Unified Strength Criterion Research Articles

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.

3D Numerical Study on the Growth and Coalescence of Pre-existing Flaws in Rocklike Materials Subjected to Uniaxial Compression

AbstractA novel, meshless numerical method, called general particle dynamics (GPD), is proposed to simulate the initiation, propagation, and coalescence of three-dimensional (3D), pre-existing penetrating and embedded flaws as well as size effects and large deformations of rock materials. On the basis of the nonlinear unified strength criterion, an elastic–brittle–plastic damage model was developed to reflect the initiation, growth, and coalescence of the 3D flaws and the macrofailure of rocklike materials by tracing the propagation of the cracks. Then, growth paths of cracks were captured through the sequence of such damaged particles. In this paper, the GPD code is applied to simulate the macrofailure, large deformation, and size effects of the heterogeneous rocklike materials. The present numerical simulations focus on the effects of sample sizes, the nonoverlapping length and types of flaws on the failure, and the complete stress–strain curves of the rocklike materials. The initiation, propagation, an...

A three-dimensional elastoplastic constitutive model for concrete

The nonlinear unified strength criterion proposed by authors in 2010 is adopted as the yield function and the plastic potential function for concrete. Four original material parameters of the nonlinear unified strength criterion are derived as functions of four conventional strength indexes of concrete. A three-dimensional elastoplastic constitutive model for concrete is then developed by using hardening and softening functions that are determined from the uniaxial compressive stress–strain relationship. The performance of the constitutive model is evaluated by comparing prediction and experimental data from literatures. The comparison shows the model is able to reasonably describe the three-dimensional strength characteristics, strain softening behavior after the peak stress and the dilatancy of various concretes. Moreover, the proposed model is integrated in the general finite element package ABAQUS via UMAT to simulate the deformation process of reinforced concrete columns under eccentric compression. The simulations show that the proposed constitutive model is able to describe the nonlinear mechanical behavior under complex stress states with high computational efficiency.

Unified strength criterion for soils, gravels, rocks, and concretes

There are both diversity and unity in the strength characteristics of different geomaterials and concretes. Based on the generalized nonlinear strength theory, a simple but unified strength criterion (USC) is proposed for various materials, such as soils, gravels, rocks, and concretes. Power function is used as the failure curve of the USC in meridian plane, while the shape of failure curve in π-plane is curved triangle, which is between the SMP and Mises criterion. With only four independent parameters, which are convenient to be determined, the proposed criterion is able to take the effects of friction, cohesion, hydrostatic pressure, and intermediate principal stress into consideration. The proposed criterion is compared with some widely used unified strength criteria, such as the Zienkiewicz–Pande criterion and the Lade criterion, against the experimental results for various soils, gravels, rocks, and concretes. The comparison between the predicted and observed results confirmed the validity of the proposed criterion used as a USC for geomaterials and concretes.

Elastic–Brittle–Plastic Analysis of Double-Layered Combined Thick-Walled Cylinder Under Internal Pressure

The elastic–brittle–plastic unified solutions of limit internal pressure are presented for double-layered combined thick-walled cylinder by the triple-shear unified strength criterion. The unified solutions obtained in this paper are especially versatile that can take into account of material brittle softening and intermediate principal stress quantitatively. The conventional existing elastic-perfectly plastic solutions, based on the Tresca yield criterion, Mises yield criterion, or twin-shear strength theory, can be categorized as special cases of the present unified solutions which can overcome their shortages. Parametric studies were carried out to evaluate the influences of various factors such as brittle softening parameter, strength theory parameter, cohesion, internal friction angle, and intermediate principal stress coefficient on the unified solutions. It is shown that proper choices of failure criterion, material behavior model, and brittle softening are significant in combined cylinder design. The new solutions can be naturally degraded to the existing formula and agree well with the results of the prevailing failure criteria. It is concluded that the unified solutions have an important practical value for the optimum design and engineering application of combined thick-walled cylinder.

Numerical Simulation of Zonal Disintegration of the Surrounding Rock Masses Around a Deep Circular Tunnel Under Dynamic Unloading

A new numerical method, which is called the General Particle Dynamics (GPD) method, is proposed to investigate the zonal disintegration mechanism of isotropic rock masses around a deep circular tunnel subjected to dynamic unloading as well as the stress distributions. A constitutive model based on the GPD method is developed to simulate the zonal disintegration phenomenon in deep rock masses. The number and size of fractured and nonfractured zones are determined using the nonlinear unified strength criterion. It is shown from the numerical results that the dynamic loads and high in situ stress are two dominant factors for the occurrence of zonal disintegration.

A three-dimensional elastoplastic constitutive model for concrete

Strength of concrete materials can be described by the theory of nonlinear unified strength criterion with four independent parameters. The failure surface of the strength criterion in the principal-stress space is smooth, and therefore it has continuous partial derivatives. The theory of nonlinear unified strength criterion is applied as a yield function, plastic shear strain is used as the hardening and softening parameters, and the hardening and softening laws are given by the stress-strain relationship under uniaxial compression. Then a three-dimensional elastic-plastic constitutive model for concrete is established. A user-defined material mechanical behavior (UMAT) is developed based on the finite element analysis software ABAQUS. The load resistance and the deformation capacity of a reinforced concrete column under eccentric compression are simulated using the present model. The present theoretical results are comparable to the available material-test data, and the numerical results have a good agreement with the experimental observations of the concrete column. This indicates that the developed constitutive model is capable of describing the strength and deformation behaviors, and representing the strain softening behavior of concrete under three-dimensional stress state. Furthermore, the model has high efficiency and accuracy in the numerical analysis.

Effects of different limit strength on plastic strains of thick walled pressure vessels

In this work, the effects of intermediate principal stress and different limit strength on the maximum plastic strain distributions for the cylindrical and spherical pressure vessels are investigated. The present analytical solution is based on unified strength criterion. The aim of this work is to give a reliable theoretical tool for the predictions of plastic strain distributions of the cylindrical and spherical pressure vessels. The numerical results including Poisson's ratio effect are presented graphically and discussed. Consequently, it can be observed that to be the significant differences between the present and previous solutions. In particular, it can be seen that these differences are more significant, for many materials having the same limit strength used frequently in the practical applications.

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC-based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.

Modeling and behaviours of rockfill materials in three-dimensional stress space

A bounding surface model incorporating a unified nonlinear strength criterion is proposed. The proposed bounding surface model contains 9 model parameters, which can be determined from the conventional triaxial tests. The bounding surface model can reproduce such behaviours as the strain hardening, the post-peak strain softening, and the volumetric strain contraction and expansion. Based on the comparisons between the predictions and the test results, the proposed strength criterion and model can well reproduce the experimental results of the strength and stress-strain behaviours of rockfill material in three-dimensional stress space. The strength behaviour of rockfill material is summarized as: (a) the failure stress ratio decreases with the initial confining pressure on the meridian plane; (b) the failure deviatoric stress decreases with the Lode angle from 0° to 60° on the deviatoric plane. The stress ratio decreases with increasing one of such factors as the initial void ratio, the intermediate principal stress ratio and the minor principal stress at the same strain when the other factors are given.

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 bearing 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.

Unified Analytical Solution for Cylindrical Cavity Expansion of Saturated Soil Based on Large Deformation and Non-Drainage

Soil around the cylindrical pore is divided into elastic and plastic regions. In the elastic region, the small deformation theory is applied while in the plastic region, the large deformation theory and unified strength criterion are applied. According to the stress equilibrium equation and the boundary condition of continuous stress and deformation, the theoretical solution to plastic region radius, limit expansion pore pressure excess pore pressure and excess pore water pressure of the cylindrical cavity expansion can be derived when considering large deformation and non-drainage problems. Compared to the theoretical results of Cao L.F., the theoretical calculation results are closer to the field test results which show that the theory has a certain value in engineering application. Through calculations and analysis, it is also derived that expansion pore pressure increase is non-linear with the increase of b value, while the excess pore water pressure is just the opposite.

Study of Strength Criterion for Dynamic Compression of Concrete under Biaxial Equal Proportion Loading

The dynamic compressive experiments of cubic concrete specimens under various biaxial equal proportion loading were preformed. The biaxial equal proportion stress in the tests were kept constant at 1:0, 1:0.5 and 1:1, respectively, and the tested strain rate ranged from 10−5/s to 10−2/s. Based on the experimental results, the influence of the strain rates on compressive characteristics of concrete under various biaxial stress ratios were researched. The unified strength criterion in terms of principal stress space considering the influence of strain rates and biaxial stress ratio is proposed. The fitting curves by the present strength criterion agree well with experimental data.

New 3D engineering curves for predicting stope stability and mining dilution in longitudinal blasthole mining operations

Graphs, numbers, pictures and engineering judgement are among the most important factors in engineering design and implementation. This study is the first of a research project which has addressed 3D potential zones of rock mass failure and relaxation. It presents results of applying numerical-empirical 3D engineering curves used for predicting stope stability and mining dilution, especially in longitudinal blasthole underground mining operations. A state-of-the-art 3D elasto-plastic finite element technique developed by CANMET was utilized in conjunction with a non-linear unified strength criterion and case histories to develop these curves. These could assist mine operators in making economic decisions on ground control, mine planning and feasibility assessments that will ensure a safe working environment. Limitations in applying the curves will be discussed.

Nonlinear Unified Strength Criterion for Concrete under Three-Dimensional Stress States

This paper shows that the mechanical behavior of concrete materials can be described by a nonlinear unified strength criterion which requires four independent parameters for model calibration. The criterion covers all the area from spatially mobilized plane curve in the lower bound to Mises circle in the upper bound on the deviatoric plane, with an exponential curve on the meridian plane in principal stress space. Four material parameters in the strength criterion have their clear physical meanings and their determination approaches are also given. Four sets of true triaxial experimental results are compared with the modeling results of the proposed criterion. It shows that the proposed criterion is capable to capture the characteristics of yielding and failure and reasonably calculate the multiaxis strength of concrete materials.

The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses

In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion.

Penetration analysis for geo-material based on unified strength criterion

A unified strength criterion is applied for penetration analysis of geo-materials. Based on the cylindrical cavity-expansion theory the relation between the radial traction on the cavity surface and the impact velocity of a rigid projectile is derived. The finial penetration depth of the projectile is analytically obtained and the effect of strength criterion on the penetration depth is investigated. By comparing with existing test results, it is found that the proposed penetration model is effective in the analysis of a rigid projectile penetrating into a semi-infinite geo-material target.

Finite Element Analysis of Dongjusi Railway Tunnel within Hard Rock Mass Based on the Unified Rock Mass Strength Criterion

The twin shear strength criterion has been proposed to consider the intermediate principal stress effect on the rock mass strength. The unified rock mass strength criterion could consider the intermediate principal stress effect on the rock mass strength. The unified rock mass elasto-plastic material model is implemented in ABAQUS user interface. As a case for study, the stability analysis of Dongjusi railway tunnel within hard rock mass is studied using the unified rock mass strength material. For comparison, the Hoek-Brown empirical strength criterion is also chosen for the rock mass material modeling. The computation results show that the plastic zone calculated using the unified rock mass strength criterion is smaller than that using the Hoek-Brown empirical strength criterion. The railway tunnel lining structure is designed according to the unified rock mass strength criterion and greatly makes use of the rock mass potential strength, which decreases engineering cost.

Reliability Analysis of Railway Tunnel Construction Process within Soft and Weak Rock Mass Using the Unified Elasto-Plastic Strength Criterion

Variability in the physical properties of rock mass is a major source of uncertainty encountered in railway tunnel stability analysis. The conventional safety factor method on stability assessment of railway tunnel within soft and weak rock mass can not represent the variability of rock mass. A formulation to compute the reliability of soft and weak rock mass, in which physical non-linearity is taken into account, is proposed. To consider the intermediate principal stress effect on the rock mass strength, the unified elasto-plastic strength criterion is proposed in the nonlinear finite element analysis. The unified rock mass elasto-plastic material model is implemented in ABAQUS user interface. The reliability analysis is performed in two steps. Firstly, the failure response is obtained by fitting the limit state function of the rock mass using the quadratic polynomial based on the nonlinear finite element analysis of the rock mass. Secondly, the JC method is proposed to obtain the design point and the reliability index of rock mass. As a case for study, the reliability analysis of Jinhuashan railway tunnel within soft and weak rock mass is studied using the proposed method. The two dimensional analysis is performed to consider the excavation stage effect and the unloading effect on the rock mass. Computation result shows that the rock mass is in stability.

Unified solution of limit loads of thick wall cylinder subject to external pressure considering strain softening

Based on the unified strength theory [1], a unified strength criterion for strain softening materials, such as concrete or rock, was derived, and the elastic and plastic limit loads of a thick-walled cylinder made of these materials subject to external pressure were also given. In addition, the influence of some factors on the limit loads of such cylinders as the ratio of the external radius to internal radius, r b/r a, the coefficient b, which reflects the effect of medium principal stress and the normal stress of the relevant surface on the material destroy degree, the ratio of tensile strength to compressed strength of the material, α, and the damage variable β were discussed in detail. Some examples were given and some meaningful results were obtained.