Liyuan Yu

Set pair analysis for risk assessment of water inrush in karst tunnels

Considering the uncertain characteristics of water inrush in karst tunnels, the set pair analysis (SPA) method was newly applied in this study for risk assessment of water inrush. First, karst hydrology and engineering geological conditions were considered, and several main influencing factors were selected as evaluation indices, such as formation lithology, unfavorable geology, groundwater level and contact zone of dissolvable as well as other factors. Second, a set pair was established with the combination of the evaluation indices and the standards of risk grade. Then, the evaluation indices of water inrush were divided into two main types: economic and cost indices. Based on set pair analysis (SPA), the graded connection degrees of evaluation indices were calculated. Finally, the established risk evaluation model of water inrush with set pair analysis was applied to the Jigongling tunnel on the line of the Fanba expressway in China. The results not only are consistent with the results of the attribute mathematical theory, but also agree well with practical situations. In addition, the method of set pair analysis used in this study could provide relatively high accuracy when applied to risk assessment of water inrush in karst tunnels. Meanwhile, SPA is simple, feasible and easy to implement. The presented method has been validated as an effective method of risk assessment for water inrush, which also has good prospects for further engineering applications.

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Selecting appropriate governing equations for fluid flow in fractured rock masses is of special importance for estimating the permeability of rock fracture networks. When the flow velocity is small, the flow is in the linear regime and obeys the cubic law, whereas when the flow velocity is large, the flow is in the nonlinear regime and should be simulated by solving the complex Navier-Stokes equations. The critical conditions such as critical Reynolds number and critical hydraulic gradient are commonly defined in the previous works to quantify the onset of nonlinear fluid flow. This study reviews the simplifications of governing equations from the Navier-Stokes equations, Stokes equation, and Reynold equation to the cubic law and reviews the evolutions of critical Reynolds number and critical hydraulic gradient for fluid flow in rock fractures and fracture networks, considering the influences of shear displacement, normal stress and/or confining pressure, fracture surface roughness, aperture, and number of intersections. This review provides a reference for the engineers and hydrogeologists especially the beginners to thoroughly understand the nonlinear flow regimes/mechanisms within complex fractured rock masses.

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

The mechanism and quantitative descriptions of nonlinear fluid flow through rock fractures are difficult issues of high concern in underground engineering fields. In order to study the effects of fracture geometry and loading conditions on nonlinear flow properties and normalized transmissivity through fracture networks, stress-dependent fluid flow tests were conducted on real rock fracture networks with different number of intersections (1, 4, 7, and 12) and subjected to various applied boundary loads (7, 14, 21, 28, and 35 kN). For all cases, the inlet hydraulic pressures ranged from 0 to 0.6 MPa. The test results show that Forchheimer’s law provides an excellent description of the nonlinear fluid flow in fracture networks. The linear coefficient and nonlinear coefficient in Forchheimer’s law generally decrease with the number of intersections but increase with the boundary load. The relationships between and can be well fitted with a power function. A nonlinear effect factor was used to quantitatively characterize the nonlinear behaviors of fluid flow through fracture networks. By defining a critical value of = 10%, the critical hydraulic gradient was calculated. The critical hydraulic gradient decreases with the number of intersections due to richer flowing paths but increases with the boundary load due to fracture closure. The transmissivity of fracture networks decreases with the hydraulic gradient, and the variation process can be estimated using an exponential function. A mathematical expression for decreased normalized transmissivity against the hydraulic gradient was established. When the hydraulic gradient is small, holds a constant value of 1.0. With increasing hydraulic gradient, the reduction rate of first increases and then decreases. The equivalent permeability of fracture networks decreases with the applied boundary load, and permeability changes at low load levels are more sensitive.

Strength degradation and anchoring behavior of rock mass in the fault fracture zone

Rock mass in the fault fracture zone has some characteristics such as low strength and poor self-stability, so the control mechanism of stability has been a difficulty in the research of underground engineering. A set of laboratory simulation method of fault fractured rock mass is developed to reflect the natural forming process of fault fracture zone. Compared with intact rock mass, the fault fractured rock mass has an obvious degradation in strength and deformation parameters, and the degradation index is between 22.79 and 84.06%. The bolt has a certain supporting effect on the fault fractured rock mass, and in the situation of end anchoring, the greater the pretightening force is, the better the enforcement effect will be. The stress field produced by high pretightening force can relieve the stress concentration around the bolt hole and make the initial cracks of rock mass away from the bolt plate. The evolution curve of bolt axial force in the process of uniaxial compression of large-scale specimen shows four stages, which are the initial compression stage, pre-peak joint load-bearing stage, post-peak joint load-bearing stage and the residual stage. Research results could provide some theory reference for the stability control of rock mass in the fault fracture zone.

An experimental study of the effect of fillings on hydraulic properties of single fractures

Fluid flow in single rock fractures considering the influences of fracture surface roughness, shearing process, normal loading, and so on has been extensively studied for several decades, yet the significant influence of fillings has not been systematically investigated due to the numerous difficulties such as determination of the physical parameters of fillings. The present study aims to estimate the hydraulic properties of single fractures filled with different graded and gap-graded fillings, based on a series of flow tests on rock-like samples using the MTS815.02 material testing system. With the increment of fracture aperture, the pressure drops before and after fillings are flowed away decrease, whereas the permeabilities before and after fillings are flowed away increase. When the ratio of mechanical aperture of fractures to maximum diameter of fillings decreases from 4 to 1.33, both pressure drop and permeability change significantly before the fillings are flowed away and then hold constant values after the fillings are flowed away. Due to the effects of fraction force and interlocking force between particles, the ratio of mechanical aperture to maximum diameter of fillings that equals to 2.67 is the inflection point, where the pressure drop has the maximum value and permeability has the minimum value. When the fractures are filled with gap-graded fillings, in which the ratio of mechanical aperture of fractures to mean diameter of fillings decreases from 5.76 to 1.45, the variations of both pressure drop and permeability before fillings are flowed away change more significantly than those after fillings are flowed away. The hydraulic aperture of fractures with fillings is approximately 2–3 orders of magnitude smaller than the mechanical aperture.

Analytical Strain-softening Solutions of a spherical cavity

This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial stresses. By simplifying the strain-softening process of the post-failure region as a Multi-step Brittle-Plastic model (MBPM), analytical solutions of the spherical cavity are derived with the consideration of the deterioration of elastic parameters. Meanwhile, critical deterioration conditions of elastic parameters are established theoretically. Both Mohr-Coulomb (M-C) and Hoek-Brown (H-B) criteria are included in the analysis. The results are compared with those obtained by former numerical methods, and the solutions are validated. Moreover, the presented results show that deteriorated elastic parameters for post-failure rock mass only has a little influence on stresses, softening radius and residual radius, but influences the deformation significantly.

Effect of Thermal Treatment on the Dynamic Behaviors at a Fixed Loading Rate of Limestone in Quasi-vacuum and Air-filled Environments

Thermal damage in rock engineering occurs in the air‐filled and quasi‐ vacuum environments of rock mass located near or far from the free sur‐ face. Meanwhile, dynamic loads are encountered frequently in engineering practice. In this study, 39 limestone samples are prepared, and a series of laboratory tests, including split Hopkinson pressure bar SHPB , nuclear magnetic resonance NMR and optical microscopy analyses, are conduct‐ ed to investigate the effects of temperature and the environment on the dynamic mechanical properties of limestone. The results show that the macro‐physical and dynamic mechanical properties of limestone after thermal treatment can be divided into two stages by a critical temperature of 450°C, at which the thermal damage factor is 0.71 and 0.75 in the quasi‐ vacuum and air‐filled environments, respectively. In the first stage, with temperatures varying from 25°C to 450°C, the thermal damage due to ex‐ pansion and fracturing slightly influences the related parameters, except the P‐wave velocity. However, in the second stage, with temperatures rang‐ ing from 450°C to 900°C, the thermal damage caused by mineral decompo‐ sition and hydration leads to a remarkable decrease in the dynamic bearing and anti‐deformation capacities. The environment plays a negligible role in the first stage but an important role in the second stage, and the dynamic compressive strength and modulus of samples after thermal treatment in the air‐filled environment are much lower than those in the quasi‐vacuum environment. Both the temperature and environment of thermal treatment should be considered in engineering practice, especially when the temper‐ ature exceeds 450°C.

Effect of Thermal Environment on the Mechanical Behaviors of Building Marble

High temperature and thermal environment can influence the mechanical properties of building materials worked in the civil engineering, for example, concrete, building rock, and steel. This paper examines standard cylindrical building marble specimens (Φ50 × 100 mm) that were treated with high temperatures in two different thermal environments: vacuum (VE) and airiness (AE). Uniaxial compression tests were also carried out on those specimens after heat treatment to study the effect that the thermal environment has on mechanical behaviors. With an increase in temperature, the mechanical behavior of marble in this study indicates a critical temperature of 600°C. Both the peak stress and elasticity modulus were larger for the VE than they were for the AE. The thermal environment has an obvious influence on the mechanical properties, especially at temperatures of 450∼750°C. The failure mode of marble specimens under uniaxial compression is mainly affected by the thermal environment at 600°C.

Elastoplastic Analysis of Circular Openings in Elasto-Brittle-Plastic Rock Mass Based on Logarithmic Strain

Rock-like materials, such as coal and soft rock, often manifest larger deformation features. The prediction values for displacement and failure region based on the commonly used small strain (SS) theory are generally larger than the field test results. Based on the Euler coordinate system, the logarithmic strain (LS) is employed to describe the actual deformation behavior. Both of the stresses and displacement of circular opening in elasto-brittle-plastic rock mass are formulated with differential equations. And a simple approach is proposed to solve the differential equations. The results show that the plastic radius depends on the elastic parameters, that is, Young’s modulus and Poisson’s ratio, which is different from SS theory. And the plastic radius and displacement of LS rock mass are smaller than those of SS rock mass, and the displacement of LS rock mass is absolutely smaller than the excavation radius. The proposed solutions can provide theoretical foundation for the optimization of supporting structure in underground engineering.