Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.

Nonlinear criterion for strength mobilization in brittle failure of rock and its extension to the tunnel scale

As underground excavations are getting deeper and field stresses increase, the behavior of intact rock blocks plays an increasingly important role in understanding and estimating the overall rock mass strength. To model the brittle behavior of intact rock blocks, the stress–strain curve is usually idealized considering a linear strength mobilization approach(cohesion-weakening-friction-strengthening, CWFS),however, it is well recognized that rock presents a nonlinear behavior in terms of the confining stress.This study extends the strength mobilization in brittle failure of rock using nonlinear criteria. To determine the model parameters, a standard statistical method that uses the complete laboratory stress–strain curves of the intact rock is employed. Several hypotheses of linear and nonlinear models are statistically compared for different types of rock and confining stress levels. Results demonstrate that the best approach to model the brittle failure of rock is to consider a nonlinear strength envelope, such as the Hoek-Brown criterion assuming a residual uniaxial compressive strength different from zero and a mi parameter that increases, both with simultaneous mobilization. This model helps to recreate highconfining conditions and a more realistic transition between peak and post-peak strength. The obtained parameters are discussed and compared with literature values to verify the validity and to develop guidelines for the estimation of parameters, providing an objective mobilization criterion. Finally, the nonlinear model was applied to a finite element code and extended to a tunnel scale in the brittle rock under high-stress conditions. A reasonable fit between the simulations and the in-situ overbreak measurements was found.

Ultimate end bearing capacity of rock-socketed pile based on generalized nonlinear unified strength criterion

In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.

Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD,material distribution and geometric morphology

Precisely quantifying the strength of the proximal femur and accurately assessing hip fracture risk would enable those at high risk to be identified so that preventive interventions could be taken.Development of better measures of femoral strength using the clinically

用于抵抗扭转采取边缘弹性约束下的单轴压缩下板材极限强度:一种新的综合方法

The ultimate strength of platings under compression is one of the most important factors to be addressed in the ship design.Current Rules for ship structural design generally provide explicit strength check criteria against buckling for simply supported and clamped platings.Nevertheless,ship platings generally exhibit an intermediate behaviour between the simple support and the clamped conditions,which implies that the torsional stiffness of supporting members should be duly considered.Hence,the main aim of this study is the development of new design formulas for the ultimate strength of platings under uniaxial compression,with short and/or long edges elastically restrained against torsion.In this respect,two benchmark studies are performed.The former is devoted to the development of new equations for the elastic buckling coefficients of platings with edges elastically restrained against torsion,based on the results of the eigenvalue buckling analysis,performed by Ansys Mechanical APDL.The latter investigates the ultimate strength of platings with elastically restrained edges,by systematically varying the plate slenderness ratio and the torsional stiffness of supporting members.Finally,the effectiveness of the new formulation is checked against a wide number of finite element(FE)simulations,to cover the entire design space of ship platings.

Modified Cam-Clay model incorporating unified nonlinear strength criterion

A unified nonlinear strength criterion(i.e UNS criterion) is proposed,for the sake of versatility,to capture the complex strength behaviors of frictional materials in geotechnical field.It covers wide ranges on the meridian and octahedral planes to describe nonlinear strength behaviors of soils.The Modified Cam-Clay model,incorporating the unified nonlinear strength criterion,is employed as an example to derive working mathematical equations and to illustrate yielding surfaces in three-dimensional stress space for improving the model's predictive capability.The unified nonlinear strength criterion,demonstrated here,is capable of capturing the experimental results of different types of soils on the meridian and octahedral planes.In addition,the revised model,based on this unified nonlinear strength criterion,though very simple,is versatile to predict the true triaxial test results from literature when considering the influences of the intermediate principal stress on strength and deformation under complex stress conditions.

Reliability analysis of aero-engine blades considering nonlinear strength degeneration

To comprehensively consider the effects of strength degeneration and failure correlation, an improved stress–strength interference （SSI） model is proposed to analyze the reliability of aeroengine blades with the fatigue failure mode. Two types of TC4 alloy experiments are conducted for the study on the damage accumulation law. All the parameters in the nonlinear damage model are obtained by the tension–compression fatigue tests, and the accuracy of the nonlinear damage model is verified by the damage tests. The strength degeneration model is put forward on the basis of the Chaboche nonlinear damage theory and the Griffith fracture criterion, and determined by measuring the fatigue toughness during the tests. From the comparison of two kinds of degeneration models based on the Miner’s linear law and the nonlinear damage model respectively, the nonlinear model has a significant advantage on prediction accuracy especially in the later period of life. A time-dependent SSI reliability model is established. By computing the stress distribution using the finite element （FE） technique, the reliability of a single blade during the whole service life is obtained. Considering the failure correlation of components, a modified reliability model of aero-engine blades with common cause failure （CCF） is presented. It shows a closer and more reasonable process with the actual working condition. The improved reliability model is illustrated to be applied to aero-engine blades well, and the approach purposed in this paper is suitable for any actual machinery component of aero-engine rotor systems.