Formulations for solving geomechanics stability problems using stress characteristics and finite element limit analysis with power type and Mohr-Coulomb yield criteria

Abstract

In geotechnical engineering, the stability analysis is often carried out to determine the ultimate collapse load that a geo-structure can possibly withstand. The accurate prediction of the exact collapse load is often very critical for ensuring the safety of any structure. Various methods of performing the stability analysis are available for solving different geomechanics problems. These are the limit equilibrium method (LEM), the method of stress characteristics (MOSC), the limit analysis (LA) method with an assumption of the collapse mechanism, and the finite element limit analysis (FELA). The present research primarily focuses on predicting the numerical solutions for different geomechanics stability problems on the basis of the MOSC and the FELA. The choice of the yield criterion is very crucial in accurately modelling the behaviour of soils. The stress-dependent yield behaviour of soils cannot be modelled effectively by a linear failure envelope- like for instance the Mohr-Coulomb (MC) failure criterion. It has been observed from numerous experimental studies that soil yield parameters are generally stress-dependent, and the soil friction angle is no longer independent of normal stress. This type of soil behaviour cannot be accurately modelled using the widely employed MC yield criterion. The non-linear power type (PT) yield criterion, which simulates in a better fashion with the experimental observations, has been employed in the present thesis to arrive at much more acceptable solutions while proposing the formulations on the basis of MOSC and FELA. In addition, the MC yield criterion was also used to provide the necessary validation. A new axisymmetric UB-FELA formulation using the second order cone programming (SOCP) has been developed for soils which obeys the MC yield criterion to provide more accurate solutions in an efficient manner. The proposed formulation is used to solve different geomechanics stability problems, including determining (i) the bearing capacity of solid circular and ring footings, and (ii) the stability numbers for unsupported vertical circular excavations for various combinations of (H/b) and the soil friction angle, ϕ; where H is the depth of the bottom of the excavation from the ground level and b is the radius of the circular excavation. The results obtained from the analysis are found to compare well with the existing studies. The proposed formulation is found to be computationally quite efficient while providing very accurate solutions. A new FELA formulation based on the non-linear PT yield criterion in conjunction with power conic programming (PCP) has been proposed to solve both axisymmetric and planar stability problems. To validate this formulation, the solutions for (i) seismic bearing capacity of a strip footing placed on horizontal ground and (ii) the bearing capacity of a circular footing on horizontal ground were obtained. To increase the computational efficiency and to obtain more accurate solutions with a given number of finite elements in the chosen soil domain, an adaptive mesh generation technique was used. The adaptive mesh was generated using an open-source software TRIANGLE - which is based on the Delaunay triangulation technique. While implementing the proposed formulation(s), it is intended to determine the seismic bearing capacity factors for a strip footing placed on horizontal and sloping ground surface by using the MOSC and the FELA. The objectives of this investigation include (i) computing the seismic bearing capacity factor N_σ for a rough strip footing on a sloping ground using the non-linear PT yield criterion by employing the MOSC, and (ii) finding the seismic bearing capacity factor N_γ (a component of ultimate bearing capacity due to the unit weight of the soil) for a rough strip footing using the MC yield criterion through the MOSC. The effectiveness of the PT yield criterion in determining the bearing capacity values which are in agreement with experimental values was shown. The seismic bearing capacity factor N_σ was evaluated for (i) different ground inclinations (β), (ii) varying horizontal earthquake acceleration coefficient ("α" _h), (iii) various values of shear strength parameters (c_o,m,σ_t,A) and soil surcharge (q). The resulting N_σ values were compared with previously reported results in literature, and were found to match well with the solutions from previous studies. The employment of a rigorous failure mechanism, which overcomes the limitations of the existing MOSC formulation to determine the seismic bearing capacity factor N_γ for a rough strip footing, has also been explored. Non-dimensional charts were created to determine the factor N_γ for various combinations of soil friction angle (ϕ), ground inclination (β) and the horizontal earthquake acceleration coefficient ("α" _h). These results were also verified through modelling in the commercially available finite element software OptumG2. The failure mechanisms and N_γ magnitudes which were determined by using the MOSC were found to be in good agreement with the results using the FELA. For all the stability problems taken up in this thesis, the solutions, including the failure mechanisms generated from the MOSC and FELA approaches, were generally found to compare well with each other. All the associated codes for performing the analysis for different problems were written in MATLAB. The optimization problem was solved by using the MOSEK toolbox. The power type yield criterion used in the thesis for both the MOSC and the FELA approaches will be able to provide better solutions than that are available in literature at present on the basis of the Mohr-Coulomb failure criterion.