Numerical Modeling in Geotechnical Engineering

The most practical advice I can give you in numerical modeling in geotechnical engineering is:” The first step in numerical modeling is to know the answer to the problem”. How? you may think. How can you know the answer to a problem you are yet to solve? well, this is done using a reliable simplified method to solve the problem as the first step. Yes, numerical modeling is a powerful tool and should be integrated more in the design process, but it should be done as a final step of the design process, as a tool for fine-tuning the design, or as a method for comparing design alternatives. Using a simplified model doesn’t necessarily mean not using computers. On the contrary, computers can be used but with simpler 2-12 lines of equations that one can code using excel or an advanced programming language like VB, Python, or MATLAB. commercially available software that implements simplified models can also be used for the task.

While numerical modeling is a very powerful tool in geotechnical modeling, its use via commercial software can become a Blackbox. To avoid this, numerical analysis results should be verified, validated, and peer-reviewed in order for the results to be acceptable. This is important because studies and practice show that when solving the same problem but by different engineers, the results don’t come the same. Schweiger (1998) provided a case where 15 experienced geotechnical engineers were asked to solve a problem of a tie-back supported excavation. The specifications of the model were the same for all the engineers. What was different is that the engineers can choose the constitutive model. Soil material parameters were not given but it was up for the engineers to input. In the experiment, soil parameters can be obtained from literature, available laboratory testing results, or from personal experience. Computational steps and construction stages had to be also simulated in the study and were given to all the engineers. Different computer programs were available for the engineers to select from to solve the problem. The maximum horizontal movement of the top of the wall was calculated between approximately -230 mm to 35 mm. The negative sign means a movement away from the wall to the excavation site. The maximum measured displacement at the top of the wall was approximately -22 mm. only 3 engineers calculated the displacement of the wall between -18 and -32 mm. A closer look at the results shows they are very scattered. The differences in results can be attributed to the different constitutive models selected and the soil material parameters selected. Few engineers used laboratory test data, many used data from the literature for the soil to be modeled and some used their own experience in selecting soil material properties.

Finite element results can also be different even if the same problem analyzed by the same engineer but with different program. Poulos (2017) provided a comparison of calculated wall movements by analyzing a 10 m excavation wall using 3 different programs, PLAXIS, WALLAP and DeepXcav (DeepEx now). Figure 1 shows the displacement calculated by these programs. DeepXcav and WALLAP predicted the wall movement at 52 mm and 49 mm respectively. PLAXIS predicted 77 mm wall movement. These results don't mean that a certain program is better than the other. It merely shows the hidden complexity of numerical modeling.

The variation of predictions is not exclusive to scholarly work. Variation in analysis results can be also be found in documented case studies. I will discuss the Burj Khalifa in Dubai as an example. Settlement design values were calculated using 4 different programs namely PIGLET, REPUTE, VDISP, and ABAQUS (Poulos & Bunce, 2008). It should be noted that results obtained using PIGLET and REPUTE assume a rigid pile cap. Furthermore, independent result verification was carried out using FLAC and another software that interestingly named PIGS. FLAC is based on the finite difference method (numerical method). Modeling in FLAC was done assuming block method in which the piled-raft and soil in between are assumed to act as one unit (a block). Among all the analyses performed, the geotechnical properties of the soil strata were the same. Results of the maximum displacement calculated using the different methods and actual final settlement (Russo et al., 2013) are shown in figure 2.

The measured final settlement of the tower in 2008 was 42 mm at 75% of the load. The design settlement was close to 72 mm which was the same as the result of the independent FLAC analysis.

This case study provides insight into the variability of different analysis results, the importance of validating and verifying numerical model results using different methods and using different software. It also shows the importance of independent results verification. One can imagine the care taken in the laboratory testing, geotechnical parameters assessment, and the modeling process in a project of such scale. Even then, variability in modeling results still persisted. This case study actually shows success in geotechnical design. Had the measured settlement been greater than design values, it would have been disastrous for the project. The case study also shows the variability in numerical modeling results.

Another case that clearly shows the Blackbox effect of numerical software is the Nicoll highway collapsed excavation in Singapore (figure 3). Lives were lost due to the collapsed excavation. The excavation was 33.7 m deep with a width of between 14 and 21 m. the supported excavation soil was marine clay. As Karlsrud & Andresen (2008) described in their paper, the geotechnical engineers used the undrained effective Mohr-Coulomb soil model in PLAXIS. For PLAXIS users, this is known as Undrained A analysis where soil parameters are input in the program in terms of effective stresses but the program checks the failure using undrained strength back-calculated from the input of the effective friction angle and cohesion. The analysis is then performed using total stresses.

Figure 3: Collapsed Nicoll Highway excavation.Source: http://www.chunwo.com/chunwoimages/files/Construction/TECHNICAL%20NOTE%20002%20Lessons%20Learnt%2C%20Collapse%20of%20Nicoll%20Highway.pdf

The undrained shear strength can be calculated from the friction angle and the cohesion as

Typically, this value should be checked against laboratory testing to confirm it. This is because it might be higher than the actual value which was the case in this excavation (Karlsrud & Andresen, 2008). If the engineers understood the short-term and long-term behavior of soil maybe they wouldn’t have made the mistake. In this case, it would have been wiser to perform short-term analysis using the laboratory/field undrained strength as a direct input and then perform long-term stability (drained analysis) using effective strength parameters to assess the long-term factor of safety. Had the engineers looked onto the use of a simple analytical model like the apparent earth pressure maybe they would have avoided this. The apparent earth pressure would require the use of undrained cohesion directly in the design process. Maybe another software should have been used to verify the results. Software that is dedicated to excavation analysis. The scale of the project wasn’t small and more rigorous analysis should have been put into the design process. All the reviewed literature about the subject tells the same thing, a numerical modeling error.

The errors in numerical modeling can be a result of different things: errors in the choice of the material model and/or its input parameters, errors from the coarseness of the mesh, or errors from boundary conditions. With a lack of proper guidance, these parameters are usually chosen based on experience and personal judgment. Trial and error should be applied in the selection of the mesh size and model boundaries, but this can lead to a time-consuming modeling process. One can look in literature for a guide but not every problem is the same in geotechnical engineering despite the similarity in some features (e.g., the same type of foundation but with different soil layers). Some problems cannot be even modeled on personal computers. As an example, if one tries to model 5-story building foundations and considering doing a soil-structure interaction study, the model should be at least 3 times the width/length of the building in all directions with very fine mesh in the area near and below the building. This not to mention that the depth of the model into the ground should be also at least 3 times the width of the building unless bedrock is encountered then the model usually stops there. Considering all the preceded factors, the result is a lot of finite elements even for powerful personal computers and it is also a lot of time to solve the problem at hand. If one uses a very coarse mesh at stress-concentration areas or model boundaries are not far enough, then the model results are simply wrong and unreliable.

In case numerical modeling is a must, a geotechnical consulting office should have a framework to perform such analysis. The framework is simple. Assuming a subsurface exploration program is sufficient for the problem at hand, these steps could be followed: 1) The design should be done with a simple method that is available in the construction codes in one's country. In more complex problems that simplified models cannot be applied to them directly, simplify and analyze with conservatism (e.g., use Newmark charts for irregular foundation shape or assume plane strain for excavation). 2) use a more advanced modeling technique like a beam on elastic springs or stress-path analysis to assess stability and deformation. 3) perform numerical modeling and have more than one engineer work on their own numerical model and then discuss and compare the results.

Numerical modeling is a powerful tool in geotechnical engineering. however, its misuse can lead to unreliable results and disasters in the worst-case scenario. Therefore numerical modeling should be verified, validated, and peer-reviewed in order for the analysis results to be acceptable. Geotechnical engineering literature is full of methods and simple models that can produce reliable results. These methods should be used prior to numerical modeling to provide a clear picture of the problem and the results that should be expected from numerical models.

References:

Karlsrud, K. and Andresen, L. (2008) ‘Design and performance of deep excavations in soft clays’, Proceedings of the 14th European Conference on Soil Mechanics and Geotechnical Engineering,

Poulos, H. G. (2017) Tall building foundation design. CRC Press.

Poulos, H. G. and Bunce, G. (2008) ‘Foundation Design for the Burj Dubai – the World’s Tallest Building’, Proceedings of the 6th International Conference on Case Histories in Geotechnical Engineering, 1(1), pp. 1–16.

Russo, G. et al. (2013) ‘Reassessment of foundation settlements for the Burj Khalifa, Dubai’, Acta Geotechnica, 8(1), pp. 3–15.

Schweiger, H. F. (1998) ‘Results from two Geotechnical Benchmark Problems’, in Proceedings of the 4th European Conference on Numerical Methods in Geotechnical Engineering. Stuttgart, Germany.