Zhiye Zhao

Experimental Investigation of Bedding Plane Orientation on the Rockburst Behavior of Sandstone

Rockburst is a violent rock failure process which poses a significant threat to human safety in mining and tunneling construction. Although many in situ investigations provided valuable insights on the rockburst mechanism, the failure and rock fragmentation process during a rockburst cannot be fully examined on the site. In this paper, a modified triaxial rock testing apparatus is employed to investigate the rockburst behavior of oriented sandstone. A high-speed camera is used to record the crack propagation and the ejection of rock fragments on the unloading surface. The microscopic characteristics of the fragments generated from the rockburst tests are observed using the scanning electron microscope (SEM) imaging technique. The trajectory sketches are drawn to calculate the initial velocities of the rock fragments ejected based on the photographs taken by the high-speed camera. The results show that the mass and velocity of fragments are the two main parameters for the identification of the energy-transferring process in the rockburst test. When the bedding orientation is perpendicular to the unloading surface, the rockburst is controlled by the specimen’s strength. However, when the bedding orientation is parallel to the unloading surface, the rockburst is dependent on the structural stability of the specimen.

Analysis of mechanically fastened composite joints by boundary element methods

This article focuses on the boundary element formulation development for analyzing a mechanically bolted composite. Boundary equations are formulated for all the member panels of the composite joints. These equations are solved together with the fastener equations to get the resultant contact forces for all the fasteners involved. The fasteners are then modeled as 1D springs that are governed by linear relationship between the fastener forces and the displacements of member panels at the respective fastener centers. After obtaining all the fastener forces from the global analysis, detailed stress analysis is performed for region around an individual fastener. The stress distributions around fastener holes are then used to evaluate the margin of safety of the composite panels. The numerical predictions on the fastener forces, failure modes and failure loads of two typical bolted composite joints using the proposed method agree well with that of the experimental results.

Fully Grouted Rock Bolts: An Analytical Investigation

This paper analytically investigates the performance of fully grouted rock bolts in typical scenarios, including pullout test, suspending loosened block, and increasing joint aperture, respectively. The interface shear stress distribution follows the model proposed by Li and Stillborg (Int J Rock Mech Mining Sci 36:1013–1029, 1999), while the axial behavior of the bolt shank obeys the elasto-plastic (yielding-hardening) constitutive model of steel. Three different failure modes are taken into account: tensile failure of bolt shank, bolt shank being pulled out along the bolt/rock interface, and loss of face plate. The evolution of the interface shear stress and the axial tensile stress are examined for both long and short bolts under displacement and load boundary conditions. The derived charts are able to predict the load capacity of fully grouted bolts in pullout test, the minimum length requirement of the bolt to suspend a loosened block, and the maximum allowed opening displacement of a rock joint for a fully grouted bolt. In addition, different potential failure modes are specified. Full range load–displacement curves are produced and compared for various failure modes. The derived charts could be directly used in rock-bolting design.

Development of Rock Bolt Elements in Two-Dimensional Discontinuous Deformation Analysis

Computer modeling can be used to explore and gain new insights into the impacts of rock bolt intersecting joints in rock masses, and to estimate the effectiveness of the rock reinforcement system. In order to achieve this goal, we couple a rock bolt element into the two-dimensional discontinuous deformation analysis (DDA2D) program. The coupling algorithm is based on the analytically-derived interface behavior between a rock bolt and the rock material for grouted rock bolts. The shear force generated by slippage along the interface is assumed to have a linear relationship with respect to the relative slipping distance between the rock bolt and the rock. The linear elastic criterion is applied to determine the material behavior of rock bolts before the axial stress reaches the yield value. The pullout tests are simulated to verify the coupling algorithm and the effects of the proposed rock bolt elements. Parametrical studies are also carried out to analyze the effectiveness of the rock bolts under various end conditions, joint locations and bond stiffness. In addition, the performance of the rock bolt during the interface debonding is analyzed using two types of constitutive laws, i.e., the friction law and the reduction law. The simulation results show that the proposed rock bolt models can predict the shear forces and axial loading along the rock bolts.

Rock Cavern Stability Analysis Under Different Hydro-Geological Conditions Using the Coupled Hydro-Mechanical Model

Rock cavern stability has a close relationship with the uncertain geological parameters, such as the in situ stress, the joint configurations, and the joint mechanical properties. Therefore, the stability of the rock cavern should be studied with variable geological conditions. In this paper, the coupled hydro-mechanical model, which is under the framework of the discontinuous deformation analysis, is developed to study the underground cavern stability when considering the hydraulic pressure after excavation. Variable geological conditions are taken into account to study their impacts on the seepage rate and the cavern stability, including the in situ stress ratio, joint spacing, and joint dip angle. In addition, the two cases with static hydraulic pressure and without hydraulic pressure are also considered for the comparison. The numerical simulations demonstrate that the coupled approach can capture the cavern behavior better than the other two approaches without the coupling effects.

Design of Metal Foam Cladding Subjected to Close-Range Blast

AbstractThe response of a blast mitigation cladding consisting of a face sheet and metal foam core subjected to a close-range blast is predicted. Whereas the cladding is sufficiently wide compared to the standoff distance between the explosion center and the cladding, the boundary of the blast induced bulge is released. The face sheet is considered as a rigid perfectly plastic membrane as the deformation of the sheet always exceeds half its thickness. A procedure predicting the depth and extent of the bulge is proposed with energy method. Subsequently, the minimum thickness of the foam layer is calculated based on the bulge depth. This design-oriented approach, in a ready-to-use manner, can be straightforwardly applied, facilitating the preliminary design of blast mitigation claddings with metal foam core.

Numerical Simulation of P-Wave Propagation in Rock Mass with Granular Material-Filled Fractures Using Hybrid Continuum-Discrete Element Method

Abstract In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.

Design sensitivity analysis with hypersingular boundary elements

The finite difference load method for shape design sensitivity analysis requires the calculation of stress and stress gradient on the boundary. In the standard boundary element method, the basic state variables-displacement and traction are continuous, and are considered as very accurate. However, the boundary stress and stress gradient, derived from the differentiation of the state variables and Hookes law, are discontinuous and have relatively lower accuracy than the basic state variables. The hypersingular boundary integral equation is introduced in this paper to determine the stress and stress gradient in the design sensitivity analysis. The numerical examples demonstrate the accuracy of the design sensitivity using the hypersingular boundary elements.

An Analytical Model for Fully Grouted Rockbolts with Consideration of the Pre- and Post-yielding Behavior

For rockbolts subjected to tensile loads, there exists a unique local slip–strain relationship as well as a unique bond–slip relationship between rockbolts and rock mass. An analytical model is presented in this study for fully grouted rockbolts under tension, based on the slip–strain relationship of rockbolts. This analytical model takes into account the trilinear bond–slip relationship and the pre- and post-yielding characteristics of the rockbolt material. The reliability and accuracy of the proposed analytical model are verified by experimental pullout tests. Verification studies show that the proposed model is capable of representing the strain and stress distributions of the rockbolts, and the overall load–displacement relationships of rockbolts before and after yielding. Additionally, the model has successfully captured the decoupling mechanism at the bolt–rock interface.

Mitigating Ground Shocks with Cellular Solids

AbstractUnderground structures are sometimes threatened by ground shocks induced by subsurface detonations. This paper proposes one possible method to mitigate the subsurface blasts by attaching a cladding consisting of a face sheet and cellular solid core to the exterior of the structure; the cellular core is foam made from relatively strong materials, such as metal or concrete, rather than typical geofoam made from polymer. A simplified model is established to distinguish three scenarios to delineate the dynamic behavior of a foam cladding subjected to a ground shock. The model compares the velocity time histories of the face sheet and the surrounding soil, in which the foam crushing velocity is not high and the foam is densified uniformly. Further, the governing equations for possible high-velocity foam crushing are established, with progressive collapse as foam crushing mode when alleviating subsurface blasts.