Numerical Analysis in Tunnel Drainage Engineering
Expert-defined terms from the Advanced Certificate in Tunnel Drainage Engineering course at London School of Business and Administration. Free to read, free to share, paired with a globally recognised certification pathway.
Adaptive Mesh Refinement #
A numerical analysis technique used in tunnel drainage engineering that automatically increases the density of the finite element mesh in areas of high gradients or complex geometry. This allows for more accurate simulations and improved prediction of water flow in tunnel systems.
Back Analysis #
A method used in tunnel drainage engineering to estimate the in-situ properties of soil or rock by comparing the results of numerical simulations to measured data. By adjusting the input parameters until the simulated results match the observed data, engineers can gain insight into the physical properties of the ground and optimize the design of tunnel drainage systems.
Computational Fluid Dynamics (CFD) #
A branch of numerical analysis used to simulate the behavior of fluids in tunnel drainage systems. CFD models can predict water flow, pressure distribution, and other hydraulic parameters in complex geometries, allowing engineers to optimize the design of tunnel drainage systems for maximum efficiency and effectiveness.
Convergence #
The process by which the solution to a numerical analysis problem approaches the true solution as the size of the finite element mesh is reduced. In tunnel drainage engineering, convergence is an important indicator of the accuracy and reliability of numerical simulations.
Discretization #
The process of dividing a complex problem into smaller, simpler elements in numerical analysis. In tunnel drainage engineering, discretization typically involves dividing the tunnel and surrounding soil or rock into a finite element mesh, allowing for the simulation of water flow and other hydraulic parameters.
Effective Stress #
The stress experienced by the soil or rock in a tunnel drainage system, taking into account the presence of water. Effective stress is calculated by subtracting the pore water pressure from the total stress, and is an important factor in the design and analysis of tunnel drainage systems.
Finite Element Method (FEM) #
A numerical analysis technique used to solve complex problems in tunnel drainage engineering. FEM involves dividing the problem domain into a finite element mesh, and solving the governing equations at each node in the mesh. This allows for the simulation of water flow, stress, and other hydraulic parameters in tunnel drainage systems.
Fluid #
Structure Interaction (FSI): The interaction between a fluid and a structure in tunnel drainage engineering. FSI can occur when water flows through a tunnel, exerting pressure on the tunnel lining and affecting its stability. Numerical simulations that account for FSI can provide more accurate predictions of tunnel behavior and optimize the design of tunnel drainage systems.
Fracture Mechanics #
A branch of numerical analysis used to study the behavior of cracks and fractures in tunnel drainage systems. Fracture mechanics models can predict the propagation of cracks under different loading conditions, allowing engineers to assess the safety and reliability of tunnel drainage systems.
Hydrostatic Pressure #
The pressure exerted by a fluid at rest. In tunnel drainage engineering, hydrostatic pressure is an important factor in the design and analysis of tunnel drainage systems, as it can affect the stability of the tunnel lining and the flow of water through the tunnel.
Inverse Analysis #
A method used in tunnel drainage engineering to determine the properties of a system based on observed data. Inverse analysis involves formulating a mathematical model of the system, and adjusting the input parameters until the simulated results match the observed data. This can provide insight into the physical properties of the system and optimize the design of tunnel drainage systems.
Iterator Function #
A function used in numerical analysis to systematically evaluate a set of data. In tunnel drainage engineering, iterator functions can be used to evaluate the finite element mesh, allowing for the simulation of water flow and other hydraulic parameters in tunnel drainage systems.
Jacobian Matrix #
A matrix used in numerical analysis to represent the derivative of a function with respect to its variables. In tunnel drainage engineering, the Jacobian matrix can be used to linearize the governing equations, allowing for the solution of nonlinear problems in tunnel drainage systems.
Lagrangian Finite Element Method #
A numerical analysis technique used to simulate the behavior of solids in tunnel drainage engineering. The Lagrangian finite element method involves tracking the motion of individual particles in the solid, allowing for the simulation of deformation, stress, and other mechanical parameters in tunnel drainage systems.
Meshing #
The process of dividing a complex problem into smaller, simpler elements in numerical analysis. In tunnel drainage engineering, meshing typically involves dividing the tunnel and surrounding soil or rock into a finite element mesh, allowing for the simulation of water flow and other hydraulic parameters.
Numerical Stability #
The ability of a numerical analysis algorithm to produce reliable and accurate results over a wide range of input parameters. In tunnel drainage engineering, numerical stability is an important factor in the design and analysis of tunnel drainage systems, as it can affect the accuracy and reliability of simulations.
Pore Water Pressure #
The pressure exerted by water in the pores of soil or rock. Pore water pressure is an important factor in the design and analysis of tunnel drainage systems, as it can affect the stability of the tunnel lining and the flow of water through the tunnel.
Residual #
The difference between the true solution and the approximate solution in numerical analysis. In tunnel drainage engineering, residuals can be used to assess the accuracy and reliability of numerical simulations, allowing engineers to optimize the design of tunnel drainage systems.
Sensitivity Analysis #
A method used in tunnel drainage engineering to evaluate the effect of input parameters on the output of a numerical simulation. Sensitivity analysis can provide insight into the importance of different input parameters, allowing engineers to optimize the design of tunnel drainage systems.
Stress Analysis #
The process of evaluating the stress distribution in a tunnel drainage system. Stress analysis can provide insight into the stability and safety of the tunnel, allowing engineers to optimize the design for maximum efficiency and effectiveness.
Subsurface Drainage #
The removal of water from the soil or rock surrounding a tunnel. Subsurface drainage is an important factor in the design and analysis of tunnel drainage systems, as it can affect the stability of the tunnel lining and the flow of water through the tunnel.
Tunnel Lining #
The structural component that surrounds a tunnel, providing support and stability. The tunnel lining is an important factor in the design and analysis of tunnel drainage systems, as it can affect the flow of water and the stability of the tunnel.
Unstructured Mesh #
A finite element mesh that does not have a regular structure. Unstructured meshes can be used to model complex geometries in tunnel drainage engineering, allowing for the simulation of water flow and other hydraulic parameters in tunnel drainage systems.
Validation #
The process of comparing the results of a numerical simulation to experimental data. Validation is an important step in the design and analysis of tunnel drainage systems, as it can provide insight into the accuracy and reliability of numerical simulations.
Virtual Work Principle #
A fundamental principle in numerical analysis used to derive the governing equations for tunnel drainage systems. The virtual work principle states that the total virtual work done by external and internal forces on a system is equal to zero, and can be used to derive the equations of motion for tunnel drainage systems.
Weak Formulation #
A mathematical formulation used in numerical analysis to derive the governing equations for tunnel drainage systems. The weak formulation is based on the principle of virtual work, and can be used to derive the equations of motion for tunnel drainage systems in a weak or integrated sense.
Note #
The above glossary terms and definitions are provided for informational purposes only and are not intended to be exhaustive or comprehensive. They should not be used as a substitute for professional advice or consultation in tunnel drainage engineering.