Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

New Asphalt Pavement Failure Criterion Based on Unified Strength Theory

This study aims to introduce an appropriate analytical method for asphalt pavement based upon unified strength theory （UST）. The traditional maximum shear stress strength theory （MSST） cannot describe the marked difference between tension strength and compressive strength or variable intermediate principal stress, which significantly affects the geotechnical materials. Our studies try to find a new asphalt pavement failure criterion that considers the influence of both tension-compression strength ratio and intermediate principal stress of asphalt mixture. In order to select a suitable theory on pavement material, the UST is introduced and compared with the traditional theory. Results show that the tension-compression strength ratio of asphalt mixture, which is used as a material parameter, dramatically affects the stress and stress distribution law in pavement; the pavement stress level increases dramatically after considering the intermediate principal stresses. Therefore, the UST which considers both tension-compression strength ratio and intermediate principal stress is more in line with the material characteristics of asvhalt pavement.

Generalized non-linear strength theory and transformed stress space

Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state. Keywords generalized non-linear strength theory (GNST) - transformed stress - constitutive model - application

Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory

This paper presents the analytical solutions for the responses of tunnels excavated in rock masses exhibiting strain-softening behavior. Since previous analyses give little consideration to the effect of the intermediate principal stress on the strain-softening rock behavior, the unified strength theory was introduced to analyze the tunnel response. Four cases of different definitions of the elastic strain in the softening and residual regions, used in the existing solutions, were considered. The tunnel displacements,stresses, radii of the softening and residual zones and critical stresses were deduced. The proposed solutions were verified by comparing with numerical simulations, model tests and existing solutions. Furthermore, the solutions of the four cases were compared with each other to investigate the influence of the elastic strain expressions on the tunnel responses. The results showed that the intermediate principal stress coefficient b has a significant effect on the tunnel displacements, stress fields, and plastic radii. Parametric studies were performed to analyze the influences of the softening and residual dilatancy coefficients,softening modulus and residual strength on the tunnel responses. The parametric analysis indicated that the existing models should be carefully evaluated in the analysis of tunnels constructed through average-quality rocks;the proposed solutions outperformed the existing models in solving the mentioned problem.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

An elasto-plastic constitutive model for soft rock considering mobilization of strength

A new elasto-plastic constitutive model is presented in the framework of plasticity theory. The strength characteristics of a diatomaceous soft rock is investigated. The friction angle and cohesion of soft rock are mobilized as a function of plastic strain. A hyperbolic hardening function for the mobilized friction and a mixed parabolic and exponential equation for the mobilized cohesion are proposed. In view of the unified strength theory and the mobilizations of strength components, a yield function is given. A plastic potential function is determined by using the non-associated plastic flow rule. An elasto-plastic constitutive model is developed and verified. The results indicate that the proposed model can predict the behavior of soft rock accurately. The advantages of the proposed constitutive model are analyzed. The evidences support that the proposed constitutive model is a mixed hardening/softening model. A hump hardening/softening function for mobilized friction is extended to a more generalized condition.

Fluid–solid coupling analysis of rock pillar stability for concealed karst cave ahead of a roadway based on catastrophic theory

In order to study the mechanism of water inrush from a concealed, confined karst cave, we established a fluid–solid coupling model of water inrush from a concealed karst cave ahead of a roadway and a strength reduction method in a rock pillar for preventing water inrush based on catastrophic theory. Fluid–solid coupling effects and safety margins in a rock pillar were studied. Analysis shows that rock pillar instability, exerted by disturbance stress and seepage stress, is the process of rock pillar catastrophic destabilization induced by nonlinear extension of plastic zones in the rock pillar. Seepage flow emerges in the rock pillar for preventing water inrush, accompanied by mechanical instability of the rock pillar. Taking the accident of a confined karst cave water-inrush of Qiyi Mine as an example, by studying the safety factor of the rock pillar and the relationship between karst cave water pressure and thickness of the rock pillar,it is proposed that rock pillar thickness with a safety factor equal to 1.5 is regarded as the calculated safety thickness of the rock pillar, which should be equal to the sum of the blasthole depth, blasting disturbance depth and the calculated safety thickness of the rock pillar. The cause of the karst water inrush at Qiyi Mine is that the rock pillar was so small that it did not possess a safety margin. Combining fluid–solid coupling theory, catastrophic theory and strength reduction method to study the nonlinear mechanical response of complicated rock engineering, new avenues for quantitative analysis of rock engineering stability evaluation should be forthcoming.

Fractional derivative statistical damage model of unsaturated expansive soil based on unified hydraulic effect

Unsaturated expansive soil is widely distributed in China and has complex engineering properties.This paper proposes the unified hydraulic effect shear strength theory of unsaturated expansive soil based on the effective stress principle,swelling force principle,and soil–water characteristics.Considering the viscoelasticity and structural damage of unsaturated expansive soil during loading,a fractional hardening–damage model of unsaturated expansive soil was established.The model parameters were established on the basis of the proposed calculation method of shear strength and the triaxial shear experiment on unsaturated expansive soil.The proposed model was verified by the experimental data and a traditional damage model.The proposed model can satisfactorily describe the entire process of the strain-hardening law of unsaturated expansive soil.Finally,by investigating the damage variables of the proposed model,it was found that:(a)when the values of confining pressure and matric suction are close,the coupling of confining pressure and matric suction contributes more to the shear strength;(b)there is a damage threshold for unsaturated expansive soil,and is mainly reflected by strength criterion of infinitesimal body;(c)the strain hardening law of unsaturated expansive soil is mainly reflected by fractional derivative operator.

Basic characteristics and development of yield criteria for geomaterials

The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference（SD） of materials in tension and compression,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,twin-shear stresses,and the convexity of yield surface.Most of the proposed yield criteria possess only one or some of these basic characteristics.For example,the Tresca yield criterion considers only single-shear stress effect,and ignores the effect of SD,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,and twin-shear stresses.The Mohr-Coulomb yield criterion accounts for the effect of SD,normal stress,single-shear stress and hydrostatic stress,but disregards the effect of intermediate principal stress,intermediate principal shear stress,and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper,we propose a new yield criterion with three features,that is,newly developed,better than existing criteria and ready for application.It is shown that the proposed criterion performs better than the existing ones and is ready for application.The development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized.According to a new tetragonal mechanical model,a tension-cut condition is added to the unified strength theory.The unified strength theory is extended to the tension-tension region.

Analysis on Autofrettage of Cylinders

Autofrettage is an effective technique to improve load-bearing capacity and safety for pressure vessels.For autofrettaged cylinder,the depth of plastic zone,or overstrain is a key factor which affects load-bearing capacity and safety.The previous research on overstrain was not done in terms of the point of view of raising load-bearing capacity as far as possible and simultaneously avoiding compressive yield for cylinders experiencing autofrettage handling,and there were no analytic solutions of autofrettage in the above view point presented,the 3rd and 4th strength theories were not applied synthetically in the research to compare the results from these two theories.In this paper,with the aid of the analytic method,based on summing up the authors＇ previous research,results from autofrettage of a cylinder based on the 3rd and 4th strength theories are studied and compared,and the laws contained in the results are looked into.Then,the essential cause and reason for the obtained laws are analyzed and the inherent and meaning relations between various parameters in autofrettage theory are revealed.It is shown that the maximum radius ratio for equivalent residual stress at inside surface never exceeds the yield strength even for a cylinder experiencing wholly yielded autofrettage,or the critical radius ratio is kc=2.218 457 489 916 7…,irrespective of the 3rd or 4th strength theories.The equation relating the depth of plastic zone with the thickness of a cylinder is identical for the 3rd and 4th strength theories.In form,the optimum load-bearing capacity of an autofrettaged cylinder is two times the initial yield pressure of the unautofrettaged cylinder irrespective of the 3rd or 4th strength theory.The revealed inherent relations between various parameters and varying laws of the parameters as well as the forms of the relations under the 3rd and 4th strength theories not only have theoretical meanings but also have prospects in engineering application.

Upper bound solution for active thrust of nonhomogeneous cohesive soil considering effects of intermediate principal stress

Considering the variation of cohesion along the depth,the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism.For a more accurate prediction,the influence of intermediate principal stress is taken into consideration using the unified strength theory.Converting the search for the active pressure to an optimization problem,the most critical failure surface can be located by a natural selection-based gravitational search algorithm(GSA).The proposed method is validated compared with existing methods for noncohesive and cohesive cases and proved to be more accordance with the limit equilibrium solution.The influences of the variation of soil cohesion and intermediate principal stress on active earth pressure coefficient are then fully studied.It can be concluded that both the variations of soil cohesion and intermediate principal stress have a significant influence on the active earth pressure coefficient.

Conversion factor analysis of self-balanced loading test of cast-in-situ piles based on analogue test method

Based on the characteristics of pile-soil interaction and the Mohr-Coulomb strength theory,a new method of determining the side friction at a pile-soil interaction is proposed.Combined with the actual engineering cases,the effectiveness of the analogue test method is verified by comparing it with the traditional anchor pile method and self-balanced method.Taking the self-balanced test of the bridge pile foundation in the Songhua River as an example,the conversion factor of sandy soil and weathered mudstone are confirmed by the analogue test method.The results show that the conversion factor of sandy soil and weathered mudstone in the Songhua River area should consider the geological conditions and the construction technology,etc.The standard values are relatively conservative.It is suggested that the engineering application should be properly revised.The recommended range of the conversion factor of sandy soil in this area is 0.65 to 0.85,and that of weathered mudstone is 1.0.

Seismic ultimate bearing capacity of strip footings on slope

The influence of earthquake forces on ultimate bearing capacity of foundations on sloping ground was studied. A solution to seismic ultimate bearing capacity of strip footings on slope was obtained by utilizing pseudo-static analysis method and taking the effect of intermediate principal stress into consideration. Based on limit equilibrium theory, the formulae for computing static bearing capacity factors, Nq, Nc, Nγ, and dynamic bearing capacity factors, Nqd, Ned, Nγd, which are associated with surcharge, cohesion and self-weight of soils respectively, were presented. A great number of analysis calculations were carried out to obtain the relationship curves of the static and dynamic bearing capacity factors versus various calculation parameters. The curves can serve as the practical engineering design. The calculation results also show that when the values of horizontal and vertical seismic coefficients are 0.2, the dynamic bearing capacity factors Nqd, Ned and Nγd, in which the effects of intermediate principal stress are taken into consideration, increase by 4%-42%, 3%-27% and 34%-57%, respectively.

Stress-Strain Relationship and Failure Criterion for Concrete after Freezing and Thawing Cycles

The research of the failure criterion and one-dimensional stress-strain relationship of deteriorated concrete were carried out. Based on the damage mechanics theory, the dsmage which reflects the alternation of internal state of material were introduced into the formula presented by Desayi and Krishman and the weighted twin-shear strength theory. As a nondestructive examination method in common use, the ultrasonic technique was adopted in the study, and the ultrasonic velocity was used to establish the damage variable. After that, the failure criterion and one-dimensional stress-strain relationship for deteriorated concrete were obtained. Eventually, tests were carried out to study the evolution laws on the damage. The results show that the more freezing and thawing cycles are, the more apparently the failure surface shrinks. Meanwhile, the comparison between theoretical data and experimental data verifies tile rationality of tile damage-based one-dimensional stress-strain relationship proposed.

Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding

A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.

A damage-based constitutive model for rock under impacting load

Using the Splitting Hopkinson Pressure Bar （SHPB） experimental system, investigations were made into the dynamic mechanical performances of underground soft rocks. The experiments proved that the measured stress-strain curves display the characteristics of plastic deformation. By making use of a revised overstress constitutive formula for the stress model and by taking into account that the strain rate and strain are a function of I - E（t）/Eo, a revised overstress constitutive formula for the stress model was simplified by applying dimensional analysis and consequently, a simplified overstress formula was obtained for the stress model. Then, by taking into consideration the effects of damage under a dynamic load on the dynamic loading strength of the rock, the continuous damage theory and the statistical strength theory were introduced into the development of the simplified overstress constitutive formula for the stress model. Hence, a damage-based constitutive formula for an overstress model, which can be appropriately applied to the analysis of full dynamic stress-strain curves, was developed. By using the simplified damage-based constitutive formula for an overstress model, the actually measured curves are fitted, indicating that the fitting curves and those actually measured are in good agreement.

Analysis of complete plasticity assumption for solid circular shaft under pure torsion and calculation of shear stress

The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship, and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension. The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section. The distribution of shear stress is still linear with the maximum shear stress ts. The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion. The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory （LSEST）. The traditional yield stress formula for plastic shaft under torsion is reasonable. The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.

Mechanics of formation and rupture of human aneurysm

The mechanical response of the human arterial wall under the combined loading of inflation, axial extension, and torsion is examined within the framework of the large deformation hyper-elastic theory. The probability of the aneurysm formation is explained with the instability theory of structure, and the probability of its rupture is explained with the strength theory of material. Taking account of the residual stress and the smooth muscle activities, a two layer thick-walled circular cylindrical tube model with fiber-reinforced composite-based incompressible anisotropic hyper-elastic materials is employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given under normal and abnormal conditions. The results of the deformation and the structure instability analysis show that the model can describe the uniform inflation deformation of the arterial wall under normal conditions, as well as formation and growth of an aneurysm under abnormal conditions such as the decreased stiffness of the elastic and collagen fibers. From the analysis of the stresses and the material strength, the rupture of an aneurysm may also be described by this model if the wall stress is larger than its strength.

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.