Modified true triaxial Hoek-Brown criterion considering intermediate principal stress effect

In order to improve the Hoek-Brown strength criterion not considering the influence of intermediate principal stress on rock strength, the evolutions of rock strength were investigated according to the results of the rock true triaxial compression test. The intermediate principal stress coefficient was introduced to quantify the effect on rock strength. Considering the relationships between the parameter of the Hoek-Brown strength criterion and the rock stress levels, the modified Hoek-Brown strength criterion for the true triaxial stress was then established with the Lagrange interpolation method. The spatial envelope characteristics of the modified strength criterion were analyzed. The best-fitting errors of seven rocks with true triaxial test results were finally compared with the three other three-dimensional strength criteria to verify the rationality of the modified strength criterion. The research results indicate that the rock strength increases gradually with the increase of minimum principal stress, and increases first and then decreases with the increase of intermediate principal stress, which presents a significant interval effect. The modified strength criterion not only has the advantage of the Hoek-Brown strength criterion in the nonlinear characteristics of the meridian plane but also describes the basic characteristics of rock strength in stress space. The spatial envelope surfaces for the modified strength criteria with the linear and quadratic interpolation are the non-equilateral hexagonal pyramidal surfaces and conical surfaces, which can meet the requirement of continuous smoothness in the tension-compression meridian plane interval. The modified strength criterion can better predict the true triaxial strength of rocks and reasonably reflect the influence of intermediate principal stress on the rock strength. The modified strength criterion with the quadratic interpolation improves the prediction accuracy of rock strength by about 1.2 to 2.0 times compared to the criterion with linear interpolation. The modified strength criterion has good agreement with the true triaxial test results of different hard and brittle rocks compared with other true triaxial strength criteria, which shows the applicability and reliability of the modified strength criterion

Elastoplastic Analysis of Circular Openings in Elasto-Brittle-Plastic Rock Mass Based on Logarithmic Strain

Rock-like materials, such as coal and soft rock, often manifest larger deformation features. The prediction values for displacement and failure region based on the commonly used small strain (SS) theory are generally larger than the field test results. Based on the Euler coordinate system, the logarithmic strain (LS) is employed to describe the actual deformation behavior. Both of the stresses and displacement of circular opening in elasto-brittle-plastic rock mass are formulated with differential equations. And a simple approach is proposed to solve the differential equations. The results show that the plastic radius depends on the elastic parameters, that is, Young’s modulus and Poisson’s ratio, which is different from SS theory. And the plastic radius and displacement of LS rock mass are smaller than those of SS rock mass, and the displacement of LS rock mass is absolutely smaller than the excavation radius. The proposed solutions can provide theoretical foundation for the optimization of supporting structure in underground engineering

Incompatible Deformation Model of Rocks with Defects around a Thick-Walled Cylinder

Before the excavation of underground engineering, joints, fissures, and voids already exist in the rock—that is, there are defects in the rock. Due to the existence of these defects, the rock produces plastic deformation, which can lead to incompatible deformation. Therefore, the classic continuum theory cannot accurately describe the deformation of the rock. In this paper, a relationship between the strain tensor and metric tensor was studied by analyzing the three states of elastic plastic deformation, and the elasto-plastic incompatible model was built. Additionally, the stress and deformation of a thick-walled cylinder under hydrostatic pressure was investigated by using a finite element program written in the FORTRAN language. The results show that the plastic strain is associated with not only deviator stress but also the distribution of defects (represented by the incompatible parameter R). With the value of R increasing, the defects in the rock increased, but the elastic plastic stiffness matrix decreased. Thus, as more rock enters the plastic state, the deformation of the surrounding rock is enlarged

Breakage Mechanism of Layered Sandstone Penetrated by TBM Disc Cutter

In this paper, the breakage mechanism of layered sandstone subjected to the TBM disc cutter was investigated. A series of typical layered sandstone specimens were prepared for true triaxial compression tests in the laboratory to simulate the disc cutter action at the tunnel face, and an acoustic emission (AE) system was used to monitor the breaking process during the penetration tests. Furthermore, a DV recorder was employed to capture the surface deformation. Then, the failure specimens were scanned by high resolution X-ray micro-CT. The results show that the failure mode of layered sandstone in terms of cracking transforms into local crushing with increasing confining stress. The propagation pattern of the cracks varies with the bedding inclination, which is distinctly different from intact rock. The results also indicate that the peak force presents linear variation with the confining stress and an increasing trend with the bedding inclination at the first penetration, and the failure mode of the second penetration is mainly related to the broken status from the first penetration

Study on the Static and Dynamic Fracturing Properties of Marble after Being Damaged Dynamically

A split Hopkinson pressure bar (SHPB) system was first used to perform the cyclic impact loading tests on notched semicircular bend (NSCB) marble specimens. Then, static and dynamic three-point bending tests were conducted on these dynamically damaged specimens, respectively. In the cyclic impact loading tests, the dynamic elastic modulus decreases gradually as the impact number increases, but dynamic cumulative damage exhibits a growing trend. In the static and dynamic three-point bending tests, when dynamic cumulative damage is less than 0.345, the dynamic fracture toughness values are larger than the static fracture toughness values, but the experimental data exhibit the opposite results when dynamic cumulative damage ranges from 0.345 to 0.369. Through the quantitative analysis of fracture surface morphologies, the roughness and area of the fracture surfaces increase with an increasing dynamic cumulative damage. Under the same dynamic cumulative damage of the specimens, both the roughness and area of the surfaces fractured by static three-point bending are larger than those fractured by dynamic three-point bending

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results. The improved model assumes that total strain is a combination of plastic, elastic, and crack strains. The constitutive relationship between the crack strain and the stress was further derived. The evolutions of mechanical parameters, i.e. strength parameters, dilation angle, unloading elastic modulus, and deformation parameters of crack, with the plastic strain and confining pressure were studied. With the increase in plastic strain, the cohesion, friction angle, dilation angle, and crack Poisson's ratio initially increase and subsequently decrease, and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease. The increasing confining pressure enhances the strength and unloading elastic modulus, and decreases the dilation angle and Poisson's ratio of the crack. The theoretical triaxial compressive stress-strain curves were compared with the experimental results, and they present a good agreement with each other. The improved constitutive model can well reflect the nonlinear mechanical behavior of granite

Experimental Study on the Characteristics and Formation Mechanism of Dynamic Filter Cake for Slurry Shield Tunneling

The key to guaranteeing excavation face stability in slurry shield tunneling is the formation of an impermeable dynamic filter cake. At the same time, the effect of the cutter head and rotation speed should be taken into account. We studied the characteristics and formation mechanism of the dynamic filter cake using a newly developed experimental apparatus. The experiment results show that the hysteretic infiltration zone appeared in the curves of stepped loading filtration while the cutter head was rotating, and the volume of water filtration increased by 11.2% compared to when the cutter head stopped. The higher the rotation speed was, the lower the conversion rate of the effective stress was. Under the same rotation speed, the formation time of the 6-cutter arm was almost 5 s slower than that of the 5-cutter arm. As the cutter arms and the rotation speed increased, the stratum’s electrical conductivity increased and stabilized at a distance of 20 cm from the cutter head. The filter cake transited from ‘filter cake plus an infiltration zone’ to ‘an infiltration zone without a filter cake’ with the increase of the rotation speed. The thickness of the dynamic filter cake was smaller than that of the static filter cake, the thickness of 10 groups decreased significantly, and the average thickness decreased by 76.15% at 1.0 rpm. The mesoscopic formation process of the dynamic filter cake can be divided into six stages. This study revealed the slurry penetration mechanism and filter cake characteristics present under cyclic damage by the shield cutter head to the filter cake and soil and provided theoretical support on how to maintain the stability of the excavation face during slurry shield tunneling