Long time monitoring is acquired to obtain the displacement data for displacement-based geotechnical material back analysis,and these data are hard to be measured under some special condition,such as earthquake.For a simple homogeneous slope,the position of a critical failure surface is determined by value of c/tan.Utilizing upper bound theorem of limit analysis,the external work rate and internal energy for normal slope under earthquake forces are given,and the formula for minimum safety factor is derived.On this basis,the equation of slip surface and the surface depth of a given position are solved.In this way,the strength parameter can be analyzed by known slip surface depth.For practical use,the surface depth for a given slope under varying strength parameter is presented.Finally,two examples are given to show its simplicity and effectiveness.
A new failure mechanism is proposed to analyze the roof collapse based on nonlinear failure criterion. Limit analysis approach and variational principle are used to obtain analytical findings concerning the stability of potential roof. Then, parametric study is carried out to derive the change rule of corresponding parameters on the influence of collapsing shape, which is of paramount engineering significance to instruct the tunnel excavations. In comparison with existing results, the findings show agreement and validity of the proposed method. The actual collapse in certain shallow tunnels is well in accordance with the proposed failure mechanism.
On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.
The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.
