tbm dem modeling

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Discrete Element Method to Predict Soft Ground Cutterhead Performance

Glenn MongilloCaterpillar Tunneling Canada Corp., Toronto, ON, Canada

Mustafa Alsaleh

Caterpillar Inc., Mossville, IL, USA

ABSTRACT: Soft ground TBM Cutterhead design has historically been driven by iterative designs based onempirical data, observations over various projects and industry rules of thumb. The ability to analyze the

performance of a cutterhead has been limited to studies conducted in-situ during TBM operations. With theuse of Caterpillar proprietary Discrete Element Method (DEM) software, Rocks3DTD, critical operationalcharacteristics can be analyzed much earlier on, during the design phase, and allow for comparison of suchkey parameters as required torque, advance rate, material flow paths, and effectiveness of loadingmechanisms. Rocks3DTD is a proprietary discrete element code, which allows for time-elapsed particle

interactions with structures, and considers particle size, shape, soil cohesive properties and density. Theresulting data allows for optimization of cutterhead opening ratio, opening geometry, tool positions, andmuck removal from the plenum. This paper will review simulations performed to date and examine howdiscrete element analysis can be applied to cutterhead performance optimization.

INTRODUCTION

Discrete Element Method (DEM), also called a distinct element method, is the family of numericalmethods used to compute the motion of a large number of particles with micro-scale size and above. In recentyears DEM has become more mature and widely accepted as a robust method to treat engineering problemsin granular and discontinuous materials, especially in granular material flows, pharmaceutical applications,rock and powder mechanics. The various branches of the DEM family are the distinct element method

proposed by Cundall in 1971, and the generalized discrete element method proposed by Hocking, Williamsand Mustoe in 1985. The theoretical basis of the method was established by Sir Isaac Newton in 1697.Williams, Hocking, and Mustoe in 1985 showed that DEM could be viewed as a generalized finite element

method. Its application to geomechanics problems is described in the book, Numerical Modeling in Rock Mechanics, by Pande, G., Beer, G. and Williams, J.R..

In geomaterials or rock-mechanics, DEM treats material particles as individual rigid bodies, where theirmotion is governed Newton’s law of motion. A cohesion model is usually introduced into the formulations torepresent the cohesive forces that exist in fine-grained materials and cementation that exists in rocks. In aDEM simulation, the model is initially generated using a certain shape of particles (most commonly used arespherical particles) with a pre-determined particle size distribution. The fact that the actual particles are notspherical in shape made developers consider clusters of spheres to represent the shape irregularities.Moreover, single spherical particles have been also used along with virtual shape representation. Developersusually prefer using spherical particles to reduce the computational cost associated with the contact detection

processes within a DEM model. Once the neighboring search process is done, force calculations will take place followed by an integration stage, which will be employed to compute the incremental change of the particle position and velocity for the next time step calculation. These processes will continue for the entiresimulation period.

Caterpillar Inc. researchers have been developing and using a DEM code for the past fifteen years; thecode is called Rocks3D

TD. It uses a very computationally efficient contact detection algorithm and can deal

with any particle shape specified by the user. The contact frictional and normal forces are computed using thewell-known Hertzian contact model for cohesion-less materials. Additional algorithms are implemented totreat cohesive-like bonds when modeling fine-grained materials and rocks. The cohesion is modeled usingcohesive pillars that bond neighboring particles together; this pillar can be strained until a strain threshold is



reached and then the bond is broken. Recently, Cosserat rotation has been added to the code kinematics alongwith particle shape indices described by Pande, Beer and Willams. This additional degree of freedom enabledthe code to capture more of the micro-structural properties for the material being modeled (angularity, size,sphericity etc.). While Rocks3DTD is used to model particulate force responses and material flows, it is

capable of linking to full machine models using in-house built codes for modeling machine dynamics, tire-ground interaction, machine hydraulics, etc.

Rocks3DTD is also capable of interacting with tracked-type tractors to pass proper forces to the machinethrough the track shoes. The machine tools can be treated as either rigid and/or flexible bodies. The code had

been parallelized to take advantage of mutli-threaded processors. It has been benchmarked against othercommercial codes; to-date, Rocks3DTD usability, simulation speeds and accuracy have been found moreencouraging. As acknowledged by many researchers, it is very challenging to obtain DEM model parametersthat best represent real materials, especially when dealing with fine-grained materials. Rocks3DTD developershave been successful in defining an engineered procedure to map these micro quantities to some material

physical and macro quantities. Both small scale laboratory testing and full machine testing are being utilizedto develop micro-macro parameter mapping functions. The particle size for instance, a very important DEM

parameter, must be chosen carefully. Choosing the particle size for a given model will always have a greatdeal of trade-off between simulation accuracy and computational cost. Special attention had been given tothis matter; the particle size distribution is established for a given model in a way to ensure highest simulation

accuracy at the lowest computational cost. This way, the model parameters (micro-mechanical propertiessuch as friction, stiffness, etc.) can be linked to macro properties to achieve better physical representation.

Rocks3DTD can predict the dynamic forces and flows of different discrete systems geometries underdynamic loading. As mentioned earlier, the contact parameters are micromechanical parameters that are verydifficult to physically measure, and very challenging to evaluate due to the fact that it is almost impossible torepresent the actual shape and size of real materials. A real material is very complex to mimic in terms ofshape, size, and size distributions.

DESIGN VARIABLES WHICH INFLUENCE SOFT GROUND CUTTERHEAD PERFORMANCE

The design of soft ground TBM cutterheads typically includes the control of several parameters thatdrive the overall look and performance of a TBM cutterhead. Over the years, these structures have seen agreat deal of evolution in the attempt to improve overall TBM performance.

The intention of using DEM software was to develop a tool to analyze the effects of changes to some orall of the major parameters which are known to affect TBM cutterhead performance. By isolating specific

parameters (such as percentage opening or face opening geometry) and keeping other parameters constant(such as tool position, and rpm) we can determine which factors may have the most significant impact or ifindeed there is an impact.

Cutterhead percentage openingWithin the Earth Pressure Balance TBM industry, a cutterhead face opening of 30% has been the typical

standard requirement for many project specifications. The value of 30% has been based primarily on baseempirical performance data and experience. This parameter is comparable to the flow coefficient of a fluidthrough a restriction, however the complex interactions within the soil itself and between the soil andcutterhead make this assumption an over simplification. While care must be taken to ensure that sufficientmaterial can enter the cutterhead chamber at a fast enough rate to meet the TBM designed advance rate, toogreat of a percentage opening can be detrimental as well.

In some soil types such as clay, larger openings can in fact lead to clogging and increase the requirement

for torque and yield less efficient muck flow into the chamber. In flowing silts it has also been observed thata reduction of cutterhead percentage opening has allowed for greater TBM thrust offsets while controllingTBM advance rate, with an observed improvement in TBM steerability in difficult silt ground conditions.This is especially important when the primary steering method is based on the creation of a net resultantmoment with the TBM propulsion system. Generally in soft ground and EPM projects a suitable cutterheadstructure is still required to provide adequate face support, which will limit the maximum allowable

percentage face opening.



Opening distribution with respect to radius from the center

Perhaps more important than the total percentage opening of the cutterhead face, is the distribution ofthe openings. Well distributed openings on the cutterhead face can make a considerable difference in muckloading. Openings positioned where greater volume of excavated material is expected can support greater

TBM advance rates, less muck clogging and more consistent loading of cutting tools. Openings at the centerof the cutterhead are important where low material velocities exist and less mixing occurs. These points tendto support triangular opening as a better choice to promote a more balanced opening ratio with respect to theradius on the face. However, in certain bolder conditions the opening shape may allow for more irregularshaped boulders to enter the chamber and ultimately slow TBM operations. In such cases rectangularopenings provide better protection from this occurring and additional rectangular openings may be used toincrease the total percentage opening.

Spacing, quantity and position of tools

Each soft ground tool represents a source of drag, whether performing a cutting action or simply beingengaged with the ground during cutterhead rotation. The combination of all the drag forces during cutterheadrotation results in the required operational torque of the cutterhead. Too few cutting tools can result in morerevolutions required to excavate sufficient material for the TBM to advance. Too many cutting tools canincrease the required cutterhead torque by increasing the overall drag and promoting blockages of material

that do not enter the chamber. Optimizing the quantity of soft ground cutting tools is a key factor to achievingthe required TBM advance rates and keeping the required cutterhead torque to an achievable level.

An equally important parameter is the spacing of tools on the cutterhead face. Typical four spokecutterhead designs within the 4m to 6m range allow for staggered tool spacing on each spoke wheresuccessive tools along the increasing cutting radii are positioned on alternating spokes. This allows for astaggered cutting action and space for material to follow between tools on the same spoke. If the spacing

between successive tools on the same spoke does not permit the flow of excavated material between them,material may build up and eventually render the tools ineffective on subsequent revolutions of the cutterhead,creating more drag, and thus increasing cutterhead torque required and reducing efficiency.

In some cases, specific tool locations on the outer rim or gauge area of the cutterhead may includeadditional cutting tools on the same path. This generally is expected to reduce the wear on any one cuttingtool by allowing the cutting action to be shared equally by all the tools on the same path. Excessive tools onthe gauge area can lead to a significant increase in required cutterhead torque since drag forces at the furthestradius from the center have a greater effect due to the larger moment arm. As well this increase in tools maylead to material blockages and inefficient loading of material into the chamber. This would also have acontributing factor in the overall performance of the cutterhead.

Obstructions to flow of material into and within the chamber

Scraper collecting tools are designed to gather excavated material from the tunnel face and direct it intothe cutterhead chamber. This action is every bit as important as the cutting action itself. A TBM’s

performance would be short lived if the material from the tunnel face was broken off but not collected andtransported away to allow for continuous cutting action. The scraper tools are critical to this action. Theymust be positioned such that once the material is cut by the cutting tools the scraper tools must direct thematerial into an adjacent opening. Cutting tools positioned too far from scraper collection tools may result inexcessive travel time for muck, the muck adhering to the cutterhead face, reconsolidation with the tunnelface, or regrinding or muck resulting in excessive wear of the structure.

In some cases grizzly bars or opening restrictions are used in soft ground cutterhead designs to limit the

size and/or shape of material entering the chamber. This can be especially useful in geology containing boulders. Boulders pose a danger of damage to the cutterhead chamber, and blockage of screw conveyoraugers in Earth Pressure Balance TBMs. While beneficial in certain geologies, they may actually hindermaterial ingress into the chamber in other geologies. Where clays and cohesive soil conditions exists it isoften recommended to remove such opening restrictions. Where geological conditions are varying andunpredictable, this may not always be possible, and therefore could lead to unexpected performance of thecutterhead when such changing geology is encountered.



SUMMARY OF SIMULATIONS PERFORMED

Methodology

For the purposes of this study, it was decided to use two past cutterhead design types of a common size

and vary only the shape of the opening (and consequently the overall percentage opening). (see Figure 1)This was done to limit the number of variable that would affect the results of the simulation. By applying aconstant cutterhead rotational speed and axial thrust to both models onto the same discrete particle pile, theresulting outputs, torque and advance rate, would then be directly compared as to the effectiveness of onecutterhead design over the other. Certain conditions needed to be defined to provide a realistic simulation andmuch of the initial work was focused on determining the properties of the discrete element pile as far asdensity, particle size, particle quantity and cohesion.

Figure 1. Cutterhead models used for simulation

Study #1 - Initial FeasibilityA first pass feasibility simulation was performed with the lowest level of complexity to allow for

efficient computational time while still demonstrating the capabilities of the code for this TBM cutterheadapplication. (see Figure 2) Spherical elements with a common size of 150 mm in diameter were chosen, whileTBM input parameters were selected to ensure some visual element motion was noticeable and the TBMmodel was moved as expected. The results of this simulation were by no means realistic as far as normalTBM operations are concerned, but they do indicate that the dynamic motion of the elements and theinteraction with the rotating cutterhead structure can be further refined to better simulate actual TBMconditions. This simulation was useful in debugging the initial TBM model and particle parameters.

One key observation is that the control of the element size is important in this application. Elementsshould be comparable to the average size of the cutterhead tools performing the cutting action. In this case,

static ripper tools have been used with a typical cross section of 75mm x 150mm. Using elements larger thanthe minimum size of the cutting tools presents a concern with the scale of interactions between the elementsand the structure. This may affect the applied force on cutting tools, the observed material flow paths and theoverall TBM performance expected from the simulation. For subsequent simulations it was determined thatelement size should be set less than 75mm in diameter.

4.2 m [167”] Dia. – 30% Opening

“No Door” Design

4.2 [167”] Dia. – 26.5% Opening

“With Door” Design



Figure 2. Initial DEM Simulation with simplified TBM model

Study #2 - Particle and Cohesion RefinementThe second simulation focused on providing a more realistic representation of the TBM cutterhead

application with an analysis of critical performance measures of required torque and advance rate. Tofacilitate a comparison between the two cutterhead designs, constant values for cutterhead rotational speedand applied thrust were used. As well, in an effort to validate the soil pile, varying degrees of particlecohesion were used to account for high and low soil stiffness. The particle size was set to 70 mm within a pile

consisting of 400,000 particles. (see Figure 3)

The simulations performed as part of this second study were as follows:

1. High stiffness pile & 30% opening “No Door” cutterhead2. High stiffness pile & 26.5% opening “With Door” cutterhead3. Low stiffness pile & 30% opening “No Door” cutterhead4. Low stiffness pile & 26.5% opening “With Door” cutterhead

The resulting animations provided a more realistic representation of soil loading into the chambercompared to the initial feasibility study. The reduced element size allowed for particles to collect and travelwith the rotation of the cutterhead, similar to real world conditions.

Some validation of the soil pile was possible with the results of the simulation. The output dataconfirmed that with higher soil stiffness (i.e., greater element cohesion) the required torque to rotate the

cutterhead was greater and the resulting TBM advance rate was lower. This is consistent with operationalexpectations of TBMs. Between the two soil stiffness models an average of 16% to 20% greater torque wasrequired for the respective cutterhead design. (see Figure 4)

Additionally, there was a demonstrated difference in the required torque between the two cutterheaddesigns used when the soil stiffness remained constant. The 30% opening “No Door” cutterhead designrequired on average 7% to 11% more torque within either stiffness of soil compared to the 26.5% opening“With Door” cutterhead design. This correlated well with the increase in payload or excavated material



within the same timeframe. The larger percentage opening design excavated more material, had a greateradvance rate, and hence required more torque.

Figure 3. Refined DEM simulation with 70mm particle size

500

750

1000

1250

1500

1750

2000

0 5 10 15 20 25 30

Time (s)

T o r q u e ( T - m )

Avg. Torque - No Door Model

(High Stiffness)

Avg. Torque - With Door Model

(High Stiffness)

Avg. Torque - No Door

Model

Avg. Torque - With Door Model

(Low Stiffness)

Figure 4. Study #2 torque comparison of both cutterhead models with high and low particle stiffness



The comparison of the output values was done at the steady state once the initial peak torque wasovercome. In this case all simulations during this phase of the study reached a steady state close to the 10second point of the 30 second simulation. The peak torque observed would be analogous to real world inertialeffects and the initial penetration of the cutterhead into the soil face.

However, the absolute values of the output torque and TBM advance rate were well beyond real worldexpectations for this size of TBM studied. Simulated required torque values were on average 10X greaterthan typically expected. Similarly, the TBM advance rates were on average 8X to 10X greater than expected.With respect to torque it was clear that with a decrease in particle cohesion a decreased amount of torque wascalculated. Therefore, to bring subsequent simulations closer to reality a significant reduction in elementcohesion was required. This, however, did not address the concern of the TBM advance rate, where it wasobserved to increase with decreasing particle cohesion. Both of these TBM performance parameters wouldseem to be at odds in this simulation when compared to real world applications. In typical soft ground TBMapplications it is reasonable to expect that with a decrease in soil stiffness there would exist less resistance tothe cutterhead motion in both rotational and axial velocity and as such would require less cutterhead torqueand the resulting TBM advance rate would be greater. In this particular simulation the TBM advance rate isalready far too high. This indicates that expected torque values may be achieved with a reduction in particlecohesion, but an additional modification must be made to correct the already high advance rate. Someimprovement in advance rate may be possible even with a reduction in overall particle cohesion by the

control of some or all of the parameters which govern the Rocks3D cohesion model. Since particle cohesionis controlled via cohesion pillars that bond elements, variations of the pillar’s modulus of elasticity, strainlimit, damage threshold, or pillar size may help to improve the high observed cutter torque and TBM advancerate. This alone may not be enough to reduce the advance rate and further improvement to the TBM modelmay be required.

Study #3 – Cohesion Refinement and Comparison to Actual DataThe third study was focused on refining the element properties to better simulate expected soil

conditions similar to a silty clayey fine grain material. This was required to achieve a more realistic value forTBM cutterhead torque and hopefully TBM advance rate, thus validating the element pile and determining agood set of parameters to simulate a typical soil pile for a TBM application.

The DEM cohesion model has five parameters that control the mechanical properties of the cohesive pillar between particles to represent either a fine grained cohesive material or a rock mass. These parameterswere refined in the final simulation to better represent a cohesive material, such as silty clay. The two main

parameters refined in this simulation were the cohesion pillar modulus of elasticity and the cohesion pillardamage parameter. These basically allow for a reduction in the cohesive pillar strength to decrease therequired cutterhead torque and an increase in the particle to particle stiffness to try to reduce the TBMadvance rate.

The adjustments made to the particle cohesion did allow for the overall cutterhead torque to be reducedto reasonable values within the range of expectations in both the No Door and With Door models. (seeFigure 5) There was however an increase in the TBM advance rate with the lower values of particle cohesion.(See table 1) This would suggest that the soil parameters may be closer to actual conditions for thisapplication, but other TBM based conditions exist that would otherwise lower the overall advance rate, whichare not included in any of the simulations to date. These external factors may include; external friction

between the TBM structure and the soil, pressure at the TBM face in the case of Earth Pressure BalanceTBMs, interactions of soil in the cutterhead chamber, and controlled extraction of material from thecutterhead chamber. With the current simplified TBM model these secondary factors are not possible toanalysis; nonetheless the particle cohesion parameters determined thus far have produced torque values of amore realistic nature, which may allow for further comparison of the two different cutterhead designs.

This final simulation still suggested that the No Door model required more torque compared to the WithDoor model. The resultant torque curve over time did, however, differ compared to the second study

performed. There was a general increase in torque over the simulation time with both design modelscompared to the previous results where the torque values leveled off towards the end of the simulation. Alogarithmic trend line was fitted to both torque curves for comparison. At the end of the simulation the No



Door model still displayed approximately a 6.5% higher torque value. This is still comparable to the resultsof study #2.

Table 1. Advance rate summary

Avg. Advance Rate

(mm/min)

26.5% With Door - Higher Stiffness 7951

26.5% With Door - Lower Stiffness 12791

26.5% With Door - Study #3 1972 2

30% No Door - Higher Stiffness 9991

30% No Door - Lower Stiffness 15241

30% No Door - Study #3 2133 2

1. Avg. Advance Rate taken in Study #2 between 10s and 30s.

2. Avg. Advance Rate taken in Study #3 between 5s and 50s.

100

125

150

175

200

225

250

275

300

0 5 10 15 20 25 30 35 40 45 50

Time (s)

T o r q u e ( T - m )

No Door Model Torque

(Operational Trendline)

Historical Calculated Torque Range

= (1.5 to 2.5)*Diameter 3̂

With Door Model Torque

(Operational Trendline)

Figure 5. Study #3 torque comparison of both cutterhead models with lower particle stiffness

The increasing torque over time suggested that the mass of particle accumulation in the chamber wasmore significant in this simulation compared to the previous. Study #2 used much greater particle cohesion



pillar strength and as such the cutting action was the predominant source of the required torque to keep thecutterhead rotating. However in study #3 the particle cohesion was decreased to bring the simulated torquecloser to a value that would typically be observed in actual TBM operation. As such the cutting action

between the cutterhead and the particle pile was less significant, where as the accumulation of particles in the

chamber accounted for a steady increase in the required torque. This value would typically level off overtime, once the chamber was full of excavated material.

CONCLUSIONS

In all the simulations performed to date the No Door model with 30% percentage opening requiredgreater torque, had a higher advance rate and subsequently allowed for greater flow of material into thecutterhead chamber when compared to the With Door model having only 26.5% percentage opening. Thiswould suggest that the DEM software did demonstrate that the parameter of cutterhead percentage opening isin fact critical to the performance of soft ground TBM cutterheads. Furthermore, if the true benefit of greaterTBM advance rates is to be realized, the higher percentage opening parameter is not without its compromisewith the requirement for greater torque.

In addition, the DEM software did allow for some validation of the soil pile by refinement of the particle

cohesion parameters to better predict the required torque of a soft ground cutterhead. It was observed thatgreater particle cohesion required greater torque, which is consistent with TBM operational conditions andexpectations. This suggests that with an accurate representation of given geological conditions for a tunnel

project, the DEM software would be able to predict the required cutterhead torque with a good degree ofaccuracy.

Finally, to better predict other TBM operational conditions such as advance rate, more refinement of themodel is required; along with the addition of external factors that were not considered in the studies

performed. These may include:• A more detailed TBM model with sealed cutterhead chamber• A controlled method to extract muck from the chamber, such as a screw conveyor• Addition of frictional forces between the TBM and surrounding geology

• Face pressure to simulate Earth Pressure Balance conditions• An upper threshold limit on advance rate based on physical TBM specifications

It is the authors’ contention, given the studies performed thus far, that the Discrete Element Method is aviable tool to predict the performance of soft ground TBM cutterheads and that with on-going improvements better simulations will advance the predictive nature of DEM to handle tunnel boring operations in the virtualworld.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Ben Conners and Paul Yassa of Caterpillar Inc. for theirassistance in the preparation of 3D models and the collection of past operational TBM data.

REFERENCES

Cundall, P.A. 1971. A computer model for simulating progressive large scale movements in blocky rock systems.Proc. Symp. Int. Soc. Rock Mech.,Nancy, pap. II-8.

Williams, J.R., Hocking, G., and Mustoe, G.G.W. 1985. The Theoretical Basis of the Discrete Element Method . NUMETA 1985, Numerical Methods of Engineering, Theory and Applications, A.A. Balkema, Rotterdam,January 1985

Williams, J.R., Hocking G., et al. 1985. The Theoretical Basis of the Discrete Element Method . NUMETA '85Conference, Swansea



Pande, G., Beer, G. and Williams, J.R. 1990. Numerical Methods in Rock Mechanics, John Wiley and Sons,Chichester, England.

SELECTED ADDITIONAL READINGS

Burger, W., 2007. Design Principles for Soft Ground Cutterheads. In Rapid Excavation and TunnelingConference Proceedings, Littleton CO.:SME

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