Effect of Intermediate Principal Stress on the Bearing Capacity of Footings in Soft Rock

The bearing capacity for footings is a fundamental scientific problem in civil engineering. The evaluation of the bearing capacity of footings usually does not take into account the effect of the intermediate principal stress. In practice, the intermediate principal stress has certain influences on the strength of geomaterials (e.g., rock and soil) or concrete. In this paper, a series of numerical solutions are presented to evaluate the bearing capacity of footings in a soft rock foundation via a two-dimensional finite difference code (FLAC) with a strain hardening/softening constitutive model based on the unified strength theory (UST). The values of the bearing capacity factor Nc and Nγ for strip, circular and square footings in a soft rock foundation were evaluated using the strain hardening/softening constitutive model. The effect of the intermediate principal stress on the bearing capacity of strip, circular and square footings in a soft rock foundation was analyzed. The results of the numerical computation show that the intermediate principal stress has a significant influence on the bearing capacity and failure mechanisms of a soft rock medium. The influence of the intermediate principal stress on the peak and residual values of the bearing capacity for a strip footing is much greater than for circular and square footings. Research works for the reasonable estimation of the bearing capacity of footings in soft rock are facilitated by this study.

Study on Model of Penetration into Thick Metallic Targets with Finite Planar Sizes by Long Rods

A finite cylindrical cavity expansion model for metallic thick targets with finite planar sizes, composed of ideal elastic-plastic materials, with penetration of high-speed long rod is presented by using the unified strength theory. Considering the lateral boundary and mass abrasion of the target, the penetration resistance and depth formulas are proposed, solutions of which are obtained by MATLAB program. Then, a series of different criteria-based analytical solutions are obtained and the ranges of penetration depth of targets with different ratios of target radius to projectile radius (rt/rd) are predicted. Meanwhile, the numerical simulation is performed using the ANSYS/LS-DYNA finite element code to investigate the variations in residual projectile velocity, length, and mass abrasion. It shows that various parameters have influences on the antipenetration performance of the target, such as the strength coefficient b, rt/rd, the shape of the projectile nose, and the impact velocity of the projectile, among which the penetration depth has increased by 18.95% as b = 1 decreases to b = 0 and has increased by 32.28% as rt/rd = 19.88 decreases to rt/rd = 4.9.

The Plastic Zone of Tunnel Surrounding Rock under Unequal Stress in Two Directions Based on the Unified Strength Theory

For the deficiencies that the existing calculation theory for the Plastic Zone of Tunnel Surrounding Rock (PZTSR) does not consider the effect of the intermediate principal stress σ2 and interaction between the surrounding rock and support structure on the PZTSR under unequal stress, the Unified Strength Theory (UST) for the rock is adopted to replace the often used Mohr-Coulomb (M-C) strength criterion to consider the effect of σ2 on the PZTSR. Meanwhile, the interaction mechanism between the surrounding rock and support structure is also considered in the proposed model. Finally, the effect of the initial elastic displacement of the surrounding rock, stiffness of the support structure, and the coefficient b of the intermediate principal stress on the plastic zone is discussed. The results show that the PZTSR will increase nonlinearly with increasing the initial elastic displacement of the surrounding rock, and when it increases to a certain value, its increase extent will be much obvious. With increasing the stiffness of the support structure, the PZTSR will gradually decrease nonlinearly, but the decrease extent is not very much. With increasing b, the PZTSR will decrease; namely, σ2 can improve the stress condition of the surrounding rock and reduce the PZTSR.

A series of equivalent area circle yield criteria based on unified strength theory

Unified strength theory considering the influence of the intermediate principal stress is widely used in geotechnical engineering, but the singularities bring inconvenience to the numerical calculation. A series of equivalent area circle yield criteria based on unified strength theory are derived. The parameters of the new yield criteria and Drucker-Prager criteria are discussed, and the flow vector coefficients of the new yield criteria are given. The new series of yield criteria are very convenient for numerical calculation and can be served as reference for the evaluation of the effects of strength theory.

Triaxial Compression Performance Research of Steel Slag Concrete on the Unified Strength Theory

To better explore the mechanical properties of steel slag concrete (SSC) under triaxial compression, true triaxial tests were performed on SSC with three replacement ratios (30%, 70%, 100%) by a servo-controlled setup (TAWZ-5000/3000). Through the test, failure modes, peak stress, and corresponding strain of SSC are obtained. Results show that the failure modes of SSC are plate-splitting and slant-shear. Compared with the corresponding uniaxial strength, the triaxial compressive strength of SSC is significantly improved and is influenced by the stress ratio and the replacement ratio. Finally, based on unified strength theory, the strength failure criterion formula of SSC with different replacement rates under triaxial compression is given.