The shear failure of intact rock under thermo-mechanical (TM) coupling conditions is common, such as in enhanced geothermal mining and deep mine construction. Under the effect of a continuous engineering disturbance, shear-formed fractures are prone to secondary instability, posing a severe threat to deep engineering. Although numerous studies regarding three-dimensional (3D) morphologies of fracture surfaces have been conducted, the understanding of shear-formed fractures under TM coupling conditions is limited. In this study, direct shear tests of intact granite under various TM coupling conditions were conducted, followed by 3D laser scanning tests of shear-formed fractures. Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress, whereas it is negatively correlated with the temperature. The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature. The anisotropy, roughness value, and height of the asperities on the fracture surfaces are reduced as the normal stress increases, whereas their variation trends are the opposite as the temperature increases. The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensile–shear and shear failures. As the normal stress increases, intragranular fractures are developed ranging from a local to a global distribution, and the macroscopic failure mode of intact granite changes from mixed tensile–shear to shear failure. Finally, 3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed, and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

Hydraulic fracturing is frequently used to increase the permeability of rock formations in energy extraction scenarios such as unconventional oil and gas extraction and enhanced geothermal systems (EGSs). The present study addresses uncertainties in the hydraulic fracturing process pertaining to EGSs in crystalline rock such as granite. Specifically, there is debate in the literature on the mechanisms (i.e. tensile and/or shear) by which these fractures initiate, propagate, and coalesce. We present experiments on Barre granite with pre-cut flaws where the material is loaded to high far-field stresses close to shear failure, and then the fluid pressure in the flaws is increased to move the Mohr's circle to the left and observe the initiation and propagation of fractures using high-speed imaging and acoustic emissions (AEs). We find that the hydraulic fractures initiate as tensile microcracks at the flaw tips, and then propagate as a combination of tensile and shear microcracks. AE focal mechanisms also show elevated levels of tensional microfracturing near the flaw tips during pressurization and final failure. We then consider a numerical model of the experimental setup, where we find that fractures are indeed likely to initiate at flaw tips in tension even at relatively high far-field stresses of 40 MPa where shear failure is generally expected.

The paper investigates the long-term seismic behaviour of an underground reinforced concrete (RC) metro tunnel in Santiago, Chile, considering the combined effects of chloride-induced corrosion and cumulative, low-amplitude seismic shaking on the structure's performance. The soil-tunnel response is evaluated with the aid of transient, nonlinear finite element analysis using a two-dimensional (2D) plane strain numerical model that adopts advanced nonlinear models for the simulation of soil and concrete plasticity and the dynamic stiffness behaviour. The effects of corrosion deterioration are demonstrated in terms of time-dependent loss of rebar area and cover concrete stiffness and strength. The study illustrates the influence of ageing and repeated seismic shaking on lining deformation, crack development, and the modal characteristics of the intact and degrading systems. The results indicate that multiple low-amplitude events drive the non-degrading RC tunnel beyond its elastic regime without significant structural response consequences. A noticeable impact of corrosion deterioration on the structure's seismic performance is revealed, increasing with the number and intensity of earthquake events. Two different tunnel embedment depths are comparatively assessed. The analyses demonstrate larger co-seismic section convergence in the case of the deeper tunnel, yet a less pronounced effect of ageing and successive seismic loading compared to the shallow section, which is evident in the RC lining cracks at the end of shaking.

Effective elastic properties of porous media are known to be significantly influenced by porosity. In this paper, we investigated the influence of another critical factor, the inter-grain cementation stiffness, on the effective elastic properties of a granular porous rock (Bentheim sandstone) using an advanced numerical workflow with realistic rock microstructure and a theoretical model. First, the disparity between the experimentally tested elastic properties of Bentheim sandstone and the effective elastic properties predicted by empirical equations was analysed. Then, a micro-computed tomography (CT)-scan based approach was implemented with digital imaging software AVIZO to construct the 3D (three-dimensional) realistic microstructure of Bentheim sandstone. The microstructural model was imported to a mechanics solver based on the 3D finite element model with inter-grain boundaries modelled by cohesive elements. Loading simulations were run to test the effective elastic properties for different shear and normal inter-grain cementation stiffness. Finally, a relation between the macroscale Young's modulus and inter-grain cementation stiffness was derived with a theoretical model which can also account for porosity explicitly. Both the numerical and theoretical results indicate the influence of the inter-grain cementation stiffness, on the effective elastic properties is significant for porous sandstone. The calibrated normal and shear stiffnesses at the inter-grain boundaries are 1.2 × 105 and 4 × 104 GPa/m, respectively.

Common problems in engineering projects that involve artificial ground freezing of soil or rock include inadequate thickness, strength and continuity of artificial frozen walls. It is difficult to evaluate the freezing state using only a few thermometer holes at fixed positions or with other existing approaches. Here we report a novel experimental design that investigates changes in ultrasonic properties (received waveform, wave velocity Vp, wave amplitude, frequency spectrum, centroid frequency fc, kurtosis of the frequency spectrum KFS, and quality factor Q) measured during upward freezing, compared with those during uniform freezing, in order to determine the freezing state in 150 mm cubic blocks of Ardingly sandstone. Water content, porosity and density were estimated during upward freezing to ascertain water migration and changes of porosity and density at different stages. The period of receiving the wave increased substantially and coda waves changed from loose to compact during both upward and uniform freezing. The trend of increasing Vp can be divided into three stages during uniform freezing. During upward freezing, Vp increased more or less uniformly. The frequency spectrum could be used as a convenient and rapid method to identify different freezing states of sandstone (unfrozen, upward frozen, and uniformly frozen). The continuous changes in reflection coefficient rφ, refraction coefficient tφ and acoustic impedance field are the major reason for larger reflection and refraction during upward freezing compared with uniform freezing. Wave velocity Vp, wave amplitude Ah, centroid frequency fc and quality factor Q were adopted as ultrasonic parameters to evaluate quantitatively the temperature T of uniformly frozen sandstone, and their application within a radar chart is recommended. Determination of Vp provides a convenient method to evaluate the freezing state and calculate the cryofront height and frozen section thickness of upward frozen sandstone, with accuracies of 73.37%–99.23%.

Surface ground motion produced by underground blasts is significantly influenced by near-surface geological conditions. However, near-surface low-propagation velocity layers were always ignored in past analyses of ground motions due to their thin thickness. With the rising concern about surface ground motions produced by the ascendant scale and frequentness of underground excavation and mining, close attention is gradually paid to ground blast vibrations. Therefore, systemic experiments were conducted and took seven months in an underground mine to clarify the variation of motion from underground rock to surface ground. The attenuation of surface ground peak particle velocities (PPVs) is compared to that in underground rock, and horizontal amplitudes are compared to vertical amplitudes. Differences between bedrock and surface ground vibrations are analyzed to illustrate the site effect of near-surface lower-propagation velocity layers. One-dimensional site response analysis is employed to quantify the influence of different geological profiles on surface ground vibrations. The experimental data and site response analysis allowed the following conclusions: (1) geological site effects mainly produce decreasing dominant frequency (DF) of surface ground vibrations; (2) the site amplification effect of blast vibration needs to be characterized by peak particle displacement (PPD); (3) shear waves (S-waves) begin to dominate and surface Rayleigh waves (R-waves) develop as blast-induced ground vibrations travel upward through rock and lower-velocity layers to the surface. The comparison of response relative displacement to a critical value is best to assess the potential for cracking on surface structures.

This article presents the stresses at the center of a Brazilian disk (BD) for transversely isotropic rocks. It is shown that the solution of stresses at the center of an anisotropic disk is a function of the disk radius and the magnitude of applied load, as well as the material orientation with respect to the load axis and two dimensionless ratios with specific physical meanings and limitations. These two dimensionless parameters are the ratios of Young’s modulus and apparent shear modulus, although the ratio of apparent shear modulus will be eliminated if the Saint-Venant assumption is considered. Considerable finite element simulations are carried out to find the stresses at the disk center concerning the material orientation and the two dimensionless parameters. Also, an approximate formula obtained from analytical results, previously proposed in the literature for solving the tensile and compressive stresses at the disk center, is re-written and simplified based on these new definitions. The results of the approximate formula fitted to the analytical results are compared to those obtained from numerical solutions, suggesting a good agreement between the numerical and analytical methods. An approximate equation for the shear stress at the disk center is also formulated based on the numerical results. Finally, the influence of the assumptions for simplification of the proposed formula for the tensile, compressive, and shear stresses at the disk center is discussed, and simple and practical equations are proposed as estimations for the stresses at the center of the BD specimen for low to moderate anisotropic rocks. For highly anisotropic rocks, the reference plots can be used for more accuracy.

Based on fracture mechanics theory and wing crack model, a three-dimensional strength criterion for hard rock was developed in detail in this paper. Although the basic expression is derived from initiation and propagation of a single crack, it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic. Besides, it can be derived as Hoek–Brown criterion when the intermediate principal stress σ2 is equal to the minimum principal stress σ3 (Zuo et al., 2015). In addition, the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient, which could be described by an empirical function and verified by 10 kinds of hard rocks. Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level. As the effects of these two factors on the strength are opposite, the intermediate principal stress effect is induced.

This paper proposed the explicit generalized-α time scheme and periodic boundary conditions in the material point method (MPM) for the simulation of coseismic site response. The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh. The explicit generalized-α time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations. Firstly, the MPM was verified against finite element method (FEM). Secondly, ability of the MPM in capturing the analytical transfer function was investigated. Thirdly, a symmetric embankment was adopted to investigate the effects of ground motion arias intensity (Ia), geometry dimensions, and constitutive models. The results show that the larger the model size, the higher the crest runout and settlement for the same ground motion. When using a Mohr-Coulomb model, the crest runout increases with increasing Ia. However, if the strain-softening law is activated, the results are less influenced by the ground motion. Finally, the MPM results were compared with the Newmark sliding block solution. The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications, the importance of geometry characterization, and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

The effect of intermediate stress (in situ tunnel axial) on a strainburst is studied with a three-dimensional (3D) bonded block distinct element method (DEM). A series of simulations of strainbursts under true triaxial in situ stress conditions (i.e. high tangential stress, moderate intermediate stress and low radial stress) of near-boundary rock masses are performed. Compared with the experimental results, the DEM model is able to capture the stress-strain response, failure pattern and energy balance of strainbursts. The fracturing processes of strainbursts are also numerically reproduced. Numerical results show that, as the intermediate stress increases: (1) The peak strain of strainbursts increases, the yield stress increases, the rock strength increases linearly, and the ratio of yield stress to rock strength decreases, indicating that the precursory information on strainbursts is enhanced; (2) Tensile and shear cracks increase significantly, and slabbing and bending of rock plates are more pronounced; and (3) The stored elastic strain energy and dissipated energy increase linearly, whereas the kinetic energy of the ejected rock fragments increases approximately exponentially, implying an increase in strainburst intensity. By comparing the experimental and numerical results, the effect of intermediate stress on the rock strength of strainbursts is discussed in order to address three key issues. Then, the Mogi criterion is applied to construct new strength criteria for strainbursts by converting the one-face free true triaxial stress state of a strainburst to its equivalent true triaxial stress state. In summary, the effect of intermediate stress on strainbursts is a double-edged sword that can enhance the rock strength and the precursory information of a strainburst, but also increase its intensity.

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy (PPD) behavior and simulate surrounding rock deformation; however, simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms. This study developed a PPD model for rocks (rock masses) based on the Alejano–Alonso (A–A) dilatancy model. The developed model comprehensively reflects the influences of confining pressure (σ3) and plastic shear strain (γp), with the advantages of a simple mathematical form, while requiring fewer parameters and demonstrating a clear physical significance. The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A–A model, particularly for Witwatersrand quartzite and jointed granite. The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated, and the model was found to be more suitable for the soft and large-scale rocks, e.g. deep rock mass. The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass, and the developed semi-analytical solution was compared and verified with existing analytical solutions. The sensitivities of the rock dilatancy to γp and σ3 showed significant spatial variabilities along the radial direction of the surrounding rock, and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elastic–plastic boundary to the tunnel wall, thereby presenting the σ3-or γp-dominated differential effects of rock dilatancy. Tunnel deformation parabolically or exponentially increased with increasing in situ stress (buried depth). The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling, which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

Heterogeneous brittle geomaterials are highly susceptible to cyclic loads. They contain inherent flaws and cracks that grow under fatigue loads and lead to failure. This study presents a numerical model for analyzing fatigue in these materials based on the two-dimensional (2D) boundary element method and linear elastic fracture mechanics. The process is formulated by coupling the displacement discontinuity method with the incorporation technique of dissimilar regions and the governing equations of fatigue. The heterogeneous media are assumed to consist of materials with different properties, and the interfaces are assumed to be completely bonded. In addition, the domains include multiple cracks exposed to constant and variable amplitude cyclic loads. The stress intensity factor is a crucial parameter in fatigue analysis, which is determined using the displacement field around crack tips. An incremental crack growth scheme is applied to calculating the fatigue life. The growth rate values are employed to estimate the length of crack extension when there are multiple cracks. The interaction between cracks is considered, which also includes the coalescence phenomenon. Finally, various structures under different cyclic loads are examined to evaluate the accuracy of this method. The results demonstrate the efficiency of the proposed approach in modeling fatigue crack growth and life estimation. The behavior of life curves for the heterogeneous domain was as expected. These curves illustrate the breakpoints caused by utilizing discrete incremental life equations. At these points, the trend of the curves changed with the material properties and fatigue characteristics of the new material around the crack tips.

In this study, an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition. The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium, equilibrium of shear and normal stresses along discontinuities, boundary conditions, yield function, and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure. A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment (V–H–M) space. The results of this study are compared and validated against three different cases including an isotropic lateral loading, anisotropic end bearing capacity, and a pile embedded in an isotropic soil deposit under general loading condition. A parametric study is conducted to evaluate the impact of different influencing factors. It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads, whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Matric suction is an important state variable required for the assessment of unsaturated soil properties. Tensiometers are commonly used for direct matric suction measurement but have a limited measuring range up to 90 kPa due to the cavitation problem. Osmotic tensiometer (OT) can improve the measuring range of tensiometers by increasing the osmotic pressure of water to avoid the cavitation. However, the long-term water pressure decay that appeared in OTs caused a gradual decrease in their measuring range. In this study, crosslinked poly(acrylamide-co-acrylic acid) potassium salt (PAM-co-PAAK) was used for the preparation of OTs (five in total) to explore the mechanism of water pressure decay of OTs. The maximum water pressure in the OT versus the volume fraction of polymer filled in the OT was described based on the Flory-Huggins polymer theories and validated using WP4C dewpoint hygrometer. The long-term pressure decay of OT-1, OT-2, and OT-3 was observed for 130 d and constant pressures were found for OT-1 and OT-2, indicating that the pressure decay of OT was mainly caused by the stress relaxation of the polymer hydrogels, and standard linear solid (SLS) rheological model was appropriate to fit the decay data. For OT-1, OT-2 and OT-3, the theoretical osmotic pressure that was calculated based on the mass of retrieved polymer from OTs after 130-d pressure observation was higher than the actual osmotic pressure as observed, indicating that polymer leakage cannot explain the pressure decay of the OT. The ultraviolet–visible (UV–visible) spectrophotometry examined the change in polymer concentrations in the water containers of OT-4 and OT-5 and demonstrated that there was no increase in polymer leakage during the period of pressure decay of OT-4 and OT-5. As a result, the pressure decay of OT was not caused by polymer leakage. The results of this research suggested that the viscoelastic properties of polymers should be taken into consideration in further OT development.

Ultimate bearing capacity (UBC) is a key subject in geotechnical/foundation engineering as it determines the limit of loads imposed on the foundation. The most reliable means of determining UBC is through experiment, but it is costly and time-consuming which has led to the development of various models based on the simplified assumptions. The outcomes of the models are usually validated with the experimental results, but a large gap usually exists between them. Therefore, a model that can give a close prediction of the experimental results is imperative. This study proposes a grasshopper optimization algorithm (GOA) and salp swarm algorithm (SSA) to optimize artificial neural networks (ANNs) using the existing UBC experimental database. The performances of the proposed models are evaluated using various statistical indices. The obtained results are compared with the existing models. The proposed models outperformed the existing models. The proposed hybrid GOA-ANN and SSA-ANN models are then transformed into mathematical forms that can be incorporated into geotechnical/foundation engineering design codes for accurate UBC measurements.

Coral sand is widely encountered in coastal areas of tropical and subtropical regions. Compared with silica sand, it usually exhibits weaker performance from the perspective of engineering geology. To improve the geomechanical performance of coral sand and meet the requirement of foundation construction in coastal areas, a novel alkali activation-based sustainable binder was developed. The alkali-activated slag (AAS) binder material was composed of ground granulated blast-furnace slag (GGBS) and hydrated lime with the amendment of biochar, an agricultural waste-derived material. The biochar-amended AAS stabilized coral sand was subjected to a series of laboratory tests to determine its mechanical, physicochemical, and microstructural characteristics. Results show that adding a moderate amount of biochar in AAS could improve soil strength, elastic modulus, and water holding capacity by up to 20%, 70%, and 30%, respectively. Moreover, the addition of biochar in AAS had a marginal effect on the sulfate resistance of the stabilized sand, especially at high biochar content. However, the resistance of the AAS stabilized sand to wet-dry cycles slightly deteriorated with the addition of biochar. Based on these observations, a conceptual model showing biochar-AAS-sand interactions was proposed, in which biochar served as an internal curing agent, micro-reinforcer, and mechanically weak point.

Settlement prediction of geosynthetic-reinforced soil (GRS) abutments under service loading conditions is an arduous and challenging task for practicing geotechnical/civil engineers. Hence, in this paper, a novel hybrid artificial intelligence (AI)-based model was developed by the combination of artificial neural network (ANN) and Harris hawks’ optimisation (HHO), that is, ANN-HHO, to predict the settlement of the GRS abutments. Five other robust intelligent models such as support vector regression (SVR), Gaussian process regression (GPR), relevance vector machine (RVM), sequential minimal optimisation regression (SMOR), and least-median square regression (LMSR) were constructed and compared to the ANN-HHO model. The predictive strength, relalibility and robustness of the model were evaluated based on rigorous statistical testing, ranking criteria, multi-criteria approach, uncertainity analysis and sensitivity analysis (SA). Moreover, the predictive veracity of the model was also substantiated against several large-scale independent experimental studies on GRS abutments reported in the scientific literature. The acquired findings demonstrated that the ANN-HHO model predicted the settlement of GRS abutments with reasonable accuracy and yielded superior performance in comparison to counterpart models. Therefore, it becomes one of predictive tools employed by geotechnical/civil engineers in preliminary decision-making when investigating the in-service performance of GRS abutments. Finally, the model has been converted into a simple mathematical formulation for easy hand calculations, and it is proved cost-effective and less time-consuming in comparison to experimental tests and numerical simulations.

According to post-seismic observations, spectacular examples of engineering failures can be ascribed to the occurrence of sand liquefaction, where a sandy soil stratum could undergo a transient loss of shear strength and even behave as a “liquid”. Therefore, correct simulation of liquefaction response has become a challenging issue in geotechnical engineering field. In advanced elastoplastic models of sand liquefaction, certain fitting parameters have a remarkable effect on the computed results. However, the identification of these parameters, based on the experimental data, is usually intractable and sometimes follows a subjective trial-and-error procedure. For this, this paper presented a novel calibration methodology based on an optimization algorithm (particle swarm optimization (PSO)) for an advanced elastoplastic constitutive model. A multi-objective function was designed to adjust the global quality for both monotonic and cyclic triaxial simulations. To overcome computational problem probably appearing in simulation of the cyclic triaxial test, two interrupt mechanisms were designed to prevent the particles from wasting time in searching the unreasonable space of candidate solutions. The Dafalias model has been used as an example to demonstrate the main programme. With the calibrated parameters for the HN31 sand, the computed results were highly consistent with the laboratory experiments (including monotonic triaxial tests under different confining pressures and cyclic triaxial tests in two loading modes). Finally, an extension example is given for Ottawa sand F65, suggesting that the proposed platform is versatile and can be easily customized to meet different practical needs.