Geomechanics and Geotechnics


The in-house developed lattice code is implemented in various Multiphysics problems, such as the simulation of the coupled thermo-hydro-mechanical processes in geomaterials, the evaluation of materials effective THM properties during the frack initiation and propagation and stress redistribution and concentration on crack tips. The developed THM lattice model can be divided into three main categorizes: 1) The mechanical model, 2) Thermo-mechanical model, and 3) Hydro-mechanical model

The Mechanical Model

The mechanical model investigated the fracking initiation and propagation in the domain. The fracking in a discretized domain using the Voronoi tessellation and Delaunay triangulation techniques is carried out with removing the elements exciding the pre-defined stress threshold.


The fracking path (red) in fracture toughness test

The Thermo-Mechanical Model

The thermo-mechanical model is based on the weak coupling scheme between the mechanical and thermal models. The thermal model is based on the heat transfer through the lattice elements, where the axial forces in the elements increase or decrease the contact quality. The fracking process as well decreases the particle to particles thermal conductivity. The thermal strains are then calculated based on the linear thermal expansion coefficient and are transferred into the mechanical model.

LEM_Heat_1   LEM_Heat_2

The thermal flow in a thin cylindrical rock sample

The Hydro-Mechanical Model

The hydro model is developed and implemented into the lattice model, where the flow network is added as a dual lattice network. The defined conduct elements transfer the flow between the conduct nodes. The mass conservation law is used to determine the in- and outflow masses, which leads to the development of the pore pressures in defined cavities. The hydraulic fracking based on the transferring the hydraulic pressures into the mechanical model is simulated. The change of the hydraulic conductivities as well as the closure or opening of the crack paths is measured.

LEM_Flow_1       LEM_Flow_2

The fluid flow and pore saturation as well as the fracking path shown in red


  • Rizvi, Z.H., Khan, M.A., Wuttke, F., Ahmad, J. (2019), "Effective Physical Parameter Evaluation of Shallow Crustal Rocks by Lattice Element Method" , Materials Today: Proceedings 18(1) 132-142. Sciencedirect
  • Khan, M.A., Irfan, S., Rizvi, Z.H., Ahmad, J. (2019) "A numerical study on the validation of thermal formulations towards the behaviour of RC beams", Materials Today: Proceedings 17(1) 227-234. Sciencedirect
  • Shrestha, D., Rizvi, Z.H., Wuttke, F., (2019), "Effective thermal conductivity of unsaturated granular geocomposite using Lattice Element Method" , Heat and Mass Transfer 55:6 1671–1683.Springer
  • Rizvi, Z. H., Nikolic, M., Wuttke, F.,(2019) "Lattice element method for simulations of failure in bio-cemented sands", Granular Matter 21:18.  Springer
  • Rizvi, Z.H., Shrestha, D.,  Sattari, A.S., Wuttke, F., (2018), "Numerical modelling of effective thermal conductivity for modified geomaterial using Lattice Element Method", Heat and Mass Transfer   54:2 483-499.  Springer
  • Sattari, A.S., Rizvi, Z.H., Motra, H.B., Wuttke, F., (2017). Meso-scale modeling of heat transport in a heterogeneous cemented geomaterial by lattice element method. Granular Matter. 19:66.  Springer