Numerical Methods in Geotechnical Engineering

The JE/Sverdrup Boston office is the first Section Design Consultant of the Central Artery/Tunnel project for the Massachusetts Highway Department (MHD) to use FLAC analyses for the slurry walls of a Support of Excavation (SOE) system. During the construction phases of the CA/T contract D015A1 and D015A2 projects, the Contractors submitted Value Engineering Change Proposals for SOE designs with a two-dimensional (2-D) approach, using the ANSYS finite element code, in lieu of the project defined one-dimensional (1-D) approach. Since ANSYS is a general structural engineering program, MHD was concerned about its applications to geotechnical problems. JE/Sverdrup, therefore, recommended using FLAC, a 2-D finite difference code for geotechnical applications, as an independent check of the ANSYS analysis results. This paper outlines the FLAC methodology, discusses a simplified modeling concept, describes the numerical stage excavation procedures, and compares ANSYS, FLAC, and 1-D analysis results. In conclusion, a suitable 2-D analysis generally results in a more cost-effective design for vertical members of an SOE system than that of the conventional 1-D approach.

The finite element method is employed to investigate the effect of retaining wall modes of deformation on the generation of earth pressures in backfill soils. Translation, rotation about the wall top, and rotation about the wall base are considered. The elastoplastic constitutive model by Lade is used to model the deformation and strength characteristics of a dry sand backfill. An incremental iterative algorithm is used to account for the elastoplastic behavior of the backfill soil, along with a stress transfer technique to release excess stresses when soil tension failure is detected. An interface element is used to model the frictional interaction behavior between the wall and the backfill soil. Active and passive limiting earth pressure coefficients as well as earth pressure distributions along the height of the wall for loose or dense sand backfill, supported by smooth or rough walls, under various modes of wall deformations are studied. Comparisons of these results with classical theories of earth pressure as well as previous numerical and experimental investigations are carried out. It is shown that the mode of wall deformation, whether translation or rotation, has a significant effect on active and passive limiting earth pressure coefficients as well as earth pressure distribution along the wall height, and a set of design recommendations to account for the effect, of deformation modes in the analysis and design of earth retaining structures is presented. These design recommendations, along with schematics of the earth pressure distributions along the height of the wall under various modes of deformations, should account for the effect of the structure mode of deformation in the design and analysis of earth retaining structures.

A rational framework for propagating uncertainty in mathematical models of physical phenomena common to geomechanics is presented. The formulation casts the uncertainty in a probabilistic framework and relies on the associated rich mathematical structure to construct a model, consistent with the probabilistic assumptions, of the behavior of the physical system.

An adaptive feed-back backpropagation artificial neural network (ANN) approach is used in this study along with proven mechanics-based knowledge/concepts to characterize the complex 3D monotonic stress-strain behavior of a sandy soil. To accomplish this objective, four consecutive modeling stages were conducted. In the first stage, mechanics-based knowledge relating to the cause and effect process (i.e., stress-strain) was used to design an appropriate general purpose stress-controlled ANN model. In the second stage, the designed model with appropriate input categories dictated by mechanics-based knowledge was trained and tested on 3D monotonic stress-strain experimental data of a sandy soil. In the third stage, statistical and graphical accuracy outcomes on training and testing stress-strain responses were used to arrive at the optimal neuro-mechanistic based model. In the last stage, the selected neuro-mechanistic based model is combined with appropriate mechanics-based concepts to create a hybrid neuro-mechanistic simulator (NMS). The developed NMS was found efficient in characterizing the 3D monotonic stress-strain behavior of Canadian River sand subjected to both shear and Hydrostatic Compression (HC) loading stress paths. Consequently, NMS can easily be used to simulate in real time any desired monotonic deformational behavior for given stress path and known initial stress and strain conditions.

The effects of the micro-properties of granular material on its shear strength and shear stress-strain behaviour have been investigated using a three-dimensional, numerical simulation of a standard laboratory direct shear test. Granular particles have been simulated by means of pairs of bonded balls, using the three-dimensional discrete element method computer code PFC3D. The numerical model contained up to fifty thousand particles. Numerical simulations with different particle shapes and sizes were carried out for a number of different vertical loads. For a given particle shape, the effect of the friction angle between particles was investigated. The results of the numerical analysis were then compared with a laboratory test using Leighton Buzzard sand with a similar relative particle size distribution. It is found that particle size relative to the shearbox had an effect on the bulk shear strength of a sample, but this effect is small when the number of particles exceeds thirty thousand. The bulk friction angle and volumetric dilation of a sample increase (from less than to greater than those of real sand), with inter-particle friction angle and as the particles become less spherical, while volumetric dilation decreased with increasing vertical stress. Also, particle rotation plays an important role in the micro-mechanism of deformation in shear zones.

The stress-strain and volume change behavior of sand under triaxial compression test was modeled using feed-back artificial neural networks. The present approach used a three layer neural net with a back-propagation learning algorithm having an adaptable learning rate and momentum factor. The experimental data obtained from published literature was used as the database in the training, testing, and prediction phases of two neural network based sand models. For a constant confining pressure, Model-1 represents the effects of mineralogy, particle shape and size distribution, and initial void ratio on the isotropically consolidated drained compression (CIDC) behavior of sand. Model-2 represents the effects of relative density, and confining pressure on the deviator stress and volumetric strain variation for Sacramento river sand. Issues related to the number of processing units in the hidden layer, magnitude of strain increment during feed-back, and over-training error are discussed. An application describing the use of these well trained sand models for predicting the three dimensional failure behavior is presented.

Traditionally the analysis of footings on the surface of granular soils using finite elements has been difficult. This has generally led to a noticeable lack of published work in this area, especially for rough footings situated on the surface of granular soils with friction angles greater than 35°. The majority of published work has concentrated on the use of simple elastic perfectly plastic soil models, due to the computational difficulties and run times involved. In the present study a combined multi-surface isotropic & kinematic hardening model is used to study the behaviour of foundations on granular soils. The model gives a much more realistic account of material behaviour and therefore advances the state of the art in this area. The paper confirms the work of De Beer in which a reduction in Nγ was observed for increasing foundation widths. The paper highlights problems due to the development of singularities adjacent to the footing edge and confirms earlier work, using a simpler model, on the influence of the element depth under the footing on the computed bearing capacity. The paper concludes by presenting the allowable bearing pressures for three different sands as a function of the footing width.

A mine waste slope that had failed previously was cut back and stabilized with soil nails. The lower section of the slope was steepened from 1H:1V to about 1H:3.7V, and the slope was monitored with slope inclinometers. To evaluate the load transfer process in the nails during the excavation of the lower slope, a finite element analysis was conducted. A typical 3-D section of the slope was analyzed, with the width equal to the horizontal nail spacing. Staged material property replacement and removal of elements was used to simulate the construction and excavation process. The analysis results were compared with slope inclinometer data from the field site, and the axial nail forces were evaluated. The build up of tension in the nails was represented in the model. To observe the load transfer mechanisms as failure was approached, a surcharge loading was then incrementally applied on the top of the finite element model of the slope. The results suggest the development of a yield zone leading to a global failure of the slope.