Numerical Investigation and Analysis of Intermediate Principal Stress Effects on Rock Failure Behaviors

A series of numerical experiments have been conducted to investigate the intermediate principal stress effects on rock failure behaviors. The numerical results show that the strength and deformation of the rock samples are significantly affected by the intermediate principal stress. The effects are inconsistent in different intervals. As intermediate principal stress ratio b increases, the rock strength increases initially and finally decreases. When b is approximately equal to 0.5, the strength of the rock sample reaches the maximum. In the microlevel, the intermediate principal stress affects the number and distribution of microcracks. The increase of the intermediate principal stress makes the projection of the microcracks on the loading plane change from uniform to uneven. On the one hand, the intermediate principal stress restricts the propagation of microcracks in the normal direction along the intermediate principal stress (or with a component in this direction), which will lead to an increase in the strength of the rock samples. On the other hand, the propagation of microcracks along the normal direction with small principal stress (or with a component in this direction) is promoted, which leads to a decrease in the strength of the rock sample. End friction can make the intermediate principal stress effect more significant because the friction of the loading end to the rock sample can result in stress deviation between the actual value and experimental value. Inhomogeneity of stress field induced by the change of stress states or end friction forces is the external factor of the intermediate principal stress effect. Also, the inhomogeneity of rock material itself is the internal factor. Intermediate principal stress will promote or restrict the failure of certain directions, thus affecting the overall strength of the rock samples. The numerical results can be very meaningful for stability analysis of rock masses in practical engineering.

Ultimate Bearing Capacity of Strip Foundations in Unsaturated Soils considering the Intermediate Principal Stress Effect

The reasonable determination of ultimate bearing capacity is crucial to an optimal design of shallow foundations. Soils surrounding shallow foundations are commonly located above the water table and are thus in an unsaturated state. The intermediate principal stress has an improving effect on the unsaturated soil strength. In this study, the ultimate bearing capacity formulation of strip foundations in unsaturated soils is presented by using Terzaghi’s theory. The unified shear strength equation of unsaturated soils under a plane strain condition is utilized to capture the intermediate principal stress effect. Furthermore, two profiles of matric suction are considered and a hyperbolic function of the friction angle related to matric suction (φb) is adopted to describe strength nonlinearity. The validity of this study is demonstrated by comparing it with model tests and a theoretical solution reported in the literature. Finally, parameter studies are conducted to investigate the effects of intermediate principal stress, matric suction, and base roughness on the ultimate bearing capacity of strip foundations. Besides, the effect of strength nonlinearity is discussed with two methods representing the angle φb.

Failure Probability Model considering the Effect of Intermediate Principal Stress on Rock Strength

A failure probability model is developed to describe the effect of the intermediate principal stress on rock strength. Each shear plane in rock samples is considered as a micro-unit. The strengths of these micro-units are assumed to match Weibull distribution. The macro strength of rock sample is a synthetic consideration of all directions’ probabilities. New model reproduces the typical phenomenon of intermediate principal stress effect that occurs in some true triaxial experiments. Based on the new model, a strength criterion is proposed and it can be regarded as a modified Mohr-Coulomb criterion with a uniformity coefficient. New strength criterion can quantitatively reflect the intermediate principal stress effect on rock strength and matches previously published experimental results better than common strength criteria.

Unified Solution of Burst Pressure for Defect-Free Thin Walled Elbows

In order to study the mechanical properties of defect-free thin walled elbows (TWE), and evaluate impacts of the intermediate principal stress effect, tension/compression ratio, and strain-hardening of materials into logical consideration, this research, in the framework of finite deformation theory, derived the computational formula of burst pressure for defect-free TWE according to unified strength theory (UST). In addition, influences of various factors on burst pressure were analyzed, which include strength disparity (SD) effect of materials, intermediate principal stress, curvature influence coefficient, strain-hardening exponent, yield to tensile (Y/T) and thickness/radius ratio. The results show that the greater the tension/compression ratio is, the higher the burst pressure is. The influence of the SD effect of materials is more obvious with the increase of elbow curvature and intermediate principal stress. The intermediate principal stress effect can bring the self-bearing capacities and strength potential of materials into a full play, which can achieve certain economic benefits for projects. Moreover, the burst pressure of defect-free TWE increases with the growth of yield ratio and thickness/radius ratio, while decreases with the rise of curvature influence coefficient and strain-hardening exponent. It is also concluded that the Tresca-based and Mohr–Coulomb-based solutions of TWE are the lower bounds of the burst pressure, the twin shear stress (TSS)-based solution is the upper bound of the burst pressure, and the solutions based on the other yield criteria are between the above two. The unified solution in this paper is suitable for all kinds of isotropous materials which have the SD effect and intermediate principal stress effect. As the deduced formula has unified various burst pressure expressions proposed on the basis of different yield criteria for elbows of any curvature (including straight pipelines), and has established the quantitative relationships among them, its applicability is broader. Therefore, the unified solution is of great significance in security design and integrity assessment of defect-free TWE.

The Changing Rule of Rock Strength under True Triaxial Condition

The intermediate principal stress effect of the rock has been demonstrated. By analyzing true triaxial test results of Dunham dolomite and Mizuho trachyte, we studied relationship between minimum principal stress and the rock strength under the same intermediate principal stress coefficient, and the relationship between intermediate principal stress and the rock strength under the same minimum principal stress condition. Research shows that the minimum principal stress has a linear relation with the rock strength, the intermediate principal stress coefficient of a quadratic function relation with the rock strength. And the mathematic expression of the intermediate principal stress effect function was calculated.

Elastoplastic Analysis of Surrounding Rocks of the Pressure Tunnel

According to the triple shear unified yield criterion, the mechanical behavior of the pressure tunnel was put forward. The calculation formulas of the radius of plastic zone were deduced with considerations of the effects of the intermediate principal stress. The results show that the intermediate principal stress effect parameter b has influences on the radius of plastic zone. With the increase of the intermediate principal stress effect parameter b, the radius of plastic zone decreases. The radius of plastic zone is increased, because of the increase of the porous hydraulic pressure.

Influence of Intermediate Principal Stress Effect on Flat Punch Problems

Using the finite difference code FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) and UST (Unified Strength Theory), the influence of the intermediate principal stress effect on the problems of flat punch are analyzed in this paper. The values of the ultimate bearing capacity resulting from numerical analyses and the analytical solution of Prandtl’s strip punch problem are compared. The three-dimensional problems of strip, rectangular, square and circular punches on a semi infinite metallic medium have been analyzed.

Analysis of Axial Bearing Capacity of Concrete-Filled Steel Tube Hollow Columns

Based on the triple shear unified yield criterion, the mechanical behavior of the concrete-filled steel tube columns was analyzed. The calculation formulas of axial bearing capacity of the concrete-filled steel tube columns were deduced with considerations of the restriction effects of steel tube and the effects of the intermediate principal stressed. The results show that the intermediate principal stress effect parameter b has influences on the ultimate bearing capacity. With the increase of the intermediate principal stress effect parameter b, the ultimate bearing capacity of the concrete-filled steel tube columns increases too. The results show that formula deduced in the paper has good applicability and the solution has an important practical value.