Numerical modeling uses complex computer programs to build a digital model of a site from which to calculate how a design will perform for various loading conditions. These methods avoid some of the simplifying and conservative assumptions that get made in simpler approaches. They help improve the efficiency of a design, predict how a design is likely to perform, show how a structure’s foundation and the groundwater will interact as a unit, and provide insight into the important mechanisms controlling how the design will perform. Improved predictions, better understanding of complex behavior, and optimized designs with minimal assumptions help reduce risks and costs for many projects.

** What is Numerical Modeling?** Numerical modeling uses digital computer models to analyze stress, strain, and deformations in a project with complicated soil, water and structural geometries and materials. Numerical modeling methods include the finite element method (FEM), the finite difference method (FDM), the boundary element method (BEM), and the discrete element method (DEM). Nonlinear material properties can be considered which allow designs to be optimized with some degree of non-linear behavior and yielding which results in less conservatism and less cost. Numerical modeling can be used to analyze almost any type of geostructural problem in two or three dimensions.

** When is Numerical Modeling Needed? **Numerical modeling is used when the structure/soil/water geometry and materials are too complicated to solve with closed-form analytical equations. The methods rely on breaking the complex geometry into smaller pieces. The behavior of each small piece is described with a stress-strain model that represents the basic understanding of each material’s behavior (bending of a beam, stress/strain behavior of a soil cube, flow of water through soil, etc.). The numerical model combines engineering mechanics equations for force equilibrium, conservation of mass, kinematic continuity, and stress-strain-strength behavior of each piece into a large set of equations describing how the pieces interact. Matrix algebra is used to combine the pieces and equations to create the digital model that gives stresses, strains, and displacements throughout the geometry for each specific load case. Examples of different types of problems addressed with a numerical model are described herein.

**Evaluating Potential to Create a Seepage Barrier with Ground Freezing**

The first example shown in Figure 1 is for a client that was designing a groundwater cutoff in an area with flowing groundwater. Flowing groundwater makes it difficult to freeze the ground (a construction technique used to provide temporary earth support and groundwater control). The left figure in Figure 1 shows a plan view (looking down from the top) of frozen soil in blue around the freeze pipe shown in white. The right three figures in Figure 1 show the frozen soil (in blue) for conditions of increasing velocities of groundwater flow. The flow direction is from the bottom to the top in the figure. Numerical modeling demonstrates to the client that flowing groundwater must be taken into account in the design of the frozen groundwater cutoff. Numerical modeling of the effects of groundwater flow saved the client millions of dollars in delays and redesign.

**Underground Storage of Compressed Gas**

In the US, compressed natural gas has been stored in solution mined caverns in salt domes since the 1960’s. Salt creep is a major factor which needs to be considered in the design and stability analysis of these underground openings. Numerical modeling is used to evaluate the stresses around the opening and predict the deformation of rock salt with use and time. When the gas pressure is cycled in an underground cavern, there are changes in temperature and stress that influence the creep rate. Under these conditions numerical modeling is the only method available to calculate the closure rates in the cavern walls. Numerical modeling provides the client with minimum and maximum cavern operating pressures and design parameters for spacing between multiple caverns. This benefits the project designers by allowing them to develop an optimized storage design based on site specific geotechnical engineering analysis and operational needs.

**Helping Design for a Complex Use Case**

In the final example shown in Figure 3, a client wanted to develop design charts to promote the use of a proprietary retaining wall system comprised of steel soldier beams with soil mix lagging spanning between the beams. Traditional design methods for lagging are mostly empirical built up from experience. Numerical modeling provided the client with a parametric design chart used to promote the use of composite soil mix retaining wall structures. The numerical models also helped show that part of the load of the final structure could be supported by these retaining walls resulting in further efficiency of the design.

In summary, numerical modeling is an important tool for analyzing complex geo-structural cases. It eliminates some of the conservatism used in regular design, reduces risk, and saves the client money. When analytical methods are not available, numerical modeling offers a great alternative to help develop safe designs without unnecessary conservatism.

*Martin Hawkes is a Senior Geotechnical Engineer with a master’s degree in Geotechnical Engineering from MIT. Mr. Hawkes has been with Geocomp for 27 years, involved with developing the early versions if iSiteCentral, developing the laboratory information database management system (LIMS) for GeoTesting Express, installing instrumentation, and geotechnical consulting. Martin provides a key role in numerical modeling with a unique skillset as a mentor for younger engineers.*