The storage of hydrogen gas in lined rock caverns (LRCs) may enable the implementation of the first large-scale fossil-free steelmaking process in Sweden, but filling such storage causes joints in the rock mass to open, concentrating strains in the lining. The structural interaction between the LRC components must be able to reduce the strain concentration in the sealing steel lining; however, this interaction is complex and difficult to predict with analytical methods. In this paper, the strain concentration in LRCs from the opening of rock joints is studied using finite element (FE) analyses, where the large- and small-scale deformation behaviors of the LRC are coupled. The model also includes concrete crack initiation and development with increasing gas pressure and rock joint width. The interaction between the jointed rock mass and the reinforced concrete, the sliding layer, and the steel lining is demonstrated. The results show that the rock mass quality and the spacing of the rock joints have the greatest influence on the strain distributions in the steel lining. The largest effect of rock joints on the maximum strains in the steel lining was observed for geological conditions of “good” quality rock masses.

The study of clastic rock failure evolution under true triaxial stress is an important research topic; however, it is rarely studied systematically due to the limitation of monitoring technology. In this study, true triaxial compression tests were conducted on clastic rock specimens to investigate the effect of cementation and intermediate principal stress (σ2) on the failure mechanism. The complete stress–strain curves were obtained, while the acoustic emission (AE) was monitored to indirectly evaluate the evolution of tensile and shear cracks, and crack evolution under true triaxial compression was imaged in real time by a high-speed camera. The results showed that the deformation and failure characteristics of clastic rock were closely related to the cementation type and intermediate principal stress. On the basis of the distribution characteristics of the ratio of rise time to amplitude (RA) and the average frequency (AF) of AE signals, tensile cracks of the contact cementation specimen propagated preferentially. Meanwhile, the enhancement of specimen cementation promoted the evolution of shear cracks, and the increase in σ2 promoted the evolution of tensile cracks. Moreover, the mesoscale cracking mechanism of clastic rock caused by cementation and σ2 under true triaxial compression was analyzed. The failure patterns of clastic rock under true triaxial compression were divided into three modes: structure-induced, structure-stress-induced and stress-induced failures. This study confirms the feasibility of high-speed camera technology in true triaxial testing, and has important implications for elucidating the disaster mechanism of deep tunnels in weak rocks.

Discontinuities are often considered as important factors responsible for the instability caused by shear failure in engineering rock mass, and energy-driven instability is the root cause of rock failure. However, few studies focus on the energy evolution during the failure process using a three-dimensional (3D) numerical model. In this study, a series of laboratory direct shear tests on rock-like samples is numerically simulated using bonded particle models (BPMs) with multiple combinations of discontinuous in the particle flow code (PFC3D), in which the location and size of the particles conform to the uniform distribution. The effects of joint row number and inclination on the stress-strain characteristics and failure mode of rock were studied from the perspective of microcrack growth and energy evolution. The results showed that, when the number of joint rows Nr > 1, the shear failure region does not change with the increase of Nr for the type B (2-columnn multiple-row at center) and the type C (2-column multiple-row at edge) as compared to the type A (1-column multiple-row at center) joint models. Notably, joints significantly increase the post-peak energy dissipation but have little effect on the proportion of energy before the peak. Friction consumes most of the energy while kinetic energy accounts for less than 1% of total energy during the shear process. Peak elastic strain energy follows the variation trend of peak shear displacement. The development and accumulation of microcracks directly affect the energy dissipation, and there is a significant linear relationship between the cumulative number of critical microcracks and the critical dissipated energy at the failure, when the dip direction of joints is opposite to the shear direction, more microcracks will be accumulated at the peak time, resulting in more energy dissipation. The results contribute to deeply understanding the shear failure process of non-persistent jointed mass.

With the development of global urbanization, the utilization of underground space is more critical and attractive for civil purposes. Various shapes of shield tunnels have been gradually proposed to cope with different geological conditions and service purposes of underground structures. Generally, reducing the burial depth of shield tunnel is conducive to construction and cost saving. However, extremely small overburden depth cannot provide sufficient uplift resistance to maintain the stability and serviceability of the tunnel. To this end, this paper firstly reviewed the status of deriving the minimum sand overburden depth of circular shield tunnel using mechanical equilibrium (ME) method. It revealed that the estimated depth is rather conservative. Then, the uplift resistance mechanism of both circular and rectangular tunnels was deduced theoretically and verified with the model tests. The theoretical uplift resistance is consistent with the experimental values, indicating the feasibility of the proposed equations. Furthermore, the determination of the minimum soil overburden depth of rectangular shield tunnel under various working conditions was presented through integrated ME method, which can provide more reasonable estimations of suggested tunnel burial depth for practical construction. Additionally, optimizations were made for calculating the uplift resistance, and the soil thickness providing uplift resistance is suggested to be adjusted according to the testing results. The results can provide reference for the design and construction of various shapes of shield tunnels in urban underground space exploitation.

It is essential to study the porosity, thermal conductivity, and P-wave velocity of calcarenites, as well as the anisotropy coefficients of the thermal conductivity and P-wave velocity, for civil engineering, and conservation and restoration of historical monuments. This study focuses on measuring the thermal conductivity using the thermal conductivity scanning (TCS) technique and measuring the P-wave velocity using portable equipment. This was applied for some dry and saturated calcarenite samples in the horizontal and vertical directions (parallel and perpendicular to the bedding plane, respectively). The calcarenites were selected from some historical monuments in Morocco. These physical properties were measured in the laboratory to find a reliable relationship between all of these properties. As a result of the statistical analysis of the obtained data, excellent linear relationships were observed between the porosity and both the thermal conductivity and porosity. These relationships are characterized by relatively high coefficients of determination for the horizontal and vertical samples. Based on the thermal conductivity and P-wave velocity values in these two directions, the anisotropy coefficients of these two properties were calculated. The internal structure and the pore fabric of the calcarenite samples were delineated using scanning electron microscopy (SEM), while their chemical and mineral compositions were studied using the energy dispersive X-ray analysis (EDXA) and X-ray diffraction (XRD) techniques.

Rock joints are one of the vital discontinuities in a natural rock mass. How to accurately and conveniently determine joint normal stiffness is therefore significant in rock mechanics. Here, first, seven existing methods for determining joint normal stiffness were introduced and reviewed, among which Method I (the indirect measurement method), Method II (the direct determination method), Method III (the across-joint strain gauge measurement method) and Method IV (the deformation measuring ring method) are via destructive uniaxial compression testing, while Method V (the best fitting method), Method VI (the rapid evaluation method) and Method VII (the effective modulus method) are through wave propagation principles and nondestructive ultrasonic testing. Subsequently, laboratory tests of intact and jointed sandstone specimens were conducted following the testing requirements and procedures of those seven methods. A comparison among those methods was then performed. The results show that Method I, i.e. the benchmark method, is reliable and stable. Method II has a conceptual drawback, and its accuracy is acceptable at only very low stress levels. Relative errors in the results from Method III are very large. With Method IV, the testing results are sufficiently accurate despite the strict testing environment and complicated testing procedures. The results from Method V are greatly unstable and significantly dependent on the natural frequency of the transducers. The joint normal stiffness determined with Method VI is stable and accurate, although data processing is complex. Method VII could be adopted to determine the joint normal stiffness corresponding to the rock elastic deformation phase only. Consequently, it is suggested that Methods I, IV and VI should be adopted for the measurement of joint normal stiffness. The findings could be helpful in selecting an appropriate method to determine joint normal stiffness and, hence, to better solve discontinuous rock mass problems.

Waterflood-induced fractures, also known as self-induced fractures, spontaneously form at injection wells during waterflooding. These fractures propagate long distances through rock, allowing injected fluids to travel far away from a well, both within and outside the flooding layer. Essentially, the mechanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures, which are intentionally created for reservoir stimulation. Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures. However, waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time. As a result, fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional (2D), a characteristic that is often ignored in a majority of modern fracturing simulators, making their application to waterflood fractures unreliable. In this work, we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators. We incorporate the developed solution into the classical Perkins-Kern-Nordgren (PKN) model of fracture growth, which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture geometry at large time. The conducted parametric study shows while a toughness-dominated regime affects fracture evolution, most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime. We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination (M˜˜ and K˜˜). Finally, we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones. The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions. The present work, thus, plays an important role in improving waterflood fracture modelling, as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

Thermally-induced changes in the fracture properties of geological reservoir rocks can influence their stability, transport characteristics, and performance related to various deep subsurface energy projects. The modified maximum tangential stress (MMTS) criterion is a classical theory for predicting the fracture instability of rocks. However, there is a lack of research on the accuracy of MMTS theory when rocks are subjected to different temperatures. In this study, mechanical theoretical analysis and failure and fracture mechanics experiments of granite under the influence of temperatures ranging from 20 °C to 600 °C are carried out. The results showed that the theoretical estimated value of MMTS differs significantly from the experimental data at 20 °C−600 °C. The Keff/KIC ratio is less than the experimental test value due to the critical crack growth radius (rc) estimated by the conventional method being larger than the critical crack growth radius (rce) derived from the experimental data. Varied temperatures affect the fracture process zone size of fine-grained, compact granite, and the MMTS theoretical estimation results. Therefore, it is essential to modify the critical crack growth radius for MMTS theory to accurately predict the fracture characteristics of thermally damaged rocks. In addition, the variation of the rock’s mechanical properties with temperature and its causes are obtained. Between 20 °C and 600 °C, the mode-I, mode-II, and mixed-mode (α = 30° and 45°) fracture toughness and Brazilian splitting strength of the granite decrease by 80% and 73%, respectively. When the rock is heated above 400 °C, its deterioration is mainly caused by a widening of its original cracks.

Objective and accurate evaluation of rock mass quality classification is the prerequisite for reliable stability assessment. To develop a tool that can deliver quick and accurate evaluation of rock mass quality, a deep learning approach is developed, which uses stacked autoencoders (SAEs) with several autoencoders and a softmax net layer. Ten rock parameters of rock mass rating (RMR) system are calibrated in this model. The model is trained using 75% of the total database for training sample data. The SAEs trained model achieves a nearly 100% prediction accuracy. For comparison, other different models are also trained with the same dataset, using artificial neural network (ANN) and radial basis function (RBF). The results show that the SAEs classify all test samples correctly while the rating accuracies of ANN and RBF are 97.5% and 98.7%, repectively, which are calculated from the confusion matrix. Moreover, this model is further employed to predict the slope risk level of an abandoned quarry. The proposed approach using SAEs, or deep learning in general, is more objective and more accurate and requires less human intervention. The findings presented here shall shed light for engineers/researchers interested in analyzing rock mass classification criteria or performing field investigation.

This paper presents the integration of seismic refraction and multichannel analysis of surface wave (MASW) measurements to investigate the anisotropy of P- and S-wave velocities. Additionally, synthetic forward modelling is presented as a tool for supporting seismic anisotropy studies. The geophysical measurements of cracks allowed to recognise the fracturing of a granite rock mass in a Paleozoic granite quarry (Strzegom, Poland) and a dolomite rock mass in a Triassic dolomite quarry (Podleśna, Poland). Application of the forward modelling supports the interpretation of seismic methods, simplifying data processing and verifying the final results based on data from difficult seismic conditions. As a result of direct measurements, two crack systems were determined in granite rock mass: NNE-SSW and NNW-SSE, and two in dolomite rock mass: NNE-SSW and NW-SE. Furthermore, the numerical results show the relationship between the highest values of P- and S-wave velocities and separated crack systems which allowed an unequivocal interpretation of the direction of stress, resulting in the deformations. The obtained information is promising to be helpful in mining exploration for optimising excavation works.

In the process of engineering construction such as tunnels and slopes, rock mass is frequently subjected to multiple levels of loading and unloading, while previous research ignores the impact of unloading rate on the stability of rock mass. A number of uniaxial multi-level cyclic loading-unloading experiments were conducted to better understand the effect of unloading rate on the deformation behavior, energy evolution, and damage properties of rock-like material. The experimental results demonstrated that the unloading rate and relative cyclic number clearly influence the deformation behavior and energy evolution of rock-like samples. In particular, as the relative cyclic number rises, the total strain and reversible strain both increase linearly, while the total energy density, elastic energy density, and dissipated energy density all rise nonlinearly. In contrast, the irreversible strain first decreases quickly, then stabilizes, and finally rises slowly. As the unloading rate increases, the total strain and reversible strain both increase, while the irreversible strain decreases. The dissipated energy damage was examined in light of the aforementioned experimental findings. The accuracy of the proposed damage model, which takes into account the impact of the unloading rate and relative cyclic number, is then confirmed by examining the consistency between the model predicted and the experimental results. The proposed damage model will make it easier to foresee how the multi-level loading-unloading cycles will affect the rock-like materials.

In this context, four specimens, i.e. (i) circumferentially notched cylindrical torsion (CNCT), (ii) circumferentially notched cylindrical direct tension (CNCDT), (iii) edge notch disc bend (ENDB) and (iv) three-point bend beam (3PBB), were utilized to measure the modes I and III fracture toughness values of gypsum. While the CNCT specimen provides pure mode III loading in a direct manner, this pure mode condition is indirectly produced by the ENDB specimen. The ENDB specimen provided lower KIIIc and a non-coplanar (i.e. twisted) fracture surface compared with the CNCT specimen, which showed a planar mode III fracture surface. The ENDB specimen is also employed for conducting pure mode I (with different crack depths) and mixed mode I/III tests. KIc value was independent of the notch depth, and it was consistent with the RILEM and ASTM standard methods. But the mode III fracture results were highly sensitive to the notch depth. While the fracture resistance against mode III was significantly lower than that of mode I, the greater work of fracture under mode III was noticeable.

Estimation of construction parameters is crucial for optimizing tunnel construction schedule. Due to the influence of routine activities and occasional risk events, these parameters are usually correlated and imbalanced. To solve this issue, an improved bidirectional generative adversarial network (BiGAN) model with a joint discriminator structure and zero-centered gradient penalty (0-GP) is proposed. In this model, in order to improve the capability of original BiGAN in learning imbalanced parameters, the joint discriminator separately discriminates the routine activities and risk event durations to balance their influence weights. Then, the self-attention mechanism is embedded so that the discriminator can pay more attention to the imbalanced parameters. Finally, the 0-GP is adapted for the loss of the discriminator to improve its convergence and stability. A case study of a tunnel in China shows that the improved BiGAN can obtain parameter estimates consistent with the classical Gauss mixture model, without the need of tedious and complex correlation analysis. The proposed joint discriminator can increase the ability of BiGAN in estimating imbalanced construction parameters, and the 0-GP can ensure the stability and convergence of the model.

Local geometric information and discontinuity features are key aspects of the analysis of the evolution and failure mechanisms of unstable rock blocks in rock tunnels. This study demonstrates the integration of terrestrial laser scanning (TLS) with distinct element method for rock mass characterization and stability analysis in tunnels. TLS records detailed geometric information of the surrounding rock mass by scanning and collecting the positions of millions of rock surface points without contact. By conducting a fuzzy K-means method, a discontinuity automatic identification algorithm was developed, and a method for obtaining the geometric parameters of discontinuities was proposed. This method permits the user to visually identify each discontinuity and acquire its spatial distribution features (e.g. occurrences, spacings, trace lengths) in great detail. Compared with hand mapping in conventional geotechnical surveys, the geometric information of discontinuities obtained by this approach is more accurate and the identification is more efficient. Then, a discrete fracture network with the same statistical characteristics as the actual discontinuities was generated with the distinct element method, and a representative numerical model of the jointed surrounding rock mass was established. By means of numerical simulation, potential unstable rock blocks were assessed, and failure mechanisms were analyzed. This method was applied to detection and assessment of unstable rock blocks in the spillway and sand flushing tunnel of the Hongshiyan hydropower project after a collapse. The results show that the noncontact detection of blocks was more labor-saving with lower safety risks compared with manual surveys, and the stability assessment was more reliable since the numerical model built by this method was more consistent with the distribution characteristics of actual joints. This study can provide a reference for geological survey and unstable rock block hazard mitigation in tunnels subjected to complex geology and active rockfalls.

Most studies on liquefaction have addressed homogeneous soil strata using sand or sand with fine content without considering soil stratification. In this study, cyclic triaxial tests were conducted on the stratified sand specimens embedded with the silt layers to investigate the liquefaction failures and void-redistribution at confining stress of 100 kPa under stress-controlled mode. The loosening of underlying sand mass and hindrance to pore-water flow caused localized bulging at the sand-silt interface. It is observed that at a silt thickness of 0.2H (H is the height of the specimen), nearly 187 load cycles were required to attain liquefaction, which was the highest among all the silt thicknesses with a single silt layer. Therefore, 0.2H is assumed as the optimum silt thickness (topt). The silt was placed at the top, middle and bottom of the specimen to understand the effect of silt layer location. Due to the increase in depth of the silt layer from the top position (capped soil state) to the bottom, the cycles to reach liquefaction (Ncyc,L) increased 2.18 times. Also, when the number of silt layers increased from single to triple, there was an increase of about 880% in Ncyc,L. The micro-characterization analysis of the soil specimens indicated silty materials transported in upper sections of the specimen due to the dissipated pore pressure. The main parameters, including thickness (t), location (z), cyclic stress ratio (CSR), number of silt layers (n) and modified relative density (Dr,m), performed significantly in governing the liquefaction resistance. For this, a multilinear regression model is developed based on critical parameters for prediction of Ncyc,L. Furthermore, the developed constitutive model has been validated using the data from the present study and earlier findings.

In this study, more than 1500 particles of lightweight expanded clay aggregate (LECA) are individually loaded up to breakage, following different patterns of contact (from 2 to 7) using a purpose-built apparatus. Consequently, a statistical model for predicting the number of fragments into which a grain breaks as a function of the number of contacts and their diameter is proposed. The number of fragments is found to follow a statistical binomial-type distribution function that depends on the number of contacts. In addition, a model based on Bayesian networks, capable of assessing the number of fragments and their size (measured as normalized weight) as a function of the number of contacts, is implemented. The proposed method is applicable when performing discrete element method (DEM) simulations on granular media in which grain breakage plays a relevant role.

In this paper, the application of Abaqus-based particle finite element method (PFEM) is extended from static to dynamic large deformation. The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion. Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy. The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error. The procedures of the proposed Abaqus-based dynamic PFEM (Abaqus-DPFEM) analysis and its implementation in Abaqus are detailed. The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples. The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

Shear strength is an essential geotechnical parameter for assessing the landslide potential of loess slopes under rainfall infiltration and farm irrigation conditions on the loess plateau. However, the hydraulic path dependence of shear strength for compacted loess under varying rainfall infiltration conditions has not been thoroughly investigated yet. To this end, a series of direct shear tests and nuclear magnetic resonance (NMR) measurements are carried out on compacted loess. The shear strength tests were continuously implemented on loess specimens under scanning wetting paths besides initial drying paths. The experimental data quantitatively verify the significant effect of hydraulic paths applied to specimens on shear strength of compacted loess. The unique failure envelope of shear strength of loess is identified under the effective stress framework based on intergranular stress, which verifies that the effective stress framework can consider the effect of hydraulic paths on shear strength. Based on the effective stress, a shear strength formula is proposed to characterize shear strengths under varying hydraulic paths, in which the parameters from the soil-water retention curve and shear strength at saturated state are simply required. The proposed shear strength formula can properly predict the measured shear strength data of compacted loess experiencing three hydraulic paths. Furthermore, the distribution curves of transverse relaxation time for pore water in soil under varying hydraulic paths are simultaneously measured using the NMR method. The physical mechanism for the difference in shear strength of loess subjected to different hydraulic paths can be uncovered based on soil-water evolutions in pores in microscale.

The disposal of mining tailings has increasingly focused on the use of dry stacks. These structures offer more security since they use filtered and compacted material. Because of the construction method and the heights achieved, the material that compounds the structure can be subjected to different stress paths along the failure plane. The theoretical framework considered in the design of these structures generally is the critical state soil mechanics (CSSM). However, the data in the literature concerning the uniqueness of critical state line (CSL) is still controversial as the soil is subjected to different stress paths. With respect to tailings, this question is even more restricted. This paper studies two tailings with different gradings due to the beneficial processes over extension and compression paths. A series of drained and undrained triaxial tests was conducted over a range of initial densities and stress levels. In the q-p′ plane, different critical stress ratio (M) values were obtained for compression and extension stress paths. However, the critical state friction angle is very similar with a slightly higher critical state friction angle for extension tests. Curved stress path dependent CSLs were obtained in the ν-lnp′ plane with the extension tests below the CSL defined in compression. Regarding the fines content, the studied tailings presented very similar M and critical state friction angle values. However, the fines content affects the volumetric behavior of the studied tailings and the CSLs on the ν-lnp′ plane shift downwards with the increasing fines content for compression and extension tests. In relation to dilatancy analysis, the fines content did not present an evident influence on the dilatancy of the materials. However, different values of mean stress ratio N were obtained between compression and extension tests and can corroborate the existence of non-unique CSLs for these materials.

As an emerging waterless fracturing technology, supercritical carbon dioxide (SC-CO2) fracturing can reduce reservoir damage and dependence on water resources, and can also promote the reservoir stimulation and geological storage of carbon dioxide (CO2). It is vital to figure out the laws in SC-CO2 fracturing for the large-scale field implementation of this technology. This paper reviews the numerical simulations of wellbore flow and heat transfer, fracture initiation and propagation, and proppant transport in SC-CO2 fracturing, including the numerical approaches and the obtained findings. It shows that the variations of wellbore temperature and pressure are complex and strongly transient. The wellhead pressure can be reduced by tubing and annulus co-injection or adding drag reducers into the fracturing fluid. Increasing the temperature of CO2 with wellhead heating can promote CO2 to reach the well bottom in the supercritical state. Compared with hydraulic fracturing, SC-CO2 fracturing has a lower fracture initiation pressure and can form a more complex fracture network, but the fracture width is narrower. The technology of SC-CO2 fracturing followed by thickened SC-CO2 fracturing, which combines with high injection rates and ultra-light proppants, can improve the placement effect of proppants while improving the complexity and width of fractures. The follow-up research is required to get a deeper insight into the SC-CO2 fracturing mechanisms and develop cost-effective drag reducers, thickeners, and ultra-light proppants. This paper can guide further research and promote the field application of SC-CO2 fracturing technology.