used for static undrained triaxial tests. As shown in the

figure, a combined loading condition of the axial compression

(AC) and the lateral extension (LE) was adopted in the

tests with constant mean total stresses throughout the tests.

As a result, stress-strain curves from AC-LE static triaxial

tests represent the same RI state as those from cyclic

triaxial tests for the first loading cycle.

In order to maintain the sample homogeneity, test

samples were produced using the undercompaction technique

recommended by Ladd (1978). Soil samples for tests were

prepared as follows. Firstly, test samples of a weight

corresponding to a target DR value (i.e., DR = 40 and 60%

in this study) were placed into the triaxial sample mold

wrapped with the rubber membrane. Test samples were

placed and compacted in five sub-layers. After the sample

preparation, CO2 gas was injected into the test sample

and de-aired water was introduced for the sample saturation.

This process was adopted for more effective sample

Table 1. Basic properties of Jumunjin sand

γdmax (kN/m3) γdmin (kN/m

3) emax emin GS D50 (mm) Cu

*Cc

**

15.7 13.6 0.719 0.625 2.63 0.52 1.35 1.14*Cu = coefficient of uniformity, Cc

**= coefficient of curvature.

(a) cyclic triaxial test

(b) static triaxial test

Fig. 4. Loading mechanisms


saturation and continued for approximately 3 hours. After

placing the sample into the triaxial loading chamber, a

back pressure equal to 150 kPa was applied for at least

2 hours to ensure the sample saturation. Once the B value

reached a value greater than 0.97, the confining stress was

applied, which was maintained for approximately 1 hour.

For shearing stage in static triaxial tests, a loading rate

equal to 0.1% strain per minute was used, while cyclic

triaxial tests were performed at a loading frequency equal

to 1 Hz.

3.2 Test Results

Fig. 5 shows stress-strain curves, mobilization of excess

pore pressures, and effective stress paths obtained from

static undrained triaxial tests. As shown in Figs. 5 (a)

and (b), no significant differences in stress-strain curves

are observed for σ'c = 100 and 150 kPa. This is because

the loading mechanism of AC-LE triaxial tests with

decreasing radial stress compensates the effect of different

initial confining stresses. Figs. 5 (c) and (d) show that

(a) σ′c = 100 and 150 kPa with DR = 40% (b) σ′c = 100 and 150 kPa with DR = 60%

(c) σ′c = 100 and 150 kPa with DR = 40% (d) σ′c = 100 and 150 kPa with DR = 60%

(e) σ′c = 100 and 150 kPa with DR = 40% (f) σ′c = 100 and 150 kPa with DR = 60%

Fig. 5. Stress-strain curves and effective stress paths from static triaxial tests


the excess pore pressures are plotted against time. From

this result, the excess pore pressures observed during

loading are decreasing with time. The excess pore pressures

increase obviously during unloading. Stress paths for the

tests are shown in Figs. 5 (e) and (f). The straight lines

plotted in the figures represent estimated ultimate state

lines described previously. Slopes of the ultimate state

lines appear to be virtually the same for both cases since

those are the intrinsic soil variable that is unique for a

given soil irrespective of density and stress states. It

should be noticed that estimated ultimate state lines in

Figs. 5 (e) and (f) may not be true ultimate state lines

as further stress hardening appears to be possible as shown

in Figs. 5 (a) and (b).

Fig. 6 shows stress-strain curves, mobilization of excess

pore pressures, and stress paths obtained from cyclic

triaxial tests. The characteristic hysteresis loops are generated

by plotting the deviatoric stress versus the strain, acting

on the sample and are shown in Figs. 6 (a) and (b). The

loops tend to grow up progressively as the sample begins

(a) σ′c = 150 kPa with DR = 40% (b) σ′c = 100 kPa with DR = 60%

(c) σ′c = 150 kPa with DR = 40% (d) σ′c = 100 kPa with DR = 60%

(e) σ′c = 150 kPa with DR = 40% (f) σ′c = 100 kPa with DR = 60%

Fig. 6. Stress-strain curves, excess pore pressure development, and effective stress paths from static triaxial tests


to liquefy; after liquefaction the curves are maintained.

As shown in Figs. 6 (c) and (d), the excess pore pressure

continuously builds up until a certain number of loading

cycles [i.e., N = 11 and 7 in Figs. 6 (c) and (d)], and

then a rapid increase and oscillation of the excess pore

pressure at a value approximately equal to the initial

confining stress is observed. This can also be seen in

effective stress paths shown in Figs. 6 (e) and (f). As

shown in the figures, effective stress paths degrade gradually

as the number of loading cycles increases. Once the

effective stress path meets a certain point, it moves

linearly to the origin of the zero effective stress state, after

which oscillation with no average shear resistance is

observed. This point, at which the linear stress degradation

initiates, therefore, can be defined as the initial liquefaction

occurrence.

4. Liquefaction Analysis Based on Dsc Model

4.1 Determination of Initial Liquefaction

Determination of the initial liquefaction is important as

it defines the liquefaction resistance for a given soil

against a given earthquake. According to Iai et al. [1992],

the initial liquefaction can be defined from the liquefaction

front state in terms of the plastic shear work, which can

be obtained from cyclic stress-strain curves. This is based

on the assumption that the excess pore pressure is also

related to the plastic shear work. When a value of the

plastic shear work, normalized with total plastic shear

work at liquefaction, reaches 1.0 or the liquefaction front

parameter defined by a current effective stress is smaller

than 0.4, the dynamic effective stress path is found to

move rapidly toward the zero effective stress state with

initiation of liquefaction.

Other common approach for the determination of the

initial liquefaction is based on the flow liquefaction surface

[Vade and Chern, 1983]. The flow liquefaction surface

can be obtained at the phase change state toward the ultimate

or steady state on effective stress paths of undrained static

triaxial tests. The flow liquefaction surface, therefore,

represents the same definition as the phase change line

described in the DSC model.

For the application of the disturbed state concept to

liquefaction, Desai et al. [1998] suggested that the

initiation of liquefaction is closely related to the critical

disturbance Dc, which corresponds to the maximum

curvature point on the disturbance function curve shown

in Fig. 2 (b). This is based on experimental observation

that the number of loading cycles to reach Dc approximately

matches that required to reach the initial liquefaction.

According to Desai et al. [1998], the critical disturbance

Dc is determined from the optimized disturbance function

curve in terms of the disturbance D and the deviatoric

plastic trajectory ξD drawn at every single loading cycle.

This indicates that values of Dc from the original DSC

model may not exactly coincide with actual liquefaction

initiations as detailed components of a single loading cycle

from compression to tension are not reflected. In the

present study, therefore, the determination of the critical

disturbance Dc and the initial liquefaction is based on the

effective stress path with more detailed loading components.

In particular, the phase change line is introduced to define

the critical disturbance and the initial liquefaction.

Comparison between different definitions for the initial

liquefaction will be further discussed.

Fig. 7 shows phase change (PCL) and ultimate state

lines (USL) obtained from effective stress paths for both

static and cyclic triaxial tests. For cyclic triaxial tests

shown in Figs. 7 (c) and (d), phase change lines were

defined as a line between the origin and the initial

liquefaction point corresponding to a point at which the

rapid decrease of effective stress initiates [i.e., PCP in

Figs. 7 (c) and (d)]. In the present study, the phase change

line obtained from cyclic tests is referred to as the dynamic

phase change line (DPCL). From Fig. 7, it is seen that

the phase change line and the dynamic phase change line

obtained from static and cyclic triaxial tests are virtually

the same, whereas the determination procedure and

mechanical features of the two tests are different. It is

also seen that, after the initial liquefaction at the dynamic

phase change line from cyclic triaxial test, there is another

line (DUSL) along which the stress paths show a cyclic

regularity. This line was found to be similar to the ultimate


state line observed from static triaxial tests. The consistency

of the phase change and ultimate state lines from both

tests is reasonable as all the test results are based on

effective stresses. This result also indicates that a single

cyclic triaxial test can provide significant soil parameters

required for liquefaction analysis using DSC model.

4.2 Classification of Dynamic Soil Phases and

Modified DSC Model

From cyclic triaxial test results, it was found that the

effective stress path under dynamic loading conditions

consists of three different phases: gradual degradation of

effective stress, initial liquefaction with rapid stress

degradation, and fully developed liquefaction. The gradual

degradation phase of effective stress corresponds to the

unstable state under which significant deformations develop,

while the fully developed liquefaction phase represents

the ultimate state with no further shear resistance available.

The initial liquefaction is defined as a stage from which

rapid development of the excess pore pressure occurs with

an effective stress path moving towards the zero-effective

stress state along the phase change line. Fig. 8 shows

different phases of dynamic soil responses and corresponding

excess pore pressure development. As shown in the figure,

the excess pore pressure accumulates continuously during

the gradual degradation phase of effective stress and then

rapid increase and full development of the excess pore

pressure are observed at the initial liquefaction and fully

developed liquefaction phases, respectively.

In the original DSC model [Desai et al., 1998], liquefac-

tion is defined to initiate at a certain number of loading

cycles corresponding to the critical disturbance Dc obtained

from the optimized disturbance function curve. For small

strain problems before failure, such as dynamic responses

of axially-loaded pile, this approach has been successfully

implemented [Desai and Rigby, 1997; Pal and Wathugala,

(a) static triaxial tests for σ′c = 100 and 150 kPa (b) static triaxial tests for σ′c = 100 and 150 kPa

(c) cyclic triaxial test for σ′c = 150 kPa (d) cyclic triaxial test for σ′c = 100 kPa

Fig. 7. Phase change and ultimate state lines based on effective stress paths


1999]. For the analysis of initiation and full development

of liquefaction, however, this approach has not been fully

verified as it does not include detailed variations of

dynamic soil phases described in Fig. 8. In this study,

therefore, a modification was made into the original DSC

model such that initial liquefaction occurrence and different

soil phases are defined in terms of the phase change and

ultimate state lines from dynamic effective stress paths.

This modification reflects more detailed dynamic soil

responses and actual liquefaction initiation observed from

experimental test results. As discussed earlier, both phase

change and ultimate state lines required in this modification

can be obtained from a single cyclic triaxial test.

The FA state in the original DSC model is defined by

the critical state model [Roscoe et al., 1958]. In the modified

DSC model, the FA state is defined by Drucker-Prager

model [1952] for which the failure envelope can be

determined from the ultimate state line of the cyclic

effective stress path. This modification represents a much

simpler procedure for the parameter determination than

the original DSC as a single cyclic triaxial test provides

key parameters for both RI and FA states. The disturbance

D from the modification is then defined as follows:

FR

OR

JJJJ

D11

11

−−

=(8)

where J1R, J1

F, and J1a are the first stress invariants for

RI, FA, and observed states, respectively.

In the original DSC model [Desai et al., 1998], values

of the disturbance D are obtained at every single cycle

in the cyclic loading process. In the new procedure for

the modified DSC model, values of D are obtained at

every 1/4 cycle of compression, unloading, extension, and

(a) dynamic effective stress path

(b) excess pore pressure development

Fig. 8. Classification of dynamic soil phases

(a) σ′c = 150 kPa and DR = 40%

(b) σ′c = 100 kPa and DR = 60%

Fig. 9. Excess pore pressure ratios and disturbances with number

of loading cycles


unloading phases for a given loading cycle. This aims at

describing more realistic and detailed liquefaction behavior

as the use of a single cycle may not detect the specific

point at which significant changes of the excess pore

pressure occur as a liquefaction initiation point.

Fig. 9 shows values of the disturbance D based on Eq.

(8) and excess pore pressures ratio uexcess/σ'c plotted at

every 1/4 loading cycle. As can be seen in Fig. 9, changes

of D with number of loading cycles appear to be nearly

identical to the mobilization of the excess pore pressure.

Results in Fig. 9 suggest that the disturbance D can be

effectively used for the description of the excess pore

pressure development and thus as an index for the assess-

ment of liquefaction potential.

4.3 Determination of Deviatoric Plastic Strain Tra-

jectory

The deviatoric plastic strain trajectory ξD for the initial

liquefaction in the original DSC model is obtained from

Dc corresponding to the maximum curvature point on the

optimized disturbance function curve. Curvature of the

optimized disturbance function curve is given by:

( ) 232

"

1 D

DR′+

=(9)

where R = curvature of the disturbance function curve

given by (4); and D' and D" = the first and second

derivatives of the disturbance function with respect to ξD.

Detailed formulation of D' and D" are:

(a) maximum curvature point for σ′c = 100 kPa and DR = 40% (b) maximum curvature point for σ′c = 100 kPa and DR = 60%

(c) determination of Dc for σ′c = 100 kPa and DR = 40% (d) determination of Dc for σ′c = 100 kPa and DR = 60%

Fig. 10. Determination of Dc from original DSC model


( ) ( )ZDZD

D

AExpAZddDD ξξξ

−×== −1' 99.0(10)

( ) ( )[ ]ZDZD

ZD

D

AZZAExpAZdDdD ξξξ

ξ−−−×== − 199.0 2

2

2"

(11)

where A and Z = material constants. Fig. 10 shows

calculation of D and ξD for the original DSC model using

the cyclic triaxial test results presented previously. Fig.

11 shows values of the critical disturbance Dc and

corresponding deviatoric plastic trajectory ξD obtained

from (5) and effective stress paths for the proposed

method. Comparing results in Figs. 10 and 11, it is

observed that the original DSC approach produces higher

values of ξD than those obtained from the modified DSC

approach. This in turn indicates that the liquefaction

resistance for a given soil from the original DSC model

may be overestimated, which is unconservative.

4.4 Calculated and Observed Cyclic Soil Responses

For the application of the DSC model to liquefaction,

numerical codes based on the incremental integral scheme

for both the original and modified DSC models were

developed and used in the comparison with experimental

test results. In the modified DSC model, the RI state was

defined with the HiSS model by Desai et al. [1991] as

in the original DSC model, while the Drucker-Prager

model [1952] was employed for the FA state. For the

original DSC model [Desai et al., 1998], dynamic soil

responses and initiation of liquefaction were defined in

terms of the critical disturbance Dc obtained at the maximum

curvature point on the optimized disturbance function

curve. The modified DSC model, on the other hand,

includes different soil phases of the gradual stress degra-

dation, initial liquefaction, and fully developed liquefaction,

(a) liquefaction initiation point from cyclic effective stress path

for σ′c = 100 kPa and DR = 40%

(b) liquefaction initiation point from cyclic effective stress path

for σ′c = 100 kPa and DR = 60%

(c) determination of Dc for σ′c = 100 kPa and DR = 40% (d) determination of Dc for σ′c = 100 kPa and DR = 60%

Fig. 11. Determination of Dc from modified DSC model


based on the dynamic phase change and ultimate state

lines shown in Figs. 7 and 8. Fig. 12 shows the computa-

tion procedure of the program developed for the modified

DSC model.

The DSC and modified DSC model involves a number

of material constants and they can be determined from

a series of static and cyclic triaxial test results. The

material constants can be divided into four categories: the

elastic state parameters, the plastic state parameters, the

ultimate state parameters, and the parameters for describing

disturbance function. The elastic state parameters E and

are found from the slopes of unloading parts of theνstrain-stress curves (Fig. 6). The parameters for the plastic

state γu and are associated with the ultimate state, whichβis defined as the locus of the stress states asymptotic to

the observed stress-strain curve. To find the plastic state

parameters γu and , which are related to the slope ofβthe ultimate envelope in J2D

0.5 - J1 space, at least two

different stress paths are required. The phase change

parameter, n is the parameter related to the point at which

the plastic volume change is zero. Fig. 7 shows phase

change (PCL) obtained from effective stress paths for both

static and cyclic triaxial tests. Therefore, the parameter

n is calculated by Fig. 7 and Eq. (6). Values of the model

parameter h1 and h2 in Eq. (7) can be estimated from theFig. 12. Computation procedure for modified DSC model

Table 2. Input parameters used in calculation

Original DSC model Modified DSC model

DR = 40%

σ′c = 150 kPa

DR = 60%

σ′c = 100 kPa

DR = 40%

σ′c = 150 kPa

DR = 60%

σ′c = 100 kPa

Elastic

state

E 175 MPa 210 MPa E 175 MPa 210 MPa

ν 0.38 0.38 0.38 0.38

Plastic

State

uγ 0.25 0.25 uγ 0.25 0.25

0 0 0 0

n 2.80 2.67 n 2.80 2.67

h1 0.059 0.152 h1 0.059 0.152

h2 0.016 0.092 h2 0.016 0.092

Ultimate

State*

m 0.5 0.5 M 0.5 0.5

λ 0.045 0.052 k 0 0coe 0.636 0.0624 - - -

Disturbance

parameters

Du 0.99 0.99 Du 0.99 0.99

A 1.458 1.771 A 1.107 1.771

Z 0.779 0.882 Z 0.671 0.882

*m, , andλ c

oe = Critical state concept model parameters; M and k = Drucker-Prager model parameters


first-order polynomial regression line that is obtained by

taking the natural log operator in both sides of Eq. (7).

The slope and intercept of this line give the values of

h1 and h2, respectively. The ultimate state parameters m,

M, , and eλ 0c are evaluated from the characteristics of

the ultimate state line (USL), where, m and M are the

slope of the USL in the J2D0.5 - J1 space (Fig. 7). e0

c is

the reference void ratio evaluated at a mean pressure (J1/3)

of 1 kPa. is the slope of the USL in e - ln(Jλ 1/3) space.

The disturbance parameters Du, A, and B are evaluated

from Eq. (4). For each test, the maximum value of the

disturbance is found and an arithmetic average value Du

is estimated from the values calculated for each test. The

calculated D and ξD together with Du are used to plot

(a) stress-strain curves with DR = 40% (b) stress-strain curves with DR = 60%

(c) excess pore pressure developments for DR = 40% (d) excess pore pressure developments for DR = 60%

(e) effective stress paths for DR = 40% (f) effective stress paths for DR = 60%

Fig. 13. Calculated and observed cyclic soil responses with original DSC model


the data in ln[-ln({Du - D}/Du)] - ln ξD space. Choosing

an average straight line through the plotted data gives the

A and Z values for the test under consideration. The input

parameters were summarized in Table 2.

Figs. 13 and 14 show calculated and observed cyclic

soil responses using the original and modified DSC models,

respectively. As shown in Fig. 13, excess pore pressures

and effective stress paths calculated from the original DSC

represent overall agreement with observed results for the

gradual degradation phase of effective stress. As the stress

path approaches to the initial liquefaction stage, however,

it is seen that the difference between calculated and

observed results becomes more pronounced with different

liquefaction initiation points. This result indicates that the

critical disturbance Dc obtained from the procedure of the

original DSC model does not match well the actual

(a) stress-strain curves with DR = 40% (b) stress-strain curves with DR = 60%

(c) excess pore pressure developments for DR = 40% (d) excess pore pressure developments for DR = 60%

(e) effective stress paths for DR = 40% (f) effective stress paths for DR = 60%

Fig. 14. Calculated and observed cyclic soil responses with modified DSC model


liquefaction initiation point observed from experimental

test results.

Fig. 14 shows calculated results using the modified

DSC model. As shown in the figure, closer agreements

are observed for excess pore pressure development and

effective stress paths including the rapid stress degradation

and initial liquefaction occurrence. Meanwhile, it is seen

that observed stress-strain curves show bigger response

in the strain than calculated stress-strain curves. This is

because actual soils after initial liquefaction behave as a

liquid material and thus produce large deformations with

significant reductions of elastic modulus. Hence, further

investigation and modification would be necessary if

detailed deformation analyses were desired.

5. Conclusion

When a dynamic force such as an earthquake is applied

to saturated sands, the excess pore pressure builds up

continuously with decreases of soil strength, and sands are

eventually liquefied. In this paper, the application of the

DSC model to the analysis of liquefaction potential was

examined through experimental and analytical investigations.

While the DSC model has been successfully verified for

many geotechnical dynamic problems, it has not been

fully implemented for a whole process of liquefaction

analysis, including definition of liquefaction potential.

For more realistic description of dynamic responses of

saturated sands, the DSC model was modified based on

two reference lines of the phase change and ultimate state

lines that were observed from cyclic triaxial tests. Both

static and cyclic undrained triaxial tests were performed

for sands with different relative densities and confining

stresses. Based on test results, a classification of liquefaction

phases in terms of the dynamic effective stress path and

the excess pore pressure development was proposed and

adopted into the modified DSC model. The initial

liquefaction and the critical disturbance Dc in the modified

DSC model is defined at a stage from which a rapid

development of the excess pore pressure occurs with an

effective stress path moving towards the zero-effective

stress state along the phase change line. While values of

the disturbance D in the original DSC model are obtained

at every single cycle in the cyclic loading process, the

procedure of the modified DSC model calculates values

of D at every 1/4 cycle, including compression, unloading,

extension, and unloading phases.

Compared with initial liquefaction, it is observed that

the liquefaction resistance for a given soil from the

original DSC model may be overestimated, which is

unconservative. From the analysis results, it was seen that

the predicted effective stress path, excess pore pressure,

and stress strain curves using modified DSC model

matches well measured results for the cyclic undrained

triaxial tests. It was also found that the parameters

required to define the model were simplified.

Acknowledgements

This work has been supported by Yonsei University,

Center for Future Infrastructure System, a Brain Korea

21 program, Korea.

References

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3. Desai, C.S. and Toth, J. (1996), “Disturbed state constitutive modelingbased on stress-strain and nondestructive behavior”, InternationalJournal of Solids and Structure, 33(11), 1619-1650.

4. Desai, C.S. and Rigby, D.B. (1997), “Cyclic interface and joint sheardevice including pore water pressure effects”, Journal of Geotechnicaland Geoenvironmental Engineering, 123(6), 568-579.

5. Desai, C.S., Sharma, K.G., Wathugala, G.W. and Rigby, D.B. (1991),“Implementation of hierarchical single surface δ0 and δ1 modelsin finite element procedure”, International Journal of Numerical andAnalytical Methods in Geomech, 15, 649-680.

6. Desai, C.S., Basaran, C. and Zhang, W. (1997), “Numerical algorithmsand mesh dependence in the disturbed state concept”, InternationalJournal of Numerical Method in Engineering, 40, 3059-3083.

7. Desai, C.S., Park, I.J. and Shao, C. (1998), “Fundamental yetsimplified model for liquefaction instability”, International Journalof Numerical and Analytical Methods in Geomech, 22(7), 721-748.

8. Drucker, D.C. and Prager, W. (1952), “Soil mechanics and plasticanalysis or limit design”, The Quarterly Journal of Mechanics andApplied Math, 10(2), 157-165.

9. Finn, W.D.L., Lee, K.W. and Martin, G.R. (1977), “An effective


stress model for liquefaction”, Journal of Geotechnical EngineeringDivision, ASCE, 103(6), 517-533.

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11. Katti, D.R. and Desai, C.S. (1994), “Modeling and testing of cohesivesoil using the disturbed state concept”, Journal of EngineeringMechanics, ASCE, 121(1), 43-56.

12. Ladd, R.S. (1978), “Preparing test specimens using undercompaction”,Geotechnical Testing Journal, GTJODJ, 1(1), 16-23.

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14. Roscoe, K.H., Scofield, A. and Wroth, C.P. (1958), “On yielding

of soils”, Geotechnique, 8, 22-53.15. Seed, H.B., Idriss, I.M. and Arango, I. (1983), “Evaluation of

liquefaction potential using field performance data”, Journal ofGeotechnical Engineering Division, ASCE, 109(3), 458-482.

16. Vade, Y.P. and Chern, J.C. (1983), “Effect of static shear onresistance of liquefaction”, Soil and Foundation, 23(1), 47-60.

17. Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G.,Christian, J.T., Dobry, R., Finn, W.D.L., Harder, L.F., Hynes, M.E.,Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson III, W.F., Martin,G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K.,Seed, R.B., Stokoe II, K.H. (2001), “Liquefaction resistance of soils:Summary report from the 1996 NCEER and 1998 NCEER/NSFworkshops on evaluation of liquefaction resistance of Soils”,Journal of Geotechnical and Geoenvironmental Engineering, ASCE,127(10), 817-833.

(received on Oct. 19, 2007, accepted on Feb. 25, 2008)

Digital Image Analysis (DIA) for Estimating the Degree of Saturation of The Soil-Water Characteristic Curves (SWCC) 53

Digital Image Analysis (DIA) for Estimating the Degree of Saturationof The Soil-Water Characteristic Curves (SWCC)

의 포화도를 구하기 위한 적용SWCC DIA

Min, Tuk-Ki1민 덕 기

Phan Thieu Huy2판 티우 후이

요 지

본 연구에서는 불포화토의 포화도를 구하기 위해 디지털 이미지기법 을 적용하였다 실험을 위한 시료는(DIA) .주문진 표준사를 사용하였다 차원 모래기둥 시험을 실시하여 일정수위상태에서의 디지털 이미지의. 1 colournumber(Cn 와 포화도 와의 상관식을 구하였다 함수특성곡선 을 구하기 위해 이 부착된) (S) . (SWCC) Buchner funnel

를 실시하였으며hanging water column test , Cn 관계식을 이용하여 각 단계에 따른- S suction head average colour로부터 포화도를 산정하였다 와 기법으로부터 산정된 포화도를 비교해 본number . Hanging water column test DIA

결과 기법을 이용하여 을 효과적으로 예측할 수 있음을 보였다, DIA SWCC .

Abstract

The aim of this study was to validate the suitability of an digital image analysis (DIA) method to measure thedegree of saturation in the unsaturated conditions. This study was carried out on the Joo-Mun-Jin standard sand.A one-dimensional sand column test was used in the constant water level condition to get the correlation equationbetween the color number (Cn) and the measured degree of saturation (S). In addition, the hanging water columntechnique to determine the soil-water characteristic curve (SWCC) was performed in a Buchner funnel. The averagedegree of saturation (Save) in the SWCC could be obtained by substituting average color number at each suctionhead value with the Cn - S correlation equation. Comparisons were made between the measured results by thehanging water column test and those obtained from DIA method. Results showed that the DIA method tested hereprovided fairly good saturation distribution values in the drying and wetting processes.

Keywords : Average color number, Correlation equation, Degree of saturation, DIA, SWCC

1 Member, Prof., Dept of Civil Engrg., Univ. of Ulsan, [email protected], Corresponding Author2 Member, Graduate Student, Dept of Civil Engrg., Univ. of Ulsan

1. Introduction

The further development of studies on soil-water required

a more general concept to express the state of water in

soil. Studies of the suction and hydraulic conductivity

models could not ignore the existence of SWCC. The SWCC

relates the gravimetric water content, w, or volumetric

water content, θw (defined as the volume of water in the

soil divided by the total volume of the soil, Vw/V), to

matric suction. This curve presents the basic characteristics

of a partially saturated soil. Gallipoli et al (2003) and

Buisson and Wheeler (2000) indicated that the relationship



between the degree of saturation, S, and matric suction

head, hm, for a given soil is non-unique because the

variation of the void ratio in deformable soils results in

changes of the void dimensions and also in changes of

the connecting passageway between them. This, in turn,

causes corresponding variation in the SWCC. Hence,

determination of the degree of saturation is one of the

key factor in that relationship.

Numerous approaches have been proposed for mathe-

matical representation (i.e., fitting) or prediction of the

degree of saturation. Table 1 summarizes the commonly

used soil-water models for estimating the degree of

saturation. In Table 1, the equations are written in Se(h)

functional form. Se, the effective saturation to describe

the water content in the soil, can be calculated using

equation (1).

re

r

S SS1 S−

=− (1)

in which S is the calculated water saturation; Sr is the

residual saturation. From Eq.1 and the Se(h) functions in

Table 1, the soil-water characteristic functions for the

models are obtained. One of most widely used relation

to represent the SWCC is the one proposed by Van

Genuchten (1980), as it is simple, requiring only two

parameters and gives the good results in case of granular

material. In this study, van Genuchten equation’s form

was used to get the correlation equation for the sand

column test and estimate the degree of saturation in the

hanging water column test. Substituting Eq.1 with van

Genuchten model in Table 1, the SWCC is defined as

the relationship between degree of saturation and suction

head, and can be expressed as

n mr rS S (1 S )[1 ( h) ]−= + − + α (2)

in which n is a curve fitting parameter which reflects the

pore-size distribution of the porous medium, and m = 1

(1/n);– (L-1) is a scaling parameter which is related

to the displacement suction head. The parameter can

be represented by two limiting values, one applied to

drainage curves and other applied to imbibitions curves.

Degree of saturation can be measured either with

destructive methods or with non-destructive methods. The

gravimetric method, which leads to a soil-water content

on the basis of weight or volume, is the most widely used

destructive technique. Non-destructive techniques that have

proved to be applicable under field conditions are: neutron

scattering (Gardner, 1986), gamma-ray attenuation (Bertuzzi

et al. 1987), capacitance method (Dean et al. 1987 and

Halbertsma et al. 1987) and time-domain reflectrometry,

TDR (Heimovaara and Bouten 1990).

Up to now, DIA has become popular approach to

quantitatively determine static and dynamic flow of water

in an unsaturated/saturated soil. Investigators have utilized

DIA to predict such parameters as dye concentration and

LNAPL (Light Non-Aqueous Phase Liquid) saturation in

laboratory experiments (Schincariol et al. 1993, Van Geel

& Sykes 1994). Furthermore, S.B. Coskun and N.C.

Wardlaw (1994) proposed an empirical method for estimating

initial water saturation by DIA. R.S. Sharma et al. (2002)

represented a method to predict the degree of saturation

from the average color number in the column test. Philip

Gachet et al. (2003) also applied DIA to study the

hydromechanical behavior of unsaturated soil.

Table 1. Summary of Empirical and Macroscopic Equations for

Modeling Unsaturated Degree of Saturation Function

Model name Model

Brooks and Corey (1964) n

ehSa

−⎛ ⎞= ⎜ ⎟⎝ ⎠

Brutsaert (1966) e n

1S1 (h / a)

=+

Van Genuchten (1980)

( )e mn

1S1 ( h)

=+ α

Tani (1982) ea h a hS 1 expa n a n− −⎛ ⎞ ⎛ ⎞= + −⎜ ⎟ ⎜ ⎟− −⎝ ⎠ ⎝ ⎠

McKee and Bumb (1987) (Fermi) eS 1/(1 exp((h a) / n))= + −

Fredlund and Xing (1994)

( )e n m

1Sln(e (h / ))

=+ α

Kosugi (1994) m

eln(h / h )S Q ⎡ ⎤= ⎢ ⎥σ⎣ ⎦

Note: definition of variables: h is soil suction; , a, n and mare fitting parameters; Q is a cumulative normal distribution

function; σ is standard deviation of lnh


The rapid development of inexpensive high resolution

digital cameras and the availability of high performance

digital image processing software open new possibilities

of the DIA method in the field of unsaturated soils. The

main aim of this paper is to estimate a degree of saturation

in the relationship with the matric suction head by

combining S-shape curve fitting equation with the DIA

results from the hanging water column test. And then,

these results are validated by the results of the degree

of saturations from the hanging water column test.

2. Material and Methods

2.1 Materials

In this investigation, Joo-Mun-Jin sand was used. The

index properties of this sand are Cu = 1.65 and Cc = 1.08

with D50 range between 0.50 and 0.55 mm. The sample

was classified as poorly graded sand. The porosity of the

sample was found to vary in a narrow band, 45 (+/-1)%.

The majority of the sand particles had the mean diameter

of 0.55 mm and the rest of the particles were very close

to the mean diameter.

2.2 Methods

2.2.1 Column Tests for DIA Application

Figure 1 shows the schematic diagram of the sand

column test commonly used for measuring the degree of

saturation in unsaturated soil testing applications. The

sand column is 0.4 m in height, and the interior is 0.19

x 0.19 m wide. The walls are made of 5 mm thick

Plexiglas. A fine mess of 5 mm thickness was placed at

the bottom of the column. Details of designs of the column

test are given in Sharma et. al 2002.

In order to reduce the angle of friction and color

differences at the interface (soil mass and Plexiglas), the

oil films have been applied. This lubricant will reduce

the adhesion at the interface and make the local flow

behavior remains unchanged between interface areas and

areas inside the soil mass. In this study, the commercial

product: WD40 spray (containing MsO2, silicone, Teflon,

and other constituents) was chosen. WD40 spray was almost

as good as silicone, being more fluid and progressively

reducing its effect on the interface (Gachet et al. 2003).

Prior to measure, well-sorted sand samples by air

pluviation method were used to fill the column. Saturated

samples were initially prepared by pouring dry sand into

a partially water-filled container. Although it is unlikely

for air to be trapped in the pore voids since dry sand

Fig. 1. Schematic diagram of sand column test


was always poured in water, the prepared samples were

left for at least 24h with water above the sand surface

to ensure that the samples initially reached full saturation.

After a day, the water level decreased to 0 cm and

it was left one more day before taking the image. After

taking the image, the sand column was brought to measure

water content by suctioning method. The sand sample in

each 2.0 cm was taken out and then water content can

be estimated using an estimate of oven dry weight. The

images and the experimental water content results are used

to make the relationship between color number and degree

of saturation following the height of the sand column.

2.2.2 Suction Tests Using the Hanging Water ColumnMethod

A hanging water column setup was used for determining

the matric suction head in the relationship with the degree

of saturation. This apparatus consists of three parts: a

specimen chamber, an outflow measurement tube and a

column of water. The specimen chamber is placed on a

fine mesh, which is connected to the outflow measurement

tube below. The end of this tube is connected to the

column of water. The column of water is used to control

the suction at the base of the sample. The specimen

chamber has internal dimensions of 19 cm x 19 cm x

15 cm. Figure 2 shows the experimental setup of the

hanging water column. A principle that applies to the

design of this apparatus is based on the method in ASTM

D 6836-02 (2004).

A digital camera was used to take the RGB (red-green-

blue) images. The images presented in this paper were

captured using an inexpensive Canon PowerShot S400

digital still camera which provides a max pixel resolution

of 2272 x 1704. Two 500-W halogen lamps were used

to illuminate the column front.

Lighting considerations must also be regarded as a high

priority item since the outcome of the analysis will depend

greatly on the quality of the recorded images, which are

in turn influenced by the quality and arrangement of the

lighting system. Several tests were carried out with

different setups of the lights and different kinds of lights

in order to obtain the one that yielded the crispest images

of the soil sample. The height of camera was adjusted

so that the centre of the lens was at the same height of

the centre of the column (Sharma et al. 2002). Additionally,

the lights were arranged at equal space above and below

the centre of the camera with light rays going to the centre

of the column as shown in Figure 2. Furthermore, all room

Fig. 2. Schematic diagram of hanging water column test


lights were switched off and also the test area was covered

to eliminate any light interference.

Specimen preparations are the same as the sand column

test above. The top of the specimen chamber was covered

with perforated PVC film to prevent evaporation. The

samples were then subjected to varying values of the

matric suction head according to the test objectives.

Drying and wetting main curves were achieved by

lowering and raising the burette to a given height in

stages, respectively (see Fig. 2). In each stage, the sample

was left for a sufficient time to reach equilibrium, which

is marked by no further flow of water from or into the

sand sample and then the images were taken. The time

given was varied depending upon the value of the suction

head and the soil properties. Details of calculations of the

degree of saturation and the suction head are given in

Sharma and Mohamed (2003b).

From the consecutive outflow and inflow volumes the

degree of saturation for each hm value was determined

to obtain the soil-water characteristic curves (SWCC)

during the main drying and wetting processes. The images

which were taken combining fitting correlation equations

from the column test will be considered and analyzed to

predict the degree of saturation for the SWCC.

2.2.3 Digital Image Analysis (DIA) Methodology

The procedure to determine the degree of saturation of

the SWCC by DIA and corresponding algorithm of computer

software are summarized in Figure 3. After taking the

image, image correction technique was applied to calibrate

the image in terms of physical measurement units (e.g.,

mm). The images consisting of 190 x 300 mm (539 x

Fig. 3. Flowchart of DIA procedures and corresponding computer softwares


850 pixels) in the sand column case and 190 x 150 mm

(539 x 425 pixels) in the case of the hanging column test

were created.

And then, following the sand column test, in order to

avoid the light variation on the border of the column,

the middle strip of the column image was selected. The

average color number for each 2.0 cm piece was auto-

matically calculated by commercial Photoshop software

in the expanded view of the histogram option. The

correlation equation will be derived from the relationship

between these color values and measured degree of

saturation.

The step above also has been repeated in the hanging

water column test, but corresponding to each suction head

value with 1.0 cm pieces. Figures 4a through 4d show the

typical images from the hanging water column test during

drying process. After these processes, the average color

numbers were calculated for each 1.0 cm height. Sub-

stitution of the color number in the hanging water column

test with correlation equation gives the degree of saturation

along the column height for each suction head value.

In this study, the degrees of saturations in the SWCC

that means the average degree of saturation at any arbitrary

value of suction head were defined as the ratio between

the area of the hatched part and the total area of the

hatched and unhatched part. Figure 5 shows the procedure

for measuring average degree of saturation. This procedure

is performed for each of the suction head value in the

hanging water column test. Finally, the SWCC is obtained

from predicted degree of saturation and measured matric

suction head.

3. Results and Discussion

3.1 Column Test Results and S-shape Curve Fitting

Equation

The results from the sand column test in the Joo-Mun

Jin sand samples are presented in order to find out the

S-shape correlation equation between degree of saturation

and color number. Figure 6 shows the relationship between

color number and column height, in this case the constant

water level at the 0 cm. The color distribution curve varied

from dark in the capillary zone to bright in the upper

zone. Typically, the two ends were pure black and pure

(a) (b) (c) (d)

Fig. 4. Typical image in the hanging water column test during drying process : (a) saturated case, (b) unsaturated case, (c) the middle

strip was selected from b, (d) after partition step

Fig. 5. Procedure for measuring average degree of saturation


white, 0 and 255, respectively. In this case, our color

results varied from 100 to 150. This distribution looks

quite similar to the degree of saturation distribution in

unsaturated zone.

Following Sharma et. al 2002, the vadose zone is

divided into three zones based on the degree of saturation

of water. These zones are: pendular zone, where water

is at residual degree of saturation, capillary fringe, where

the degree of saturation of water is close to 100%, and

funicular zone, where the degree of saturation varies from

residual to almost full saturation. From the above distri-

bution, in order to simulate this situation, a form of the

van Genuchten’s equation (Eq.2) can be applied. In this

case, the matric suction head value (hm) has been replaced

by the average color number (Cn). Hence, the relationship

between the degree of saturation and color number as

shown in equation 3, is similar to those presented by

Sharma et.al 2002.

( ) ( )cb

r r nS S 1 S 1 aC−

⎡ ⎤= + − +⎣ ⎦ (3)

in which S is the estimated degree of saturation, Sr is

the residual degree of saturation, Cn is the average color

number (measured from the test); a,b and c are the fitting

parameters with c=1-(1/b).

Table 2 summarises the fitting parameters for this

equation for the color number results in Figure 7. These

parameters were used to present the correlation equation

between the average color numbers and the degree of

saturations. Figure 7 shows the results of measured and

estimated degree of saturation using Eq.3. It should be

noted that the fitting values in the capillary and residual

zone are very close to the measured values.

To validate the results and the above fitting parameters,

another measured data have been used for checking.

Figure 8 shows the validation results. In that figure, the

symbols show the measured data in test 2 and the solid

line is the estimated curve by inputing the measured data

Test 2 into Eq.3 with the parameters in Table 2. It is–observed from Figure 8 that the estimated curve is close

to the measured data, especially in the capillary and

residual zone, though it is not so for some points in the

transition zone. Based on these results, the above

0

5

10

15

20

25

30

90 100 110 120 130 140 150Average Colour Number, Cn

Col

umn

Hei

ght,(

cm)

Fig. 6. Color distribution versus column height

0

20

40

60

80

100

90 100 110 120 130 140 150

Average Colour Number, Cn

Deg

ree

of S

atur

atio

n, S

(%)

Measured data - Test 1

Estimated data - Test 1

Fig. 7. Measured and estimated degree of saturation, using Eq.3

0

20

40

60

80

100

90 100 110 120 130 140 150 160

Average Colour Number, Cn

Deg

ree

of S

atur

atio

n, S

(%)

Measured data - Test 2

Estimated data - fromTest 1

Fig. 8. Validation using S-shape curve equation (Eq.3)

Table 2. Fitting parameters for S-shape equation

Sr a b c r2

9.634 0.00856 21.474 0.9534 0.998


correlation equation (Eq.3) can be used for estimating the

degree of saturation and was applied to the following part

in this study.

3.2 Suction Test Results

The hanging water column technique to determine

SWCC is performed in a Buchner funnel, which is also

known as a Haines apparatus (Haines, 1930). Figure 9

shows the comparison between the soil water characteristic

curves for measured and estimated values during main

drying and wetting processes. The symbols show the

measured data and the solid line is the estimated curve.

It was observed that just a small amount of water drained

in the capillary zone. Once the value of the applied suction

head increased over bubbling pressure head, a considerable

amount of water drained out of the sample. The bubbling

pressure head is highlighted on this figure.

In addition, it can be seen from Figure 9 that a

minimum degree of saturation of 20% was reached at a

value of suction head of 27 cm. This degree of saturation

did not decrease anymore even with further increase in

matric suction head, which means this is the residual

saturation.

In the wetting path, the degree of saturation reached

84% although the matric suction head had dropped to zero.

This suggested that 16% of air was trapped inside the

sample. It is clear from these results that there is a

hysteresis in the relation between the degree of saturation

and matric suction head. The amount of hysteresis is

described here by the difference between the values of

matric suction head in drying and wetting. The amount

of hysteresis is 8 cm. The estimated values have been

calculated by using van Genuchten’s equation (Eq.2) and

the fitting parameters for drying and wetting paths are

also presented in Table 3.

It should be noted that there is a little discrepancy in

the residual zone between calculated and fitted values.

Furthermore, based on Fig. 9 and the error rate values

in the Table 3, the estimated results from the wetting

process can be obtained better than the results from the

drying process.

3.3 Predicting the Degree of Saturation in the SWCC

Using DIA Method

Fig. 10 and Fig. 11 show the color distribution results

in the hanging water column test for drying and wetting

processes, respectively. The legend boxes in these graphs

show the free outflow level of water in the burette. The

results indicated that the color numbers vary along the

column height corresponding to the variation of water

Fig. 9. Measured and predicted the degree of saturation versus

matric suction head for the main paths

Table 3. Fitting parameters for S-shape curves from Van

Genuchten’s equation (1980)

Processes Sr (%) n m r2

Dry 20.967 0.0628 31.06 0.9678 0.986

Wet 20.52 0.1327 13.686 0.9269 0.996

0

2

4

6

8

10

12

14

16

90 100 110 120 130 140

Average Color Number, Cn

Col

umn

Hei

ght,(

cm)

0 cm4 cm8 cm15 cm16 cm17 cm18 cm20 cm22 cm24 cm26 cm27 cm

Fig. 10. Color distribution versus column height in drying process


content from wet to dry condition and inversely. The

shape of these results are the same as those which are

obtained from the constant water level (refer to Fig. 6).

In the saturated condition, the variation of the average

color numbers are insignificant, but once the free outflow

level of water reaches to 16 cm the distribution curves

begin to move to the right side and gradually shape the

transition zone. The transition zone continually increases

with the decrease in capillary zone and then gradually

shapes the residual zone at 24 cm. As shown in Figure

10, the distribution curves from 24 cm to 27 cm are very

close in the top part. This means the residual zones are

already shaped. On the other extreme, the variation of

the average color number along the column height in the

wetting process presented imbibition condition. Refer to

Fig. 11. These processes can be realized from the

movement of the color distribution curve from the right

to the left side.

Fig. 12 and Fig. 13 show the estimated degree of

saturation in drying and wetting processes by using the

correlation equation. Substituting the average color number

in Fig. 10 and Fig. 11 with Eq.3, the relationship between

the degree of saturation and column height can be

estimated. The results show significant variations of the

conditions of soil sample from the saturated, unsaturated

to the dry conditions. As it may also be seen from these

graphs, in the saturation case, the degree of saturation can

get to 97% - 99% (~100%) and in the residual condition,

the residual degree of saturation can reach to 19%.

In addition, in Figure 12 and 13, the variation of the

slope of the transition zone can be also realized. When

the free outflow level of water slightly increases, the slope

of the transition zone is gentle. On the contrary, if they

sharply increase, the slopes are very steep. Furthermore,

these curves are parallel with one another with a

difference distance before they reach at the residual level

in the transition zone. This implies that a considerable

amount of water drained out and was absorbed in this

zone in the drying and wetting processes. Besides, this

amount of water also equals with one another corresponding

to each process on the transition zone.

The measured and the estimated degree of saturation

values for the SWCC are shown in Figure 14. In this

figure the round symbols show the measured data from

0

2

4

6

8

10

12

14

16

90 100 110 120 130 140

Average Color Number, Cn

Col

umn

Hei

ght,(

cm)

0 cm5 cm7 cm9 cm10 cm12 cm14 cm15 cm16 cm17 cm18 cm20 cm27 cm

Fig. 11. Color distribution versus column height in wetting process

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100

Degree of Saturation, S(%)

Col

umn

Hei

ght,(

cm)

0 cm4 cm8 cm15 cm16 cm17 cm18 cm20 cm22 cm24 cm26 cm27 cm

Fig. 12. Estimated degree of saturation in drying process using

S-shape curve equation

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100Degree of Saturation, S(%)

Col

umn

Hei

ght,(

cm)

0 cm5 cm7 cm9 cm10 cm12 cm14 cm15 cm16 cm17 cm18 cm20 cm27 cm

Fig. 13. Estimated degree of saturation in wetting process using

S-shape curve equation


the hanging water column test and the triangle symbols

show successive estimated data from the DIA method. The

estimated degree of saturation for drying and wetting

SWCC is close to that from the experiment. But its shape

does not fit the experimental data very well in the pendular

zone. Also the similarity between the estimated air entry

value and those which are obtained (refer to Fig. 9) in

the experiment is clearly expressed. These results show

that in the main paths of the SWCC the application of

the estimated curve equation can be used and gives us

the good agreement.

4. Conclusions

(1) Based on the sand column and the hanging water

column test results during wetting-drying cycles, the

DIA method for estimating the degree of saturation

has been established.

(2) Comparisons between experimental and estimated

results show that the DIA method was effective and

could give the degree of saturation results in the

drying and wetting SWCC rapidly at low suction

cases.

(3) The determination of the degree of saturation of an

unsaturated soil is time consuming and sometimes

difficult. Hence, DIA has become a conventional

engineering practice to estimate the unsaturated degree

of saturation. To obtain reliable estimation of the

degree of saturation, it is important to take into

account some factors such as the arrangement of the

lighting system, an evaporation of water and the shape

of the air-water interface.

The results of this study are encouraging to use DIA

method for the determination of the degree of saturation

of the SWCC for granular materials. Furthermore, DIA

method can be a useful tool for the future estimation

of unsaturated problems, taking the place of complicated

or expensive instruments.

Acknowledgement

This research was supported by the 2008 Research Fund

of University of Ulsan.

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(received on Jan. 4, 2008, accepted on Mar. 26, 2008)

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