Influence Of Intermediate Principal Stress Research Articles

Estimation of Active Earth Pressure Against Rigid Retaining Walls Considering Soil Arching Effects and Intermediate Principal Stress

Abstract In this study, a novel analytical approach is proposed for the calculation of active earth pressure on rigid retaining walls considering the influence of intermediate principal stress and ...

Limit Analysis of Basal Heave Stability in Unsaturated Soils Based on the Unified Strength Theory

An evaluation method was presented on the basal heave stability in unsaturated soils. A basal heave failure mechanism was established wherein the admissible velocity field was constructed in the light of the Prandtl failure mode. The shear strength theory based on two independent stress state variables was employed for unsaturated soils. The unified strength theory was introduced to account for the influence of intermediate principal stress. Analytical solution of safety factor (Fs) was then deduced based on the upper bound theory of limit analysis, and relevant numerical solutions were solved by means of the strength reduction method. It is found from parametric analysis that the intermediate principal stress and matric suction have a significant impact on Fs. Specifically, Fs is seriously underestimated if they are ignored. The theoretical framework in this work provides a new idea for analyzing the basal heave stability of unsaturated soils.

Influence of intermediate principal stress on the mechanical properties of rocks containing fractures

The excavation fracture zones develop during the staged excavation of caverns and tunnels, which still have bearing capacity. However, further excavation and support activities will change the stress state in these areas until these activities cease. The influence of intermediate principal stress, σ2, on the strength and deformation characteristics of the surrounding rocks is not clear. In this paper, multi-step true triaxial tests are carried out on rock specimens containing stress-induced fractures to investigate the influence of σ2 on the mechanical properties of these specimens. The experimental results show that Young's modulus decreases with decreasing σ2, while the ratios of deformation in the two lateral directions increase. However, due to the fractures induced by true triaxial stress parallel to σ2, this fractured rock strength is not influenced by σ2, so a strength criterion that does not consider σ2 effect should be adopted in this failure pattern. This study deepens the understanding of the deformation and the bearing capacity of surrounding rocks.

Theoretical Analysis on Soil Pressure Acting on End-Suspended Pile Supporting Structure to Foundation Pit in Soil-Rock Mixed Stratum

By taking Sanshandao Gold Mine Foundation Pit Supporting Project as an example, targeting at the end-suspended pile supporting structure applied in soil-rock mixed stratum common in mountainous and hilly area, this paper introduces unified strength theory and revised Hoek-Brown strength criterion to calculate and analyze active soil pressure, passive soil resistance and overall stability of supporting structure, during which not only the influence of intermediate principal stress, but also the influence of structural surface, weathering degree and disturbing degree of the rock can be taken into consideration. Therefore, theoretically speaking, it is much more scientific than traditional soil pressure theory, and the results are closer to actual engineering properties, thus being of critical theoretical significance and engineering reference value to perfecting design calculation theory of end-suspended pile supporting structure and optimizing design of foundation pit supporting structure.

Multilaminate Mathematical Framework for Analyzing the Deformation of Coarse Granular Materials

Abstract Coarse granular materials such as railway ballast and rockfill are often subjected to three-dimensional (3D) stress conditions including the influence of intermediate principal stress. Mod...

Influence of the unified strength theory parameters on the failure characteristics and bearing capacity of sand foundation acted by a shallow strip footing

The unified strength theory can account for the influence of intermediate principal stress using a specified parameter b, with which the determination of the values and influences of b is significant. In this research, a physical model test was carried out in combination with the numerical simulations to explore the effect of b on a sand foundation loaded by a shallow strip footing. Variation of parameter b would produce significant effect on the deformation characteristics, stress response, failure model, as well as bearing capacity of the sand foundation. In general, a larger b could be adopted to yield smaller magnitudes of stress. The calculated ultimate bearing capacity Pult increases linearly with increase in b, and an increment of 470% can be obtained using b = 1.0 relative to b = 0.0. The comparison of the bearing capacities of physical model test and numerical simulation suggests that b = 0.89–0.99 is the appropriate value for the experimental sand foundation, that ultimately results in a capacity increase in 420%–465% relative to the result of Mohr–Coulomb failure law.

Analysis on Loose Circle of Surrounding Rock of Large Deformation Soft‐Rock Tunnel

With the rapid development of tunnel construction in China, deep buried and long tunnel projects are emerging in areas with complex engineering geological conditions and harsh environment, and thus large deformation of tunnels under conditions of high in situ stress and soft rock becomes increasingly prominent and endangers engineering safety. Therefore, it is of great significance to control the deformation and improve the stability of surrounding rock by analyzing the thickness and distribution law of loose circle according to the unique mechanical properties and failure mechanism of surrounding rock of large deformation soft‐rock tunnel. Based on unified strength theory, this paper deduces the radius calculation formula of the loose circle by considering the influence of intermediate principal stress. Furthermore, the theoretical calculations and field tests of the loose circle in the typical sections of grade II and III deformation of Yuntunbao tunnel are carried out, and the thickness and distribution law of loose circle of surrounding rock of large deformation soft‐rock tunnel is revealed. The results show that the formula based on the unified strength criterion is applicable for a large deformation tunnel in soft rock.

Analysis of Three‐Dimensional Damage Constitutive Model of Frozen Sand Based on the Influence of Intermediate Principal Stress and Temperature

To study the mechanical properties of frozen soil, it is necessary to understand the damage characteristics of frozen soil. Four types of three‐dimensional indoor tests of frozen sand were carried out at −5°C, −10°C, and −15°C to study the mechanical damage properties. These include different stress path tests with the principal stress coefficients of 0, 0.25, 0.5, and 0.75 while analyzing the entire failure process. First, the three‐dimensional compression test of frozen sand was studied to analyze the influence of temperature and intermediate principal stress coefficient on the large principal stress of frozen soil. The damage cost of frozen sand under the influence of different temperatures and intermediate principal stress coefficients was also established. Second, using the characteristics of discreteness and randomness of the distribution of the microelements inside the frozen soil and assuming that the failure of the microelement of the frozen soil obeys the Weibull distribution, the Drucker–Prager strength criterion was used as the statistical distribution variable of the microelement of the frozen soil based on the strain equivalence hypothesis, statistical theory, and continuous damage mechanics. This allows for a constitutive model of frozen sand damage under the three‐dimensional stress state to be established. Finally, the model parameter values through low‐temperature three‐dimensional test data were able to be determined. This model allows for the physical meaning of Weibull distribution parameters F0 and m to be analyzed, and the distribution parameters with temperature and intermediate principal stress coefficient can be modified to obtain a modified frozen sand damage constitutive model. The results show that the modified damage constitutive model can simulate the entire process curve of the large principal stress‐strain of frozen sand. It shows that the large principal stress of frozen sand increases with the increase of temperature and intermediate principal stress coefficient. Concurrently, the frozen sand damage constitutive model proposed in this paper can describe the deformation behavior of frozen soil under different temperature and stress paths and can be adapted to various other sediment types.

Effect of the intermediate principal stress on hydraulic fracturing in granite: an experimental study

The fracturing behavior of hard rock under fluid pressure is affected by maximum, minimum, and intermediate principal stress. To investigate the effect of the intermediate principal stress on the hydraulic fracturing behavior, including the fracturing pressure, fracture pattern, fluid pressure evolution, etc., a series hydraulic fracturing experiments of granite under true triaxial compression conditions was conducted. Constant minor and major principal stresses (10 and 30 MPa, respectively) and variational intermediate principal stresses (10, 15, 20, and 25 MPa) were considered. Acoustic emission was used to monitor the hydraulic fracturing process. The effect of different intermediate principal stresses, i.e., various horizontal principal stresses, on the fluid fracturing pressure and failure pattern was studied. With higher intermediate principal stress, the hydraulic pressure fluctuates in the hydraulic fracturing process, whereas at lower intermediate principal stress, the pressure fluctuation phase becomes shorter. The higher intermediate principal stress makes the fracture plane simpler, straighter, and more planar. When the intermediate principal stress equals to the minimum principal stress, the fracture plane tends to be non-planar. In this case, the hydraulic fracture is mainly influenced by heterogeneity of the rocks. With the increase of intermediate principal stress, the formation breakdown pressure of granite decreases, which is different from the effect of minor principal stress. A modified criterion is proposed to reflect the influence of intermediate principal stress on the formation breakdown pressure.

Influence of initial state and intermediate principal stress on undrained behavior of soft clay during pure principal stress rotation

It is important to be fully aware of the dynamic characteristics of saturated soft clays under complex loading conditions in practice. In this paper, a series of undrained tests for soft clay consolidated with different initial major principal stress direction ξ were conducted by a hollow cylinder apparatus (HCA). The clay samples were subjected to pure principal stress rotation as the magnitudes of the mean total stress p, intermediate principal stress coefficient b, and deviator stress q were all maintained constant. The influences of intermediate principal stress coefficient and initial major principal stress direction on the variation of strain components, generation of pore water pressure, cyclic degradation and non-coaxiality were investigated. The experimental observations indicated that the strain components of specimen were affected by both intermediate principal stress coefficient and initial major principal stress direction. The generation of the pore water pressure was significantly influenced by intermediate principal stress coefficient. However, the generation of pore water pressure was merely influenced by initial major principal stress direction when b = 0.5. It was also noted that the torsional stress–strain relationships were affected by the number of cycles, and the effect of intermediate principal stress coefficient and initial major principal stress direction on the torsional stress–strain loops were also significant. Stiffness degradation occur under pure principal stress rotation. Anisotropic behavior resulting from the process of inclined consolidation have considerable effects on the strain components and non-coaxial behavior of soft clay.

A Novel Polyaxial Strength Criterion for Rock Materials Under General Stress Condition

Yielding or failure of rocks under the action of external loading is complicated due to the dependence on pressure sensitivity and Lode angle. In this study, a generalized hyperbolic strength criterion is proposed to describe the strong nonlinear characteristics of rocks over a wide range of confining pressures. The relationship between failure stress and instantaneous friction angle of rocks is analyzed based on nonlinear Mohr strength envelope. In order to reflect the influence of intermediate principal stress on the strength of rock materials, the generalized hyperbolic criterion has further been extended to complicated stress state. The failure criterion allows the possibility of transitions from an equilateral triangle to circle, which greatly improves the durability and applicability to describe the strength characteristics of various rocks under complicated stress state. The validity of the proposed criterion is verified by comparing predictions with experimental results of rocks.

A New Triaxial Apparatus Imposing Nonuniform Shearing for Deep Learning of Soil Behavior

Abstract Soil behavior is commonly characterized based on laboratory tests with imposed or assumed uniform stress and strain distribution within a given soil specimen for convenient data reduction. This uniformity assumption limits the interpretation of each test to a single stress-strain path, and therefore, extensive laboratory testing is required to represent field soil behavior under a broad range of loading paths. This article presents the development of a modified, next-generation, triaxial device (NG-TX) to generate multiple loading paths in a single test that can be interpreted using an evolutionary deep-learning inverse analysis. This device inherits all features of a conventional triaxial test and adds lateral restraint clamps to increase nonuniformity in specimen deformation, combined with a digital photogrammetry system to measure the 3-D deformed shape of the specimen. The design of the restraint clamps was optimized using numerical simulations, which showed that the sheared specimen includes shear modes that cannot currently be mobilized with available testing devices. By coupling SelfSim, a deep-learning algorithm, with the modified triaxial device (NG-TX), the shear behavior of Ottawa sand was extracted. The SelfSim-extracted Neural Network material models were able to successfully capture the global behavior of each test and extract the nonuniform stress-strain behavior from within the specimens. The interpreted stress paths cover broad portions of stress space that current laboratory tests cannot cover. The stress-strain behavior is interpreted in terms of the mobilized secant friction angle using 2-D and 3-D failure criteria. The mobilized secant friction angle interpretation shows better agreement with empirically developed envelopes when computed along the octahedral plane accounting for the influence of intermediate principal stress.

Thermo-elastoplastic Model for Soft Rock Considering Effects of Structure and Overconsolidation

In this study, a critical state-based thermo-elastoplastic model for soft rock is proposed. The model is able to describe the basic mechanical behavior of soft rock such as strain-hardening, strain-softening and the influence of intermediate principal stress, but also temperature dependency with a unified set of parameters. In the model, concepts of subloading and superloading are introduced to describe the influence of overconsolidation and structure on the deformation and strength of soft rock. The influence of intermediate principal stress is also properly taken into consideration by adopting a transformed stress tensor tij. In order to consider the temperature effect, a thermo-induced equivalent stress is proposed to consider the influence of temperature on yield surface, evolution of overconsolidation and structure during shearing. By comparing the calculated results with test results under different loading and temperature conditions, the availability and the accuracy of the proposed model are carefully investigated. Finally, the performance of the proposed model is discussed with a series of parametric studies in detail.

Characteristic Stress Levels and Brittle Fracturing of Hard Rocks Subjected to True Triaxial Compression with Low Minimum Principal Stress

In this study, true triaxial compression tests were carried out on three types of hard rocks (i.e., granite, marble and sandstone) using rectangular prismatic specimens (50 × 50 × 100 mm3) with low minimum principal stress σ3, and various intermediate principal stresses σ2. The main purposes were to establish the relationship between the characteristic stress levels (i.e., crack initiation stress, crack damage stress and peak stress) and the corresponding principal stresses and to investigate the brittle fracturing process of hard rocks near excavation boundaries. The test results indicated that the stress–strain curves were primarily characterized by the linear-elastic–brittle behavior. The failure planes of the specimens in the tests were found to be adjacent to the σ3 loading surface, and almost parallel to the σ1–σ2 plane, which were analogous to the spalling of the surrounding rock. With the aid of scanning electron microscopy, it was shown that cleavage fractures accounted for the majority of the fracture morphology in the sandstone specimens. Two revised methods were developed to determine the crack initiation stress of hard rocks under true triaxial compression, and these characteristic stress levels could be appropriately fitted by utilizing both the parabolic and power functions. Although the power function achieved better fitting results, the parameters in the parabolic function could be associated with the tensile cracks induced during the loading process. The influence of intermediate principal stress on the strength, deformation and failure was significant. In addition, the brittle fracturing process could be illustrated by the crack-induced strains in three principal stress directions.

A Novel True Triaxial Apparatus for Studying the Time-Dependent Behaviour of Hard Rocks Under High Stress

The study introduced a true triaxial testing apparatus for conducting time-dependent experiments on hard rocks under high stress. The apparatus consists of two-rigid loading platens to apply the maximum and intermediate principal stresses, and a flexible loading system with which to apply the minimum principal stress, under constant-temperature control. It includes a simple sample-installation system, an acoustic emission acquisition system, data acquisition system, and a software interface. The novel apparatus overcomes the long-term eccentric loading problem faced when testing rock samples using a biaxial double-closed-loop servo-control mode. In addition, using an integrated structural design, the stiffness of the apparatus was increased, which was conducive to improving the data precision obtained in small-scale deformation experiments involving hard, stiff, or strong, rock samples. It also provides the possibility of studying the post-peak time-dependent behaviours of hard rocks under high stress. To verify the advantages of this apparatus and investigate the influence of intermediate principal stress on the time-dependent behaviour of hard rock, this study demonstrated the experimental methods and results for pre- and post-peak time-dependent of hard rock under true triaxial compression. The experimental results showed that intermediate principal stress exerted a significant influence on the time-dependent behaviour, and long-term deformation and strength, of hard rocks: post-peak fractured rocks still exhibited a certain time-dependent strength. The results also validated the reliability of this true triaxial time-dependent apparatus.

Modification of Mohr's criterion in order to consider the effect of the intermediate principal stress

Mohr-Coulomb (M-C) criterion is widely used for isotropic brittle materials, although it has some disadvantages which limit its wider application. One important disadvantage of this theory is that it ignores the effect of the intermediate principal stress, although it has an important influence on materials behaviour. Therefore, Mohr-Coulomb theory is actually used only for materials in biaxial state of stress. In this paper, a modified form of Mohr's criterion has been suggested, in order to overcome this limitation. The modified criterion takes into account the influence of intermediate principal stress in the case of materials under triaxial loading conditions. On the basis of two new hypotheses, a real triaxial state of stress is replaced by a virtual biaxial state of stress. The above mentioned stress states are considered to be equivalent for a material when the failure is imminent in both cases. Both Mohr's theory and the concept of equivalence of stress states are combined in order to obtain the virtual biaxial state of stress, which is determined using all three principal stresses. The modified Mohr's theory can be used only for triaxial state of stress. For biaxial and uniaxial state of stress it is reduced to the classical one. The proposed hypotheses have an important advantage because does not require additional material coefficients. The calculated values using the virtual biaxial state of stress and the linear M-C criterion are in good agreement with experimental data for grey cast iron. The article also presents a compact statistical analysis for both stresses and errors, in order to objectively assess the effectiveness of the formulated hypotheses.

Influence of Intermediate Principal Stress and Principal Stress Direction on Drained Behavior of Natural Soft Clay

Influence of Intermediate Principal Stress and Principal Stress Direction on Drained Behavior of Natural Soft Clay

A Mogi-Type True Triaxial Testing Apparatus for Rocks With Two Moveable Frames in Horizontal Layout for Providing Orthogonal Loads

The Mogi-type true triaxial apparatus (TTA) for rocks provides numerous advantages in terms of complexity, loading capacity, permeability measurement, and cost. However, the spring support design limits the improvements to the loading capacity and stiffness of the vertical frame, which are essential in acquiring the complete stress-strain behavior of relatively large specimens. In this paper, a new TTA achieved by modifying the original Mogi-type design with two moveable frames in a horizontal layout is developed. In addition to the design of stiffer frames with low moving resistance, such a modification provides convenience for experimental operation. Moreover, a positioning device built in the triaxial vessel enables the accurate placing of the specimen. Technical details, including off-center loading, end friction effect, and strain measurement are carefully examined. Calibration and repeatability tests show that the apparatus is stable and reliable. The apparatus is used to conduct tests to examine the influence of intermediate principal stress on the mechanical behaviors of marble. The results demonstrate that, in addition to strength, some other characteristics, including brittleness, fracture angle, volumetric modulus, and stress at the onset of dilatancy of marble also increase initially, but subsequently decrease with an increase of intermediate principal stress. The measurement of the permeability of mudstone during compression reveals that the increase in permeability is closely related to the dilatancy of the mudstone.

Limit Analysis of Unsaturated Soil Slope Stability Considering Intermediate Principal Stress and Strength Nonlinearity

Natural and man-made slopes are mostly in unsaturated soils, and the saturated or dry condition is just a particular case. This paper investigates the stability of unsaturated soil slopes. The influence of intermediate principal stress is considered by introducing the unified shear strength formulation, and the strength nonlinearity of unsaturated soils is addressed by means of two different methods. Based on the upper bound theorem of limit analysis, analytical expressions of the critical height of slope are deduced. Relevant numerical solutions are obtained through optimization and parametric analysis is then conducted. It is found that: the critical height of slope increases with the increase of UST parameter b or matric suction, while it decreases with the increase of slope angles. Besides, as regards the strength nonlinearity, it’s suggested to adopt Method II when parameter $$m$$ can be reasonably determined.

Nonlinear Visco-Elasto-Plastic Model for Surrounding Rock Incorporating the Effect of Intermediate Principal Stress

This paper focuses on the influence of intermediate principal stress on visco-elasto-plastic solution of surrounding rock. Assuming that the surrounding rock satisfies the spatially mobilized plane (SMP) failure criterion, the H-Kelvin model was adopted and improved by considering the effect of intermediate principal stress. For elasto-plastic surrounding rock, an analytical approach was presented. For strain-softening surrounding rock, the potential plastic zone was subdivided into a finite number of concentric annuli and a numerical model for calculating the stress and displacement of each annulus was presented. Thus, based on SMP failure criterion and the improved H-Kelvin model, the nonlinear visco-elasto-plastic models considering the effect of intermediate principal stress were proposed for elasto-plastic and strain-softening surrounding rock, respectively. The accuracy of the proposed approaches were validated with the published results. Comparisons show that the long-term creep deformation based on M-C failure criterion is 9.4 mm which is 34.3% greater than the results of SMP failure criterion. Taking the safety factor as 1.5, the proposed model is applied in predicting the long-term deformation of Shangxinzhai Tunnel, the deformation is calculated to be 8.5 cm which is 29.2% smaller than the designed value.