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In engineering practice, horizontal layers of reinforcement geosynthetics are widely used to improve the bearing capacity of foundations. However, there are few studies on the seismic bearing capacity of foundations on reinforced soil, and there is a lack of derivation of theoretical formulas in this direction. In this paper, based on the upper bound theorem of limit analysis, the seismic bearing capacity of foundations on reinforced soil is studied for the first time using the modified pseudo-dynamic approach. Seismic forces are calculated using a slicing method that adapts to spatial and temporal variations. Based on three different failure mechanisms, three different formulas and constraints are used. Each formula contains 61 variables, and the bearing capacity value is optimized by MATLAB program. By comparing the calculation results of three failure mechanisms, the exact upper bound solution of seismic bearing capacity for sliding failure is obtained. Considering the temporal as well as spatial characteristics of seismic forces, the effects of the coefficient of seismic acceleration, the internal friction angle, the damping ratio, the normalized frequency, and the reinforcement burial depth on the seismic bearing capacity are analyzed, providing a theoretical basis for the application of reinforced soil foundations in engineering practice. [ABSTRACT FROM AUTHOR]

This work aims to develop a numerical-analytical framework within the kinematic approach of limit analysis to assess the stability of non-circular tunnel faces under seepage conditions with tensile strength cut-off from a discretization-based perspective. Considering the overestimation of the tensile strength of the soil by the Mohr-Coulomb criterion, a modification based on the concept of tensile strength cut-off is recommended to reduce or eliminate the tensile strength. A modified 3D rotational discretization-based failure mechanism incorporating the tension cut-off is generated point-to-point starting from a real non-circular tunnel face to model the face failure, where the failure surface on the top intersects more rapidly due to the increasing rupture angle in the tensile regime. The seepage towards the non-circular tunnel face is numerically simulated, and then the numerical seepage field is extracted into the 3D discretization-based failure mechanism. Within the kinematic approach, the seepage effect is introduced from two aspects: pore pressure and seepage force. A hybrid optimization routine is employed to search for the maximum required face pressure. The developed framework is validated by comparisons with numerical fluid-mechanical simulations and previous studies. Afterward, parametric analyses are carried out on different seepage conditions, different face pressure distributions, different soil strengths, and different tension cut-off conditions. The developed framework can give insight into the combined effect of the tension cut-off and seepage on the stability of non-circular tunnel faces under various conditions. [ABSTRACT FROM AUTHOR]

Abstract Tunnels are becoming more popular in the transportation system, which makes it imperative to study the surrounding soil tunnel stability. However, in previous studies, researchers generally regarded soil as an isotropic and homogeneous material, which is not consistent with real conditions. Therefore, on the basis of the upper bound theorem, the influence of the anisotropy and non-homogeneity of soil on the earth pressure and the failure mechanism of shallow square tunnels is studied in this paper. The failure mechanism of the surrounding soil for excavation tunnel is obtained using a discrete technique. Considering the anisotropy and non-homogeneity of soil, the earth pressure formula is derived and the optimal solution is obtained. Compared to other results, it is shown that the present approach is feasible and effective. In addition, taking the tunnel of Daganxi II, Longyong expressway of Hunan province as an example, a numerical calculation is conducted, in which the displacement field corresponds to the theoretical one proposed in this paper. After discussing the impact of the anisotropy and the non-homogeneity of soil on earth pressure, the tunnel stability is studied with the presence of the pore water pressure. The effect of pore water pressure and the change of the water table level are then investigated. [ABSTRACT FROM AUTHOR]

In order to give a more accurate prediction of the required face pressure, this work revisits the three-dimensional (3D) face stability problems of rock tunnels excavated in Hoek-Brown media. The Piecewise Linear Method (PLM) is introduced to account for the nonlinearity of the rock strength rather than the simple linear substitution for the strength envelope. A novel multi-cone rotational mechanism consisting of n truncated curvilinear cones is generated respecting the plastic normality flow rule. Two typical linearized measures: Generalized Tangential Technique (GTT) and Equivalent Mohr-Coulomb parameters Method (EMM) are also included in this study for comparison and analysis. In terms of the energy-work balance equation, the required face pressure is formulated as an optimization problem depending on 2 n variables and is resolved by a recently-proposed Marine Predators Algorithm (MPA). Parametric study implies that the solution of two-dimensional (2D) analysis is very conservative, despite being safe in engineering, it is uneconomical compared with 3D analysis. In 3D analysis, the required face pressure predicted by PLM is significantly improved by 9 % compared with that of GTT, and the results calculated from EMM show a good consistency with PLM and GTT for heavily fractured rock mass, while for high-quality rock masses, the diversity between the results of EMM and other two methods is distinct. To further extend the application of such modified mechanism, design charts of the normalized face pressure are calculated for a quick assessment of face stability in rock masses with different quality. [ABSTRACT FROM AUTHOR]

For tunnels excavated in the unsaturated soils with changing water levels, there may be steady-state unsaturated flow above the water table and saturated flow below the water table toward the tunnel face due to the excavation. Changing water levels affect the adverse effect of the underwater saturated flow and the contribution of the unsaturated flow to the shear strength. To figure out the regularity concerning the region and magnitude of unsaturated and saturated flow effects, an analytical framework is developed within the kinematic approach of limit analysis combined with the numerical simulation. A suction stress-based equation is employed to express the contribution of unsaturated flow to shear strength. The development of the saturated flow below the water table is numerically simulated, and the resulting pore pressure distribution is extracted and interpolated on a 3D discrete rotational failure mechanism. The work rate balance equation incorporating the apparent cohesion due to unsaturated flow and the pore pressure affected by the saturated flow is established to optimize the critical face pressure. The proposed analytical framework is verified by comparisons with previous literature and numerical simulations of hydromechanical analysis. A parametric analysis is conducted to investigate the effect of groundwater levels, flow types, unsaturated properties, and hydraulic hysteresis on the tunnel face stability. The results show that it is only necessary to consider the effect of unsaturated flow and the differences caused by various unsaturated characteristics when the unsaturated zone is large enough. This work can provide a good reference for the design of face supports in the initial stage for tunnels excavated in unsaturated soils with changing groundwater levels. [ABSTRACT FROM AUTHOR]

Bearing capacity evaluation for shallow foundations is conventionally completed according to the equations derived for dry or saturated soils neglecting the effect of matric suction. However, many shallow foundations are mostly constructed upon the soil layer above the groundwater table, where a large portion of soils under shallow foundations is in fact in unsaturated conditions. The failure of shallow foundations is usually related to shear failure which is one of the main engineering properties required in foundation design. The shear strength of unsaturated soils depends on the matric suction which usually changes with depth. Since the discretization technique of limit analysis is particularly suitable for considering the variation of soil parameters, the bearing capacity for shallow foundations considering the shear strength of unsaturated soils is therefore evaluated by this technique. The results obtained by the present technique are compared with the ones obtained from different authors, and good agreement is observed. Then a parametric analysis is performed using the present technique, and the bearing capacity for shallow foundations are given considering different soil types, foundation widths, effective internal friction angle φ ′ , air-entry pressure 1/ α with various n values, different water table depth with surface flux boundary conditions, different unit weight of soil γ , and surcharge load q 0. Some useful conclusions are given and a useful method is therefore provided for the bearing capacity evaluation of shallow foundations on unsaturated soils. [ABSTRACT FROM AUTHOR]

Foundation pit excavation may disturb the initial stress field and induce the deformation of the surrounding rock mass. Due to the excavation, the originally compact rock mass and lining structure may become loose with adverse impacts on the normal operation of the existing tunnel. A new failure mechanism is constructed on the basis of the deformation characteristics of the rock mass around an existing tunnel induced by an adjacent excavation. Using this failure mechanism, the upper bound solution of the slip surface equation for the rock mass around an existing tunnel is derived in the framework of the upper bound theorem in conjunction with a variational approach. The shape and range of the slip surface are plotted for different parameters. A three-dimensional numerical model is constructed to simulate the deformation of the rock mass around the existing tunnel induced by adjacent excavation. By comparing the analytical results for the slip surface with the failure surface provided by numerical simulation, it is found that the differences between the analytical results and the numerical results are small. This comparison shows that the proposed method is valid for investigating the deformation of the rock mass around the existing tunnel induced by adjacent excavation. [ABSTRACT FROM AUTHOR]