Rev. 1 – as of October 16, 2015
Guide to numerical modeling in geomechanics  PDF Download
The present document is a quick guide to numerical modeling in geomechanics. It addresses some major issues about the general numerical approach, the choice of material constitutive model and different modeling steps. It is clear that the information given here provides only a general guideline which should be further adjusted for each specific problem.
Modeling of geoengineering problems often involves complex issues related to several geomechanical variables and the corresponding coupling effects. Compared to many engineering material, geomaterials exhibit a highly nonlinear behavior. Often, there is no straightforward closed form analytical solution for such problems.
Furthermore, in many cases, the analyses of geoengineering problems have to be done with little or no information about the insitu geotechnical condition. This is often the case for tunneling or excavation projects where the design has to be verified or completed using the information from the encountered geotechnical condition. It is therefore important to have numerical modeling as a fast, reliable and powerful tool for a systematic analyses and design of the problem.
In general, numerical modeling in geomechanics MAY have the following main benefits:
The above mentioned features, among others, could in general result in cost reduction and optimization in geoengineering problems.
On the other hand, however, blind using of numerical modeling could have catastrophic consequences. When running a code, it is always tempting to play with the parameters and get nice contour map results; but – Garbage in, Garbage out. Computers will unquestioningly process unintended wrong data and produce undesired wrong output. Here comes the important role of engineering judgment. Indeed, the engineering judgment should run through the whole process including data preparation, modeling procedure, and verification of results. It is therefore important to keep in mind that numerical modeling in geomechanics is more an Engineering Task rather than a Computer Operating Task.
In order to set up the model, three fundamental components should be defined by answering to the following 3W questions:
Any geoengineering problem can be converted into an initialboundary problem for numerical modeling. This can start by answering “what do we know” in the project and drawing a global picture of the problem. Example for few engineering application are given in Table 1.
Table 1 . Examples of Initial boundary value problems in geomechanics
No.  Application 
Project concept: 
Modeling concept: 
1 
Static analysis of double arch concrete dam 


2 
Dynamic analysis of fissured gravity concrete dam 


3 
Dynamic analysis of earth dam 


4 
Deep cylindrical shaft excavation 


5 
Large underground cavern excavation 


In general, initialboundary value problems (IBVproblems) in geomechanics could be divided into two main groups: uncoupled and coupled problems.
Uncoupled problems involve only one primary variable:
Coupled problems involve more than two variables and their coupling effects:
The answer to the question “What are we looking for?” helps in defining the required type of analysis. Table 2 gives some examples.
Table 2 . Examples of analysis type in geomechanics
No.  Application 
Project concept: 
Modeling concept: 
1 
Static analysis of double arch concrete dam 


2 
Dynamic analysis of fissured gravity concrete dam 


3 
Dynamic analysis of earth dam 


4 
Deep cylindrical shaft excavation 


5 
Large underground cavern excavation 


An appropriate choice of the mechanical constitutive model for soils is the key issue for successful engineering modeling of geomechanical problems. In general, geomaterials exhibit nonlinear behavior in a wide range of stress; thus, a realistic prediction/simulation of their behavior can be achieved by using constitutive models capable of addressing such nonlinearity. However, the choice of constitutive model depends also on the specific application and requirements of the problem. Table 3 gives a general guideline for the choice of constitutive model.
Table 3 . Constitutive models for geomechanics
Level of complexity  Model 
Examples 
General application 
Basic 
Linear elastic 


Standard 
Elastic perfectly plastic 


Advanced 
Hardenning elastoplastic 


Complex 
Combination with other geomechanical factors: time, saturation, soil structure 


In general, the answer to the question “What are the involved materials?” helps in defining the type of constitutive model. Some examples for the previously mentioned engineering applications are given in Table 4.
Table 4 . Examples of constitutive models used in geomechanics
No. 
Application 
Project concept: 
Modeling concept: 
1 
Static analysis of double arch concrete dam 


2 
Dynamic analysis of fissured gravity concrete dam 


3 
Dynamic analysis of earth dam 


4 
Deep cylindrical shaft excavation 


5 
Large underground cavern excavation 


Once the general approach defined, an appropriate numerical method should be selected for the modeling. Numerical methods can be in general divided into two main groups:
The detailed description of these methods is beyond the scopes of the present document and can be found in the literature (also for few other methods not mentioned above). All the methods provide a rigorous solution by reaching equilibrium (within the defined tolerance); the difference lies only in the numerical method and algorithm employed to reach the equilibrium. Therefore, apart from some numerical preferences, the main choice is between continuum and discontinuum approach. Some general guidelines are given in Table 5.
Table 5 . Choice of continuum versus discontinuum approach in geomechanics
Primary material / behavior  Numerical method 
Example application 

Soil 
Continuum approach 
Soil slope stability, excavation, earthdam 

Rock 
Homogenous Rock mass behavior 
Continuum approach 
Dam foundation, overall displacement of underground caverns 
Jointed rock behavior dominated by discontinuities 
Discontinuum approach 
Jointed rock slope stability, tunneling in fractured rock 
When dealing with numerical modeling, a significant time is usually spent on data preparation and postprocessing. Therefore, apart from their technical capabilities, the numerical codes with more userfriendly pre and postprocessing interfaces are better accepted by the geotechnical engineers.
Among others, some of the most commonly commercial numerical codes can be listed (but not limited) as in Table 6. The choice of the numerical codes, more than anything else, depends on the following issues:
Table 6 . Some of numerical codes used in geomechanics
Approach  Code 
Method 
Developer 
Continuum 
Plaxis 2D, 3D 
FEM 
Plaxis BV 
FEM 
RockScience 

FEM 
TNO DIANA BV 

EXAMINE 
FEM 
RockScience 

FEM 
Zace Ltd 

FLAC, FLAC 3D 
FDM 
Itasca cg 

ABAQUS 
FEM 
Hibbit, Karlson & Sorensen, Inc 

Discontinuum 
EDEM 
DEM 
DEM Solutions 
DEM 
Itasca cg 

DEM 
Itasca cg 
The procedure and numerical modeling in geomechanics, regardless of method and code, can be simplified in 8 steps as follows
At the onset, the engineer should define the main problem and objectives based on the defined general approach. At this step, it should be decided if the modeling is used to predict or reproduce the soil/rock behavior. In many Often, the results are to be compared with monitoring data and the main objective would be to reproduce and understand the behavior and mechanism of movements rather than its prediction.
Once the objective defined, an overall engineering sketch of the problem should be prepared. At this stage, decision should be made about the level of details which are to be included in the model. The critical assumptions and simplifications should be all addressed in this engineering sketch.
The first models are to be prepared without the details and based on an idealized form of the engineering sketch. The numerical performance and results are to be verified. This can be done, for instance, by comparing the model results at given condition/points for which the analytical close form solution can be obtained (e.g. effective stress at the lower limit, pore pressure at the different seepage directions).
Once the simple model is verified, the model should be enhanced by assigning the appropriate constitutive model and material parameters. Some hardening elastoplastic models need to be applied and verified at different steps to ensure a good numerical performance and predictions.
The last step before running the final model is to add the necessary details and finetuning the model. Some required geometrical details, final material properties, length of structural elements and etc are to be adjusted at this step.
The final model is to run and its numerical performance is to be verified by checking different numerical aspects of the model. A good numerical performance is satisfied if a solution to equilibrium is achieved in a stable condition with reasonable numerical parameters (tolerance, stepping, time increments, etc.). If needed different numerical algorithms can be tested to ensure about the stability of the results within acceptable tolerance.
Once the performance of the model verified, the results can be taken for further analysis and problem solving. Based on the general approach and objectives previously defined, the results of main interest can be extracted in the postprocessor (or from the log files) and presented for interpretation.
The final step in modeling is interpretation of the results in combination with engineering judgment. The issue of primary importance should be identified and sought in the results. The general trend of the results should be always compared with knowledgebased engineering expectation. If anomalies observed, the engineer should find out the numerical or physical reason behind it. If necessary, some or all of the abovementioned steps should be then repeated to achieve enhanced model with realistic results.
The present document provides a general quick guide to numerical modeling in geomechanics regardless of the method and approach. Of course, it needs to be adjusted and further developed for each case according to specific needs of the corresponding geoengineering problems. The above presented information can be summarized in the flowchart of Figure 1.
Figure 1 . Recommended general procedure for numerical modeling in geomechanics