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Characterizing the permeability variation in fractured rocks is important in various subsurface applications, but how the permeability evolves in the foundation rocks of high dams during operation remains poorly understood. This permeability change is commonly evidenced by a continuous decrease in the amount of discharge (especially for dams on sediment-laden rivers), and can be attributed to fracture clogging and/or hydromechanical coupling. In this study, the permeability evolution of fractured rocks at a high arch dam foundation during operation was evaluated by inverse modeling based on the field time-series data of both pore pressure and discharge. A procedure combining orthogonal design, transient flow modeling, artificial neural network, and genetic algorithm was adopted to efficiently estimate the hydraulic conductivity values in each annual cycle after initial reservoir filling. The inverse results show that the permeability of the dam foundation rocks follows an exponential decay annually during operation (i.e. K/K0 = 0.97e−0.59t + 0.03), with good agreement between field observations and numerical simulations. The significance of the obtained permeability decay function was manifested by an assessment of the long-term seepage control performance and groundwater flow behaviors at the dam site. The proposed formula is also of merit for characterizing the permeability change in riverbed rocks induced by sediment transport and deposition.

Discrete fracture network (DFN) is an effective means of describing the coupling of heat flow in an underground fractured rock mass. In this paper, an improved DFN is proposed by introducing the correlation function of fracture trace length and aperture, which is more consistent with the real fracture data. Next, based on the improved model, the influence of fracture roughness on the fluid flow and heat transmission was evaluated, and the relationship between the fracture aperture and the joint roughness coefficient (JRC) is established. Finally, based on the exponential function between confining pressure and aperture, the influence of confining pressure on the heat‐flow coupling process is considered in the improved model. Besides, the reliability of the model was verified by comparing with the analytical solution of the two‐dimensional single‐fracture heat‐flow coupling problem. The results show that under the same conditions, considering the correlation between the geometric parameters of the fracture, the seepage and heat transfer rates of the model increased, the outlet boundary flow reached the maximum value, and the average outlet temperature dropped rapidly. However, the fracture roughness reduces the outlet flow rate and the decline rate of average temperature. The confining pressure will lead to a decrease of about 3.5% in the outlet flow of the model, which is consistent with the seepage law in practical engineering. The model presented in this paper is an effective supplement to the two‐dimensional fracture network heat‐flow coupling model and can provide a theoretical basis and a numerical calculation tool for related underground rock mass engineering.

Connectivity evaluation of fracture networks is important in the design, assessment, and development of reservoirs in various engineering applications involving geothermal exploitation and the petroleum industry. By employing nonhomogeneous Poisson distribution and annealing arithmetic, this study generates fracture networks that fit well with actual outcrop fracture data. Based on Allard's definition of the connectivity index, a weighted factor is introduced, and an extended connectivity evaluation method is proposed to consider the effects of the aperture and its correlation with trace length. The results of the analysis show that the extended method improves the accuracy and reliability of connectivity evaluation compared with the traditional method. Moreover, the extended method is effective and accurate at predicting potential preferential flow paths in a practical example of the Dragon and Tiger Mountain (Jiangxi, China), and can better show the anisotropy with a change in the aperture. Hence, the proposed method extends the function of connectivity analysis and can benefit well location optimization in geothermal or petroleum exploration.

A series of physical tests were carried out using three different particle sizes to investigate the influence of tailings size on the failure process of a tailings dam subjected to overtopping. In addition, the overtopping failure process was simulated with a computational fluid mechanics model. The tests results showed that with increased tailings size, the mode of failure gradually changed from undercut erosion to surface scouring, while the gully cut by the water had a greater width to depth ratio. In addition, the particle size also affected the characteristics of the discharge process and its duration. Numerical simulation results were basically consistent with the physical model results with respect to both discharge process and duration time. The comparison shows that the numerical method could possibly be useful for other studies on the overtopping failure of tailings dams.

Conventional supervised and unsupervised machine learning models used for landslide susceptibility prediction (LSP) have many drawbacks, such as an insufficient number of recorded landslide samples, and the subjective and random selection of non-landslide samples. To overcome these drawbacks, a semi-supervised multiple-layer perceptron (SSMLP) is innovatively proposed with several processes: (1) an initial landslide susceptibility map (LSM) is produced using the multiple-layer perceptron (MLP) based on the original recorded landslide samples and related environmental factors; (2) the initial LSM is respectively classified into five areas with very high, high, moderate, low and very low susceptible levels; (3) some reasonable grid units from the areas with very high susceptible level are selected as new landslide samples to expand the original landslide samples; (4) reasonable non-landslide samples are selected from the areas with very low susceptible level; and (5) the expanded landslide samples, reasonable selected non-landslide samples and related environmental factors are put into the MLP once again to predict the final LSM. The Xunwu County of Jiangxi Province in China is selected as the study area. Conventional supervised machine learning (i.e. MLP) and unsupervised machine learning (i.e. K-means clustering model) are selected for comparisons. The comparative results indicate that the SSMLP model has a considerably higher LSP performance than the MLP and K-means clustering in Xunwu County. The SSMLP model successfully addresses the drawbacks existed in the conventional machine learning for LSP.

The impact of blast vibrations on cement-grouted rock is an unresolved challenge in construction projects where blasting is conducted near the grouted areas. This study investigates the blast vibration resistance of cement-grouted rock using both theoretical and experimental approaches. An analytical model is first presented based on structural characteristics and mechanical properties to describe the stress wave propagation in cement-grouted rock mass and to investigate the failure modes at its bonding interfaces. A model to calculate the safe vibration velocity (SVV) is then proposed to study the effects of the incident angle, in-situ stress, and bonding strength on cement-grouted rock. Next, an experiment was conducted to analyse the blast vibration resistance of cement-grouted rock and to validate the SVV model. Finally, several recommendations regarding safe blast vibration velocities for grouted areas were provided. The results indicate that cement-grouted rock has a high blast vibration resistance, which can be improved by increasing the incident angle, in-situ stress, or bonding strength. A normally incident wave was identified as the most dangerous for cement-grouted rock; thus, the SVV is the minimal in that case. For 3, 7, and 28-day-old cement-grouted rock, the SVV is suggested to be 6, 9, and 13 cm/s, respectively.

To perform landslide susceptibility prediction (LSP), it is important to select appropriate mapping unit and landslide-related conditioning factors. The efficient and automatic multi-scale segmentation (MSS) method proposed by the authors promotes the application of slope units. However, LSP modeling based on these slope units has not been performed. Moreover, the heterogeneity of conditioning factors in slope units is neglected, leading to incomplete input variables of LSP modeling. In this study, the slope units extracted by the MSS method are used to construct LSP modeling, and the heterogeneity of conditioning factors is represented by the internal variations of conditioning factors within slope unit using the descriptive statistics features of mean, standard deviation and range. Thus, slope units-based machine learning models considering internal variations of conditioning factors (variant slope-machine learning) are proposed. The Chongyi County is selected as the case study and is divided into 53,055 slope units. Fifteen original slope unit-based conditioning factors are expanded to 38 slope unit-based conditioning factors through considering their internal variations. Random forest (RF) and multi-layer perceptron (MLP) machine learning models are used to construct variant Slope-RF and Slope-MLP models. Meanwhile, the Slope-RF and Slope-MLP models without considering the internal variations of conditioning factors, and conventional grid units-based machine learning (Grid-RF and MLP) models are built for comparisons through the LSP performance assessments. Results show that the variant Slope-machine learning models have higher LSP performances than Slope-machine learning models; LSP results of variant Slope-machine learning models have stronger directivity and practical application than Grid-machine learning models. It is concluded that slope units extracted by MSS method can be appropriate for LSP modeling, and the heterogeneity of conditioning factors within slope units can more comprehensively reflect the relationships between conditioning factors and landslides. The research results have important reference significance for land use and landslide prevention.

The environmental factors of landslide susceptibility are generally uncorrelated or non-linearly correlated, resulting in the limited prediction performances of conventional machine learning methods for landslide susceptibility prediction (LSP). Deep learning methods can exploit low-level features and high-level representations of information from environmental factors. In this paper, a novel deep learning–based algorithm, the fully connected spare autoencoder (FC-SAE), is proposed for LSP. The FC-SAE consists of four steps: raw feature dropout in input layers, a sparse feature encoder in hidden layers, sparse feature extraction in output layers, and classification and prediction. The Sinan County of Guizhou Province in China, with a total of 23,195 landslide grid cells (306 recorded landslides) and 23,195 randomly selected non-landslide grid cells, was used as study case. The frequency ratio values of 27 environmental factors were taken as the input variables of FC-SAE. All 46,390 landslide and non-landslide grid cells were randomly divided into a training dataset (70%) and a test dataset (30%). By analyzing real landslide/non-landslide data, the performances of the FC-SAE and two other conventional machine learning methods, support vector machine (SVM) and back-propagation neural network (BPNN), were compared. The results show that the prediction rate and total accuracies of the FC-SAE are 0.854 and 85.2% which are higher than those of the SVM-only (0.827 and 81.56%) and BPNN (0.819 and 80.86%), respectively. In conclusion, the asymmetric and unsupervised FC-SAE can extract optimal non-linear features from environmental factors successfully, outperforms some conventional machine learning methods, and is promising for LSP.

A new 2D hydromechanical rigid block spring method is developed for studying hydraulic fracturing in cohesive porous materials. The continuum medium is discretized into an assembly of discrete rigid blocks. Macroscopic deformation and failure are related to local properties of interfaces between blocks. Fluid flow in porous continuum is described by an equivalent discrete fracture network model. Biot's theory is extended to discrete porous interfaces for studying interactions between fluid flow and mechanical behavior. Further, the hydraulic conductivity evolution due to fracture propagation is taken into account through the change of aperture of interfaces. The proposed discrete hydromechanical model is first verified through the response of an elastic isotropic thick-walled cylinder subjected to an inner pressure under the steady state flow condition. The obtained numerical results agree well with the corresponding analytical solutions. Further, the numerical model is applied to studying the hydraulic fracturing of the thick-walled cylinder. The effect of transient flow on fracturing pressure is highlighted. The effect of materials strength anisotropy on fracturing process is also studied. It is shown that the proposed discrete model provides an efficient tool for modeling hydraulic fracturing in cohesive rock-like materials.

In tunnel blast applications, vibration monitors are typically placed on tunnel surfaces to measure the responses of rock to explosion loads for statutory compliance. Few publications in the open literature have focused on the differences between the blasting vibration on tunnel surfaces and inside the surrounding rock. During blasting excavation of the experimental tunnels in the China Jinping Underground Laboratory, velocity sensors were arranged both on the tunnel walls and inside the surrounding rock to monitor far-field vibrations. In this paper, the vibration characteristics on the tunnel surfaces and inside the surrounding rock are presented based on the recorded field data. Corresponding empirical formulae for peak particle velocity (PPV) attenuation and dominant frequency variation are derived from these data. A three-dimensional dynamic finite-element model is used to verify the site survey results. The field and numerical studies show that compared with the inside vibration, the tunnel surface vibration has a higher, more readily attenuated PPV and a lower frequency with a slower rate of decline in the dominant frequency. The mechanisms that cause the differences between the surface and inside vibration are discussed in detail. The tunnel surface vibration in the far field is dominated by surface waves, which occupy more than 75% of the total vibrational energy. For this reason, the results presented in this paper do not apply to vibration in the near field, where body waves are expected to be dominant.

The flux-driven displacement of a wetting fluid by a non-wetting fluid in two-dimensional channels with flat parallel plates and sinusoidal surfaces is investigated via a multi-relaxation time multi-component lattice Boltzmann method. The co-current flow and the capillary filling problems are used for the validation of the numerical method. The results have shown that the present method is effective in simulating the viscous and capillary forces during the displacement process. For flat parallel plates, the effect of wettability on the development of fingering flow and the relationship between the developed finger width ratio and the capillary number are investigated. The results are compared to the previous research. The fingering flow is enhanced with a strongly wetting condition and the finger width ratio decreases as the capillary number is raised. For periodic sinusoidal channels, discontinuous interfaces appear due to the roughness of channel walls. The residual behavior of the wetting displaced fluid is enhanced with the wetting condition, as a strongly wetting condition would lead to a slower contact line motion. Finally, a quantitative study of the combined effect of roughness and wettability on the residual saturation is made.

In water-rich rock masses from underground excavations, the flow pressure and confining pressure significantly affect the seepage properties of the fractured rock induced by complex stress...

Conditional random field model can make best use of limited site investigation data to properly characterize the spatial variation of soil properties. This paper aims to propose a simplified approach for generating conditional random fields of soil undrained shear strength. A numerical method is adopted to validate the effectiveness of the proposed approach. With the proposed approach, the analytical posterior statistics of spatially varying undrained shear strength conditioned on the known values at measurement locations can be obtained. The conditional random field model of undrained shear strength is constructed using the field vane shear test data at a site of the west side highway in New York and the probability of slope failure is estimated by subset simulation. A clay slope under undrained conditions is investigated as an example to illustrate the proposed approach. The effects of borehole location and borehole layout scheme on the slope reliability are addressed. The results indicate that the proposed approach not only can well incorporate the limited site investigation data into modelling of the actual spatial variation of soil parameters by conditional random fields, but also can capture the depth-dependent nature of soil properties. The realizations of conditional random fields generated by the proposed approach can be well constrained to the site investigation data.

A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.

High temperature associated with geothermal fields affects the performance of bedrocks. Evaluation of physical and mechanical behavior of rocks in the process of thermal cycling at high temperature is one of the main issue in this application, which is also the main topic of the present study. In this study, microscopic observation and uniaxial compression tests with acoustic emission (AE) monitoring were conducted on two bedrocks (i.e., marble and granite) after treatment with different thermal cycles at high temperature. It is found that the P-wave velocity decreases as the number of thermal cycle increases. The characteristic stress levels and Young’s modulus decrease with the increase of the number of thermal cycle in the treatment. The peak strain and the maximum volumetric strain show an increasing trend as the number of thermal cycle increases. After failure, more fragments are observed in specimens treated with more thermal cycles and the integrity is also found to be lower than specimens treated with less thermal cycles. The AE technique is able to capture the failure process and the associated micro-cracking behavior during loading. The degradation of macro-properties of the rocks is to a large extent attributed to the generation of grain boundary and intra-grain micro-cracks inside the rock specimens due to the applied thermal stress. Overall, the thermal cycling weakens the mechanical properties of rocks; however, the weakening effect will become not pronounced with the increase of the number of thermal cycle in the treatment if a high temperature is applied as in this study (i.e., 600 °C).

Shear deformation-induced hydraulic conductivity change in fracture has been studied for decades. However, the existing models to link shear deformation and hydraulic behaviors are less accurate due to complex flow in rock fractures. This study presents an improved flow model for calculating nonlinear flow behaviors in rock fractures during shear. In this model, the linear and nonlinear coefficients in the Forchheimer equation were determined using mechanical aperture and fracture roughness coefficients. The mechanical aperture was equal to the initial aperture plus the change of the aperture due to shear-induced dilation. The dilation curve was divided into three stages and analytical expressions for modeling the dilation curve were established by incorporating the joint roughness coefficient (JRC) and the mobilized roughness coefficient (JRCmob). In addition, shear-flow tests were conducted on marble and granite fractures with normal stress between 0.5 and 3.0 MPa. The experimental data were used to verify the proposed model. The results show that the proposed model predicts flow in rock fractures well.

A multi-objective inverse analysis method for slope excavation was proposed, in which orthogonal design, numerical simulation, back propagation neural network (BPNN) and elitist non-dominated sorting genetic algorithm (NSGA-II) were integrated. The multi-objective model is constructed by minimizing a set of multi-objective error functions between the time series of observations and corresponding calculated values. Compared with the back-analysis methods that uses traditional algorithms, the proposed method is validated by a numerical example to be more effective for multi-objective optimization. The methodology is also applied to the excavation of a right bank slope at the Dagangshan hydropower station located in the Sichuan Province, China. The obtained inversion parameters are used in forward analysis to predict displacements. In this case application, three types of field observations are used simultaneously in the back-analysis, which include displacements in the Dadu River water flow (y-) direction, transverse (x-) direction and vertical (z-) direction. Compared with the field displacement data, the trend of the predicted displacements agrees well with the measurements. The results indicate that the proposed method can more precisely and reliably predict the slope deformation induced by excavation.

High pressure packer test (HPPT) is an enhanced constant head packer test widely applied for characterizing the permeability or coupled hydromechanical properties of fractured rocks under high water pressure condition, but it remains an issue about how to choose a representative quantity from the test data for the design of impervious barriers in high-head geotechnical projects. In this study, the typical type curves of HPPTs are summarized and related to the intactness of rocks, flow condition in fractures and the possible hydraulic fracturing phenomenon in the tested rocks. Based on an interpretative model recently developed for HPPTs, a criterion is proposed to determine a proper permeability rate from the HPPT data for design of grout curtains by taking into account the type curves and the transition of flow conditions, and is applied to illustrate the implication of the proposed criterion for the design of impervious barrier in a high arch dam foundation. The proposed criterion could be of significance in the design of impervious barriers for reducing the risk of leakage in rocks under high water pressure condition.

The hysteresis of water retention curve has a profound influence on the coupled hydro-mechanical behaviors in unsaturated soils, but numerical implementation with consideration of this property was rarely reported due to the difficulties in the integration of the coupled constitutive models. In this study, a numerical formulation is proposed for modeling the coupled flow–deformation processes with hydraulic hysteresis. A return mapping scheme is developed to integrate the water retention curve model with hydraulic hysteresis and the elasto-plastic model simultaneously within a time step, and the deformation-dependent nature of the water retention curve is considered rigorously by modifying the coefficient matrices in the discretized governing equations. The performance and efficiency of the proposed numerical formulation is validated by two existing laboratory tests and a computational example, demonstrating better performance and convergence of the proposed formulation. The proposed procedure is then applied for modeling the coupled flow–deformation processes in a soil slope under rain infiltration. The simulated results reveal the significant effects of hydraulic hysteresis on the coupled water–air two-phase flow and elasto-plastic deformation processes. The solid deformation and the evolution of the shear band would be remarkably overestimated, and the slope failure would be early predicted when neglecting hydraulic hysteresis.

Reinforced concrete (RC) slabs are the major components for building structures and underwater engineering plants. However, blast loading, especially from contact explosion, can cause significant damage to the target structures both in air and water. The objective of this paper is to compare the damage characteristics of RC slabs subjected to air and underwater contact explosions. Three methods, i.e. fully coupled Eulerian-Lagrangian (CEL) method, smoothed particle hydrodynamics (SPH) method, and coupled finite element method and smoothed particle hydrodynamics method (FEM-SPH), are first employed to simulate the damage features of an RC slab to air contact explosion. Damage profiles of the RC slab to air contact explosion using the three methods are compared with the experiment results in the literature, and the applicability and suitability of these methods are discussed. Subsequently, the most effective method (i.e., FEM-SPH) is used to describe the dynamic response of the RC slab subjected to underwater contact explosion. Shock wave propagation characteristics from air and underwater contact explosions are discussed. Damage features of the RC slab to air and underwater contact explosions are compared. Damage characteristics and plastic deformation of reinforcement steel bars are also investigated.

Packer test is a tool that has been long developed and widely used for characterizing the permeability of formation. The flow in the tested formation tends to transition from laminar to non-Darcian regime with increasing flow velocity and hydraulic gradient. But as the non-Darcian effect becomes important, how the borehole inclination and groundwater level influence the interpretation of packer test data remains unclear. In this study, a Forchheimer's law-based analytical model incorporating the effects of groundwater level and borehole inclination was presented by image method and velocity integration, which can be immediately reduced to Zangar's (1953) equation for vertical borehole under laminar flow condition and approximately reduced to Chen's (2015b) model when the test interval is at a moderate depth below the groundwater level. The proposed model was validated by numerical simulations. Parametric and error analyses indicate that the hydraulic conductivity will be overestimated while the non-Darcy coefficient will be underestimated if the effects of groundwater level and borehole inclination are neglected. The proposed model was applied to data interpretation of packer tests performed in fractured sedimentary rocks in Hainan Province, China. The results show that significant non-Darcian flow occurred in the tests. The borehole inclination has little influence on the estimation of hydraulic parameters, but demonstrates the anisotropy and heterogeneity of the rocks.

Block theory has been widely applied to stability analysis of rock engineering due to its clear concept and elegant geometrical theory. For a general block with multiple discontinuity planes, it is assumed that contact is only maintained on a single plane (single-plane sliding) or two intersecting planes (double-plane sliding) in block theory analysis. Since the normal forces and shear resistances acting on the other discontinuity planes are omitted, it can cause unreasonable estimations of block failure modes and incorrect calculation of factors of safety. In this study, a new method is presented that permits to consider the contribution of the normal forces and shear resistances acting on each discontinuity plane to the block stability. The proposed method meets all of the force-equilibrium and moment-equilibrium conditions and provides a rigorous solution for stability of general blocks with any number of faces and any shape. Some typical polyhedral blocks in rock slopes are analyzed using block theory and the proposed method. The results indicate that the traditional block theory may give a misleading conclusion for the predictions of stability and sliding direction of rock blocks when contact occurs on more than two discontinuity planes.

Models used for data interpretation of constant-rate tests (CRTs) are commonly derived with the assumption of Darcian flow in an idealized integer flow dimension, where the non-Darcian nature of fluid flow and the complexity of flow geometry are disregarded. In this study, a Forchheimer's law-based analytical model is proposed with the assumption of buildup (or drawdown) decomposition for characterizing the non-Darcian flow in a generalized radial formation where the flow dimension n may become non-integer. The proposed model immediately reduces to Barker's (1988) model for Darcian flow in the generalized radial formation and to Mathias et al.'s (2008) model for non-Darcian flow in a two-dimensional confined aquifer. A comparison with numerical simulations shows that the proposed model behaves well at late times for flow dimension n > 1.5. The proposed model is finally applied for data interpretation of the constant-rate pumping tests performed at Ploemeur (Le Borgne et al., 2004), showing that the intrinsic hydraulic conductivity of formations will be underestimated and the specific storage will be overestimated if the non-Darcian effect is ignored. The proposed model is an extension of the generalized radial flow (GRF) model based on Forchheimer's law, which would be of significance for data interpretation of CRTs in aquifers of complex flow geometry in which non-Darcian flow occurs.

Underground rock caverns have been considered as an effective technique for oil storage, commonly with water curtains for maintaining a desired and stable groundwater level and preventing the products from escaping. This study presents a three-dimensional analysis of groundwater flow in the surrounding rocks of water-sealed underground oil storage caverns. The water curtain consisting of numerous boreholes of small diameter, long extension and dense spacing is accurately modeled with a substructure technique. The influence of the oil vapor or mixed gas pressure in the caverns on the groundwater flow is considered by integrating it into the water head and complementary boundary conditions. The proposed method is applied to assess the performance of the water curtain system in the Huangdao oil storage caverns, the first-built underground oil storage project in China. The numerical results show that the gas pressure in the caverns leads to development of gas invasion zones around the cavern roofs, which decreases the thickness of the groundwater barrier and increases the risk of oil and oil vapor leakage. Based on the numerical observations, the design criteria for the water curtain system are discussed and modified.

This paper numerically investigates the fluid flow behavior through single fractures with directional shear dislocations. Synthetic fractures are generated with directional shear dislocations, and the lattice Boltzmann method is used to simulate the fracture flow. With an ignorance of tortuosity effect, a notable overestimation of hydraulic conductivity is observed when the simplified local cubic law is used. During the closure process, the decreasing rate of conductivity is found to be highly related to the roughness of fractures. The conductivity of smoother fractures decreases faster than that of rougher fractures. By conducting simulations on fractures with a constant shear displacement, the effective conductivity is found to vary with the shear directions. The results show that the conductivity of rougher fractures is less sensitive to the shear directions than that of smoother fractures. As fracture surfaces come into contact, a sharp decrease in effective conductivity is observed and the decreasing trend flattens as the contact ratio continues to increase. A new model is proposed based on the bottleneck model to predict the conductivity of sheared fractures. By integrating the tortuosity and channeling effects into the original model, the proposed new model shows a better performance in predicting the conductivity, especially for fractures with rougher surfaces.

Many nonlinear models have been proposed to forecast groundwater level. However, the evidence of chaos in groundwater levels in landslide has not been explored. In addition, linear correlation analyses are used to determine the input and output variables for the nonlinear models. Linear correlation analyses are unable to capture the nonlinear relationships between the input and output variables. This paper proposes to use chaos theory to select the input and output variables for nonlinear models. The nonlinear model is constructed based on support vector machine (SVM). The parameters of SVM are obtained by particle swarm optimization (PSO). The proposed PSO-SVM model based on chaos theory (chaotic PSO-SVM) is applied to predict the daily groundwater levels in Huayuan landslide and the weekly, monthly groundwater levels in Baijiabao landslide in the Three Gorges Reservoir Area in China. The results show that there are chaos characteristics in the groundwater levels. The linear correlation analysis based PSO-SVM (linear PSO-SVM) and chaos theory-based back-propagation neural network (chaotic BPNN) are also applied for the purpose of comparison. The results show that the chaotic PSO-SVM model has higher prediction accuracy than the linear PSO-SVM and chaotic BPNN models for the test data considered.

Three-dimensional (3D) morphology of rock fracture has a great influence on its hydraulic behavior. To experimentally investigate the 3D roughness dependent non-linear flow characteristics in deformable rock fractures, water flow tests through non-mated fractures were conducted under normal stresses ranging from 1.0 MPa to 5.0 MPa. Three types of granite samples were selected to produce rock fracture with different roughness. A 3D morphology parameter was used in the experiments to better understand the influence of joint roughness on the flow characteristics. By incorporating the 3D roughness metric, we proposed a new formula to describe the non-linear flow in rock fracture. The non-linear flow characteristics including the critical Reynolds number, Forchheimer's linear coefficient and nonlinear coefficient are analyzed and discussed. In addition, comparison among the proposed equation, Lomize's equation, Forchheimer equation and Izbash's law are examined from the perspective of the rationality of the formula. The limitations of Lomize's equation, Forchheimer equation and Izbash's law are analyzed in detail. The results show that the proposed equation is easier in the structure and more meaningful from an engineering point of view.

The post-peak strength behavior of rocks is important for stability analysis of underground excavations. This paper studies the confinement and plastic strain dependent post-peak strength of intact rocks. First, the post-peak behavior of rocks is studied by conducting triaxial compression tests on a coarse marble. The post-peak strengths of the rock under different confining pressures and plastic strains are obtained using the recorded stress–strain curves. A strength degradation index is then proposed to represent the post-peak strength degradation, and a negative exponential function, which includes a shape parameter n, is used to describe the relation between the strength degradation index and the confining pressure. Parameter n is plastic strain dependent, which decreases with the increase of plastic strain. The proposed strength degradation model can well capture the post-peak strength envelopes of the coarse marble under different plastic strains. Finally, two sets of triaxial compression test data from previous studies are used to further verify the strength degradation model. The peak and post-peak strength behaviors of two marbles are well represented using the proposed model. The approach proposed in this study also provides a simple yet useful method for determining the realistic residual strength of intact rocks.

How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the “max” and “min” functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.

This paper proposes a multivariate chaotic Extreme Learning Machine (ELM) model for the prediction of the displacement of reservoir landslides. The displacement time series of the Baishuihe and Bazimen landslides in the Three Gorges Reservoir Area in China are used as examples. The results show that there are evidences of chaos in the displacement time series. The univariate chaotic ELM model and the multivariate chaotic model based on Particle Swarm Optimization and Support Vector Machine (PSO-SVM) model are also applied for the purpose of comparison. The comparisons show that the multivariate chaotic ELM model achieves higher prediction accuracy than the univariate chaotic ELM model and the multivariate chaotic PSO-SVM model.