A Simple Three-Dimensional Failure Criterion for Jointed Rock Masses under True Triaxial Compression

The joint configuration and the intermediate principal stress have a significant influence on the strength of rock masses in underground engineering. A simple three-dimensional failure criterion is developed in this study to predict the true triaxial strength of jointed rock masses. The proposed failure criterion in the deviatoric and meridian planes adopts the elliptic and hyperbolic forms to approximate the Willam–Warnke and Mohr–Coulomb failure criterion, respectively. The four parameters in the proposed failure criterion have close relationships with the cohesion and the internal friction angle and can be linked with the joint inclination angle using a cosine function. Two suits of true triaxial strength data are collected to validate the correctness of the proposed failure criterion. Compared with other failure criteria, the proposed failure criterion is more reasonable and acceptable to describe the strength of jointed rock masses.

Unloading Mechanics and Energy Characteristics of Sandstone under Different Intermediate Principal Stress Conditions

The TRW-3000 true triaxial rock testing machine was used to conduct loading and unloading tests of sandstone under different σ 2 , and the true triaxial lateral unloading mechanics and energy characteristics of sandstone under different σ 2 were studied. The experimental results show the following: (1) compared with the results of the loading test, the peak strength of the sandstone under the unloading σ 3 path is reduced, the unloading direction has obvious expansion and deformation, and the amount of expansion increases significantly with the increase of σ 2 ; sudden brittle failure occurs at the end of unloading. E gradually decreases with the increase of H, and it performs well to use the cubic polynomial to fit the curve of E-H. (2) The Mogi–Coulomb strength criterion can accurately describe the true triaxial strength characteristics of sandstone under loading and unloading conditions. Compared with the results of the loading test, the values of c and φ obtained based on this criterion under the unloading σ 3 path are reduced. (3) Under the condition of unloading σ 3 , U, U e , and U d , when the specimen is broken, are all linearly positively correlated with σ 2 . U d increases nonlinearly with the increase of H, and as σ 2 increases, the slope of the U d -H curve becomes larger, and the specimen consumes more energy under the same unloading amount. Most of the energy absorbed by the specimen under the unloading σ 3 path is converted into U e , but as σ 2 increases, U d / U increases, and the energy consumed when the specimen is broken is greater.

Assessment of strength and deformation of lightweight concrete and its components under triaxial compression, taking into account the macrostructure of the material

The paper presents the results of experimental studies on the strength and deformations of lightweight concrete, mortar matrix and hardened cement paste under triaxial compression. Tests on samples were carried out using short-term triaxial proportional σ1 > σ2 = σ3 loading (i.e. axial compression + lateral hydrostatic pressure). During the loading, the ratio of the main stresses (both axial and lateral) was kept constant up to the end of tests. The experimental studies were carried out for different low ratios of σ2/σ1. A theoretical estimation has been discussed to approximate experimental results and prediction of triaxial strength values for different types of lightweight concrete. An estimation of the confining pressure parameter K has been done for the used mode of loading.

Triaxial Strength Criteria in Mohr Stress Space for Intact Rocks

Conventional triaxial strength criteria are important for the judgment of rock failure. Linear, parabolic, power, logarithmic, hyperbolic, and exponential equations were, respectively, established to fit the conventional triaxial compression test data for 19 types of rock specimens in the Mohr stress space. Then, a method for fitting the failure envelope to all common tangent points of each two adjacent Mohr’s circles (abbreviated as CTPAC) was proposed in the Mohr stress space. The regression accuracy of the linear equation is not as good as those of the nonlinear equations on the whole, and the regression uniaxial compression strength (σc)r, tensile strength (σt)r, cohesion cr, and internal frictional angle φr predicted by the regression linear failure envelopes with the method for fitting the CTPAC in the Mohr stress space are close to those predicted in the principal stress space. Therefore, the method for fitting CTPAC is feasible to determine the failure envelopes in the Mohr stress space. The logarithmic, hyperbolic, and exponential equations are recommended to obtain the failure envelope in the Mohr stress space when the data of tensile strength (σt)t are or are not included in regression owing to their higher R2, less positive x-intercepts, and more accurate regression cohesion cr. Furthermore, based on the shape and development trend of the nonlinear strength envelope, it is considered that when the normal stress is infinite, the total bearing capacity of rock tends to be a constant after gradual increase with decreasing rates. Thus, the hyperbolic equation and the exponential equation are more suitable to fit triaxial compression strength in a higher maximum confining pressure range because they have limit values. The conclusions can provide references for the selection of the triaxial strength criterion in practical geotechnical engineering.