Numerical Modeling & Analysis

numericalNumerical modeling has been driven by a perceived need in recent times. It has led to large, clumsy and complex numerical models. This is not always because numerical modeling is an integral part of the design process, but sometimes because it is considered irresponsible to not bolster a design with plots of stress and displacement contours. Advanced numerical modeling is not a subject that lends itself to a research proposal, higher degree or paper publication. Properly performed numerical modeling will lead engineers to think about why they are building it – why build one model rather than another – and how the design can be improved and performed effectively.

TerraDol provides high end numerical modeling and analysis in Geotechnical and Tunneling field, specialized in Finite Element Analysis (FEM), Finite Difference Analysis (FDM), Discrete Element Analysis (DEM) and advanced Hydrocodes and Computational Fluid Dynamics (CFD).


  • Rock Support Design / Rock Wedge Analysis
  • Tunnel Stability Analysis
  • Tunneling Induced Settlement Analysis
  • Geological Frame Model
  • Groundwater Flow Model and Seepage Analysis
  • Fate & Transport Modeling
  • Coupled Hydromechanical Analysis
  • Blast Analysis
  • Progressive Collapse Analysis
  • Seismic Analysis
  • Tunnel Ventilation & Evacuation Analysis

Continuum AnalysisNume_3

FEM, FDM and BEM are continuum analysis methods, where the domain is assumed to be a homogeneous media. These methods are used extensively for analysis of underground structure’s stability problems. To account for the presence of discontinuities in a rock mass, mechanical and hydraulic properties of rock mass are reduced from those measured from intact samples. TerraDol utilizes FLAC, PHASES, PLAXIS, MIDAS GTS, SEEP/W, and MODFLOW for the continuum analysis.

Discrete Element AnalysisNume_4

If the domain contains predominant weak planes and are continuous and oriented unfavorably to the underground structures, then a discrete element method (DEM) should be considered to understand behavior and stability of surrounding rock mass.

DEM permits a large deformation and finite strain analysis of an ensemble of deformable (or rigid) body (intact rock block), which interact through deformable, frictional contacts (rock joints). In hydraulic analysis, the DEM permits flow-networking analysis, which is suitable in ground water flow in jointed rock mass.

Coupled Hydromechanical Analysis

The coupled hydromechanical analysis is another powerful strength of DEM analysis because a flow in jointed rock mass is closely related with applied loading.  This type of analysis requires details of joint flow, aperture and disclosure relationships and is suitable only if dominating weak planes are well identified with their properly quantified properties. UDEC, 3DEC and HYDROBLOCKS are the most predominant programs.

3D Interactive Nonlinear Dynamic Analysis


3D interactive nonlinear dynamic analysis is considered for dynamic and thermal analysis including structural
response under extreme loadings such as earthquake, fire and explosion. TerraDol utilizes a Hydrocode analysis
to simulate nonlinear dynamics, large strains and deformations, fluid-structure interactions, explosions, shock and
blast waves,impact and penetration, and contact problems. Hydrocode is a finite difference, finite volume and
finite element-based program. 

Euler-Lagrange Coupling


Proper assessment of nonlinear dynamic analysis requires sophisticated analytical simulations taking into account the peak pressure as well as the impulse associated with the shock front, which are extremely high and amplified by the confining tunnel structures. The dynamic loading process and interaction can be properly modeled by Euler-Lagrange coupling. The coupling is a very powerful feature for modeling fluid-structure and gas-structure interaction problems. This type of analysis requires a fully integrated program specifically designed for nonlinear dynamics problems.

Numerical Modeling Softwares

There are a number of commercial computer programs available in the market. The problem is in knowing how to use these programs effectively and in having an understanding of their strengths and weaknesses. All the programs require the user to have a sound understanding of the underlying numerical models and constitutive laws. The user interface is improving with the most recent Windows programs, although the learning curve for all the programs should not be underestimated. The numerical modeling programs currently used in TerraDol are briefly summarized below.

Numerical modeling programs used in TerraDol (Click here for more information)