1CE 601: Dynamic Properties of Soil

Soil Properties

Monotonic Loading (Shear strength properties of soil)

Angle of Internal Friction () Cohesion (c)

Dynamic Loading (Dynamic properties of soil)

Shear Modulus (G)

Damping Ratio (D)

2Dynamic Properties of Soil

Shear Modulus G = V 2Shear Modulus, G .VSShear wave velocity = VS (m/sec)

Mass density = /g) (Kg/m3)Unit weight of soil = (KN/m3)Acceleration of gravity = g (m/sec2)Acceleration of gravity g (m/sec )

Damping, D = decay in energy

Shear Modulus (G) is measured in KN/m2 & Damping (D) in %

Dynamic Properties of Soil

Low Strain Amplitude test

For strains (10-6% to 10-4%)

Frequency range: 10 Hz to 200Hz

Vibratory loading (Rotating Machinery etc)

High Strain Amplitude test

For strains (10-4% to 10-2%)

Frequency range: 0.1 Hz to 2 Hz (in general)

Blast loading, Earthquake

3Dynamic Properties

High Strain Amplitude testg p

Cyclic Triaxial Test

Cyclic Simple Shear Test

Low Strain Amplitude test

Bender Element Test

Resonant Column Test

Cyclic Triaxial Test (High strain amplitude test)

Dynamic properties of properties of soil using Cyclic Triaxial system:

1. Shear Modulus (G)

2. Damping p gratio (D)

4Dynamic Properties of Soil using Cyclic Triaxial Test

dStress Dynamic aStrain Axial

DDamping EModulus Young Dynamic

Grain size distribution: Kutch soil

KutchSoil(Dhori)( )Gravel 0%Sand 19%Silt 81%

Sample Remouldedwatercontent 25%bulkdensity 1.78gm/ccRemarks 14%Micapresent

(XRDdata)

5Dynamic Behavior of Kutch soil

Strain Controlled Dynamic Triaxial Test(0.5 Hz, 1% strain amplitude, Effective confining pressure =300 kPa)

Kutch soil

Kutch soil

6Grain size distribution: Sabarmati soil

SabarmatiSoilGravel 0%Sand 86%Silt 14%

Sample Remouldedwatercontent 20%bulkdensity 1.90gm/ccRemarks frombanks

ofsabarmati river

Strain Controlled Dynamic Triaxial Test

Dynamic Behavior of Sabarmati soil

(0.5 Hz, 1% strain amplitude, Effective confining pressure =300 kPa)

Sabarmati soil

7Sabarmati soil

Dynamic Behavior of soil using Cyclic Triaxial setup

w/c:Watercontent:Bulkdensity

C h i

Soil w/c c Liquefaction G0 G1 G2 G3 G4 G5(%) (gm/cc) (kPa) (deg) (noofcycle) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)

Kutch 25 1.78 0 28 12cycles 10082 7101 5310 4334 3501 2894Sabarmati 20 1.90 0 26 5cycles 8824 4570 2584 1434 827 475

c:Cohesion:FrictionangleG:Shearmodulusofsoilobtainedfordifferentcyclesofloading

8Dynamic Behavior of Soft clay

Strain Controlled Dynamic Triaxial Test(0.004 Hz, 3% strain amplitude, Effective confining pressure =300 kPa)

SoftclaySand 0%

Sachan (2012)

Sand 0%Silt 2%Clay 98%

Sample Slurryconsolidatedwatercontent 49%bulkdensity 1.75gm/ccRemarks Commerciallyavailable

Kaolinite clay

Soft claySachan (2012)

9Cyclic Instability in Slurry consolidated specimens of soft clay

Dynamic Behavior of Soft Clays using Cyclic Triaxial Testing

CyclicInstabilityinSlurry consolidatedspecimensofsoftclay

Soil w/c c Cyclic

Instability G0 G1 G2 G3 G4 G5(%) (gm/cc) (kPa) (deg) (noofcycle) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)

Softsoil(slurry

consolidated) 49 1.75 0 21

15cycles(EPP=97%

ECP) 1810 1029 817 715 659 603

w/c:Watercontent:Bulkdensityc:Cohesion:FrictionangleG:Shearmodulusofsoilobtainedfordifferentcyclesofloading

Cyclic Simple Shear Test (High strain amplitude test)

Digitally controlled Electro-mechanical actuators are used to apply the stress or strain controlled loading

OutputOutput: : Shear modulus (G), Damping (D)

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Cyclic Simple Shear System

Cyclic Simple Shear Test (High strain amplitude test)

nShearStraisShearStres

DDamping GusShearModul

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Dynamic properties of Dynamic properties of Sand (SW) using Cyclic simple shear

Bender Element Test (Low strain amplitude test)

Bender Elements (made by Piezoelectric material)

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Bender Element Test (Low strain amplitude test)

Thebenderelementsystemiscomprisedofthefollowingcomponents:TwobenderelementsinsertswithadoptedtopcapandpedestalExternalcontrolboxBenderelementwithspecimeninsidethetriaxialcellHighspeedcomputerdata

i iti d t l dacquisitionandcontrolcardWindowsbasedBenderelementsystemcontrolandacquisitionsoftware

Bender Element Test (Low strain amplitude test)

Piezo-ceramic elements distort or bend when subjected to a change in voltage. g

Two Piezoelectric bender elements are placed opposite one another and inserted a small distance into a soil sample. One bender element work as source and other as receiver.

The voltage in one element is varied creating shear waves through the sample, which are received by the opposite element. The input voltage, (created using a function generator) and the received signal are recorded

i l i ill ll i h l i f h h continuously using an oscilloscope, allowing the travel time of the shear waves to be measured from which the dynamic elastic shear modulus (G) can be determined.

Bender elements provide a reliable, cost effective alternative to undertaking locally instrumented stress path triaxial tests and can be readily performed on unconfined samples in the laboratory.

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Bender Element Test (Low strain amplitude test)

TransmissionofSwave

Small-strain modulus (Gmax) of geotechnical fill materials is a key parameter in defining the material response to static loading.

Gmax is also important in small-strain dynamic analyses to predict soil behavior under machine & traffic vibrations.

Bender Element Test: Cross correlation technqiue

Typical Bender Element test results: Input

xyCC

Output Cross-correlated signals

1

Cross-correlation between two signals: The cross-correlation function is a quantitative operation in the time domain to describe the relationship between data measured at a point and data obtained at another observation point. In Mathematical form, the cross correlations between two signals: X(t) and Y(t), can be defined as

1lim ( ) ( )xy TT

CC X t Y t dtT

T is the total time length of the signal and is the time shift between the two signals. The above equation is simply the common area subtended by the signal X, which has been shifted by time and the signal Y. As such, for an impulse wave that has been recorded between two spaced points, will attain a maximum value for the time shift that equals the travel time of an impulse between two points.

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Bender Element Test: Cross correlation technqiue

0.6

0.8

Input signalOut put signal

0.45ms=tcc

-0.4

-0.2

0

0.2

0.4

Am

plitu

de o

f the

sig

nal(m

v)

Out put signal

Clean ganga sand pi' = 500 Kpa

Cross correlation

-0.8

-0.6

0 0.2 0.4 0.6 0.8 1 1.2Time scale(ms)

0.39ms=tm

p p Time period =0.1

B B'

travel time determined by cross-correlation (tcc =0.45) method that fits at best the input and the output signals. The delayed time tm over estimated shear wave velocity

Bender Element Test

es

LVt

G = .VS2t

Lt = * LLo = L - Lt

shear wave velocity is calculated by dividing the corrected length (Le) by the travel time of the wave from the transmitter to the receiver; tTravel length of the wave is considered to be the length of the specimen minus the length of the bender elements (mid-to-mid distance).

o tLe = L0 e

L = total length of the triaxial sand specimen, e = effective height of tip of the transducer, Lo = the length between the tips of the transducers, Le = Effective length of wave propagation with increasing strain rate, and = Axial strain.

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Resonant Column Test (Low strain amplitude test)

The basic principle of the resonant column device is to excite one end of a confined cylindrical soil specimen in a fundamental mode of vibration by means of torsional or longitudinal excitation.

Once the fundamental mode of resonance frequency is established, measurements are made of the resonance frequency and amplitude of vibration from which wave

ti l iti d t i propagation velocities and strain amplitudes are calculated using the theory of elasticity.

The Resonant Column Test provides laboratory values of Shear modulus (G) and Damping ratio (D).

Resonant Column Test (Low strain amplitude test)

With known value of the resonant frequency it is possible to back-calculate possible to back calculate the velocity (vs or vl) of the wave propagation and thereby G or E

After measuring the resonant condition, the drive system is cut of and the specimen is brought to a state of free vibration.

(a) Specimen is excited at the bottom and the response is picked up at the top (velocity or acceleration)(b) Driving force is applied on the top. The response pickup is also placed on the top

Damping is determined by observing the decay pattern

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tiCt e)(

Resonant Column Test:Determination of Shear Modulus of soil (G)

Acc.

ff

Resonant freq. f1+

Sample Geometry+

End restraint+

Wave equation (torsion)

2

1220 2

Ts F

fHvG

Resonant Column Test:Damping properties of soil (D

D = 1/21

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Thank You