The group conducts research in the field of computational geomechanics using a variety of methods such as the finite element method (FEM), the lattice element method (LEM), or the material point method (MPM) with applications to landslides and slope failures, tunneling and soil-pipeline interactions and deep borehole drilling.

#### Energy Geotechnics

Methane hydrate and geothermal are clean unconventional energy resources, which will replace traditional fossil fuel like coal, natural gas, and oil.

Methane hydrate is an ice that contains methane gas inside, and it is found in offshore soil where one could also find conventional oil and gas. If methane gas can be released from the ice without disturbing the surrounding soil, it could be produced as natural gas and used as an energy resource. Methane hydrate is often found in nations with poor energy resources such as Japan, and thus the development of methane hydrate could help such nations to be more energy-independent. The main objectives of this project are (1) to reveal the mechanism of sand production, (2) to estimate the long-term methane gas production potential and geomechanical behaviors of methane hydrate reservoirs, and (3) to investigate the wellbore integrity during methane gas production. Commercial finite element software such as ABAQUS and COMSOL are employed to conduct the numerical simulation. Laboratory experiment utilizing a high-pressure soil chamber is also carried out to look into the sand production phenomena. This project is funded by Japan Oil, Gas, and Metals National Corporation (JOGMEC).

Geothermal energy is generated and stored in the earth, which requires an understanding of deep underground. The motivation for geothermal energy research is to advance understanding of the impacts of the urban underground on a subsurface temperature increase at the city-scale. This research is driven by the recently emerging data on the impacts of underground basements and tunnels on subsurface temperature. The data indicate that the magnitude of anthropogenic heat fluxes into urban groundwater is increasing and its quality and natural flow are changing. In tunnels and stations, the thermal discomfort due to the temperature rise also highlights the lack of reliable ground temperature data for efficient underground development, including the design of efficient ventilation systems. The ambition of this project is to develop a framework for predicting temperature and groundwater maps at high resolutions in the presence of underground heat sources and sinks. This can be achieved via a combination of numerical modeling, continuous temperature and groundwater monitoring, and statistical analysis.

#### Material Point Method

Material Point Method (MPM) is a particle-based method that represents the material as a collection of material points, and their deformations are determined by Newton’s laws of motion. The MPM is a hybrid Eulerian-Lagrangian approach, which uses moving material points and computational nodes on a background mesh. This approach is very effective particularly in the context of large deformations.

Illustration of the MPM algorithm: (1) a representation of material points overlaid on a computational grid. Arrows represent material point state vectors (mass, volume, velocity, etc.) being projected to the nodes of the computational mesh; (2) the equations of motion are solved on the nodes, resulting in updated nodal kinematics; (3) the updated nodal kinematics is interpolated back to the material points; (4) the state of the material points is updated, and the computational mesh is reset

The CB-Geo MPM code uses a dynamic explicit MPM formulation to solve large-scale problems in continuum mechanics. We focus on developing our in-house MPM code to simulate numerous large deformation problems in geomechanics, including landslides, deep excavation, and dam erosion. These simulations are aimed to provide better insights into soil failure behavior and adjacent structures.

Three simulations are shown below to demonstrate the capabilities of MPM and our code. The first is a general foundation case which includes the construction of structures, excavation of soil, and failure collapse. The second is a run-out simulation of an earthquake-induced landslide of a dam. The third is a 3D debris-flow simulation.

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#### Lattice Element Method

Lattice Element Method (LEM) is a numerical method that can be used to investigate fracture development in rock materials. It is a novel approach with relatively low computational cost and without the need to predefine the fracture path. It represents 3D solid material and fracture flow by two fully coupled 3D lattice networks (as shown below). Heterogeneity is modeled by the statistical distribution of lattice properties and existing fractures are modeled by breaking certain lattices. This method simplifies the 3D multi-physics problem into a 1D beam-element lattice network, which could be simulated with a relatively low computational cost but provides an opportunity to examine complex interactions of tensile and shear fracture generations in heterogeneous 3D porous media.

A C++ code based on this method is under development. It is capable of simulating 30 million lattices and could be run on High-Performance Computer Systems (HPCS) to simulate a real-field scenario of hundreds of kilometers using Xeon and Xeon Phi architectures.

Related publication:

- Wong, J. K. (2018). Three-dimensional multi-scale hydraulic fracturing simulation in heterogeneous material using Dual Lattice Model (Doctoral thesis). https://doi.org/10.17863/CAM.17439. University of Cambridge.

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#### Lattice Boltzmann Method

The Lattice Boltzmann equation Method (LBM) is an alternative approach to the classical Navier-Stokes solvers for fluid flow, which solves the discrete Boltzmann equation with collision models. This method works on an equidistant grid of cells, called lattice cells, which interact only with their direct neighbors (He & Luo, 1997). The fluid domain is divided into a rectangular grid or lattice, with the same spacing ‘h’ in both the x- and the y-directions, as shown in the figure. The streaming and collision processes of fluid particles on a regular grid are simulated directly, and this macroscopically could fully recover the Navier–Stokes equations and represent the viscous flow. Multiple Relaxation Time (MRT) with Large-Eddy Simulations is used to model turbulent behavior at high Reynolds numbers.

The Lattice Boltzmann approach can accommodate large grain sizes and the interaction between the fluid and the moving grains can be modeled through relatively simple fluid – grain interface treatments. Further, employing the Discrete Element Method (DEM) to account for the grain – grain interaction naturally leads to a combined LB – DEM procedure (Kumar, Soga, & Delenne, 2012). The Eulerian nature of the LBM formulation, together with the common explicit time step scheme of both LBM and DEM makes this coupling strategy an efficient numerical procedure for the simulation of grain – fluid systems.

Related publication:

- Kumar, K. (2015). Multi-scale multiphase modelling of granular flows (Doctoral thesis). https://doi.org/10.17863/CAM.14130. University of Cambridge.
- Kumar, K., Soga, K., & Delenne, J. Y. (2014). Underwater granular flows down inclined planes. Geomechanics from Micro to Macro, 473.
- Kumar, K., Soga, K., & Delenne, J. Y. (2012). Granular flows in fluid. Discrete element modelling of particulate media.

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