Constant Normal Stiffness Research Articles

Shear Behavior and Asperity Damage of 3D Rough Joints under CNS Boundary Conditions Based on CZM Simulation

Although boundary conditions can significantly impact the shear behaviors and asperity damage evolution of jointed rocks, numerical studies on the damage of 3D rough rock joints under the constant normal stiffness (CNS) boundary condition have rarely been reported. In this work, the three-dimensional model of the irregular joint surface is established by using point cloud reconstruction technology. Based on the cohesive zone model (CZM), we simulate the shear behavior of three-dimensional rough rock joints under the CNS boundary condition, which is realized by using embedded spring elements implemented with a Python subroutine. We conducted laboratory direct shear tests under CNS boundary conditions. The agreement with the laboratory experimental results verifies the fidelity of the numerical method. Our results show that boundary conditions can significantly affect the shear behavior of rock joints, especially in the post-peak stage. Under the same initial normal stress, the peak shear stress and the number of microcracks in the asperities increase significantly with the increase of normal stiffness. The proportion of shear cracks positively correlates with the normal stiffness, indicating that the normal stiffness affects the joint failure mode. The damaged area and the volume of asperities increase with the increase of normal stiffness. Moreover, the distribution of shear-induced asperity loss becomes more nonuniform, and the loss of joint roughness increases rapidly and nonlinearly.

Experimental investigation of soil–structure interface behaviour under monotonic and cyclic thermal loading

The effect of temperature on the monotonic and cyclic shearing response of a soil–structure interface is of critical importance for the application of thermal-active geo-structures. To investigate this, soils and soil–concrete interfaces were comprehensively tested with a temperature-controlled direct shear device under both fixed temperatures and thermal/mechanical cycles within the range of 2–38 °C. Monotonic and cyclic shearing with various boundary conditions, including constant normal load (CNL), constant normal stiffness (CNS) and constant volume (CV), were conducted to resemble the conditions that thermal-active-geo-structures may experience. The strength properties of the sand, clay, and sand–concrete and clay–concrete interfaces were partially influenced by heating and cooling under all boundary conditions. However, several effects were observed which could affect the performance of thermo-active structures. Heating cycles caused the clay–concrete interface to be overconsolidated, implying a lower excess pore pressure would be generated during shearing. The cyclic CNS tests suggested that the interface strength could degrade due to (thermally induced) cyclic shear displacements, with this effect strongly related to the state of the soil rather than the temperature directly. In these tests, the medium-dense sand–concrete interface degraded to almost zero shear strength after 5 cycles, whereas the clay–concrete interface asymptotically degraded to around 60% of its strength after 10 cycles.

Study on surface roughness effect on shear behavior of concrete-soil interface

Concrete piles have been widely used in practice due to their large bearing capacity and small settlement. The roughness of concrete-soil interface has a significant influence on load transfer of piles and deformation between piles and soil. To investigate the surface roughness effect on shear behavior of concrete-soil interface, a series of laboratory shear tests, e.g., monotonic and cyclic shear tests, were carried out by using a self-developed large-scale constant normal stiffness (CNS) cyclic shear apparatus. In the laboratory shear tests, the simulation method on the surface roughness of pile body was proposed according to the measured hole diameter along the depth of in-situ bored piles, and concrete samples with different surface roughness values were formed by using carving machine. Based on the results of shear tests on the interface between concrete and standard sand under monotonic and cyclic shear, the relationship between the shear stress and the corresponding displacement was obtained, and the fitting relationship between the shear strength and roughness of concrete-sand interface was established. The shear displacement field of sand was analyzed by using a digital photogrammetric measurement software. The results show that the maximum thickness of the intense shear zone is observed to be 6.25 times the median particle diameters.

A three-dimensional (3D) analytical solution for the ultimate side shear resistance of rock-socketed shafts

This paper presents a new analytical solution to the ultimate side shear resistance τsf of rock socketed shafts with consideration of three-dimensional (3D) strength and shaft sidewall roughness. Specifically, the shaft sidewall profile is simplified as triangular asperities and micro-mechanical analysis is performed on the shear behavior of one representative asperity. A 3D version of the Hoek-Brown (HB) criterion for rock mass and the equilibrium equations in a cylindrical coordinate system are first utilized to derive the governing equations. Then the governing equations are solved by using the method of characteristics. Finally, the τsf is obtained by considering the constant normal stiffness condition and the relative displacement of the rock mass due to sliding along the shaft-rock mass interface. Twenty-four (24) model and field test shafts with measured τsf are collected for analysis to verify the proposed solution. The results indicate that the predicted τsf values are in good agreement with the measured τsf values. Extensive parametric studies are also conducted to investigate the effects of rock mass properties, shaft dimensions, and sidewall roughness parameters on the ultimate side shear resistance factor αf (the ratio of τsf to the unconfined compressive strength of intact rock σc) of rock socketed shafts. The results indicate that the αf increases with rock constant mi, geological strength index (GSI) and asperity half chord length λ, but decreases with shaft diameter B, σc and disturbance D. Furthermore, the αf first increases and then decreases with the asperity inclination angle δ, resulting in an optimum asperity inclination angle δOp. Therefore, it is important to reduce the disturbance of rock mass from construction and select a proper asperity inclination angle when designing a rock socketed shaft.

A micromechanics-based model for concrete-rock interface with similar triangular asperities

Direct shear tests on samples containing similar triangular asperities have been carried out under constant normal stiffness (CNS) conditions, and observations demonstrated that there exists local lift-off of shallower asperities across the interface, resulting in a redistribution of local stresses and further impacting the global shear behavior . This study further modifies the existing theoretical model based on multiple-asperity configurations, previously presented by the authors. The proposed method relates the normal and shear stresses on the individual asperity to interface strength and corresponding displacement in terms of the asperity inclination and contact areas. The emphasis is on quantifying the number of shallower asperities that would be lifted off when the closely contacted asperities are dislocated by an amount of interface dilation. In addition to the mechanism of local lift-off itself, the resultant redistribution of global shear stress on remaining asperities can be also taken into account. The proposed model is verified by predicting experimental observations published elsewhere, and the comparison appears to be satisfactory.

Experimental Study on the Influence of Hydromechanical Boundary Conditions on Shear-Flow Coupling Characteristics of Granite Joints

The instability of jointed rock mass is usually the shear process of the rock mass along discontinuities under the influence of groundwater flow. By conducting laboratory tests and numerical experiments on the shear-flow coupling of rock joints under constant normal stiffness (CNS) and constant normal stress (CNL) boundary conditions, the influence of normal boundary conditions and seepage pressure on the shear mechanical and flow characteristics of joints were investigated. The test results were as follows: The joint shear stiffness, peak, and residual shear strength under the CNS boundary condition were predominantly larger than those under the CNL boundary condition. Overall, these parameters were positively correlated with the initial normal stress σ n 0 . When σ n 0 > 2 MPa, the postpeak shear stress of the CNS boundary condition showed a sharp decrease, whereas that of the CNL boundary condition changed from a slowly decreasing type ( σ n 0 = 4 MPa, 6 MPa) to a sharply decreasing type at σ n 0 = 8 MPa. The peak dilation rate under the CNS boundary condition at all levels of normal stress was lower than that of CNL, and the strain softening in postpeak of the latter was more remarkable. In the process of joint shear, the hydraulic aperture displayed a four-stage variation law of “steady-sudden increase-slow increase-basically stable.” Moreover, the hydraulic aperture under the CNS boundary condition was always lower than that under the CNL boundary condition. The seepage pressure increased from 0.5 MPa to 1.5 MPa, and the average hydraulic aperture in the stable stage under normal stress at all levels increased from 0.146 mm to 0.187 mm. In addition, the average peak shear stress and average shear stiffness decreased by 0.9 MPa and 0.83 GPa/m, respectively. We also established a numerical model of a real rough three-dimensional joint, compiled a calculation program for the shear-flow process of a joint under CNS boundary conditions, and visualized the flow channel inside the joint. The seepage flow bypassed the area where the joints contacted each other, forming obvious flow channels. The flow rate increased at the intersection of the flow channels.

Shear behaviour of infilled rock joints under different boundary conditions

The use of commercial software for the analysis and design of rock slopes, underground structures, mining projects, foundations of infrastructure projects, piles and so on is becoming more commonplace. However, such software sometimes has limitations and cannot be used directly for determining the strength and deformation behaviour of rock joints when they are subjected to external loads due to construction. Correct predictions of the strength and deformation behaviour of rock joints are important for safe, economical and sustainable design. The strength and deformation behaviour of unfilled and infilled rock joints were numerically studied using the commercial software Universal Distinct Element Code (Udec) under different boundary conditions (constant normal stiffness (CNS) and constant normal load (CNL)). The numerical results were compared with experimental results of physical model tests. The strength predicted by the numerical model was in close agreement with the experimental results at low initial normal stress and for CNL boundary conditions, as asperity degradation during the shearing process was almost same throughout the test. However, the numerical model did not correctly predict the shear strength of rock joints under CNS boundary conditions and at high normal stress under both CNL and CNS conditions because Udec does not consider the effect of asperity degradation during shearing. The Udec code was thus modified for applicability under both CNL and CNS boundary conditions and at high initial normal stress at CNL boundary conditions. Comparison of the predicted and experimental results indicated most predictions to lie in the 95% confidence band.

Effect of particle breakage on the behavior of soil-structure interface under constant normal stiffness condition with DEM

Previous studies show that extensive particle breakage occurs at the soil-structure interface, which may influence the shear strength, but a corresponding comprehensive micro-mechanical analysis, particularly with constant normal stiffness (CNS), is missing. In this study, a series of interface shear tests under CNSs are simulated with the discrete element method (DEM) to understand the role of particle breakage at the interface. Through a rigorous calibration process, the interface model in DEM is first validated with identifying micro-mechanical parameters. Then, by modifying the reference tensile strength of particles, the effect of particle breakage on the behavior of soil-structure interface is quantitatively investigated. All results demonstrate that, particle breakage decreases the dilation, normal stress, shear stress, and shear zone thickness in the interface shear test; particle breakage decreases the peak friction angle while increases the residual friction angle at the interface; and particle breakage decreases soil anisotropy at the interface. In addition, the degree of particle breakage is increased by normal stiffness. The findings of this study may provide deeper insights on the role of particle breakage at the interface with CNS and allow engineers to have a better estimation of the interface strength.

Failure mechanism of fine-grained soil-structure interface for energy piles

The response of the soil-structure interface can significantly affect the performance of any geotechnical structure. Thermal cycles are a new factor that influence the response to all structures that have an energy function in addition to the structural one, such as energy piles foundations. In this study, a theoretical interpretation of the failure mechanism at the pile-soil interface subjected to cyclic thermal loads and a dedicated constitutive model is presented. The phenomenon is characterised by large localised strains concentrated in a thin layer around the pile surrounded by soil behaving under oedometric conditions. The theoretical framework refers to direct shear tests at a constant normal stiffness, as well as oedometric tests on clayey soil. Observations indicate a negligible effect of the temperature cycles on the soil-structure interface response for typical temperature ranges of energy piles (ΔT= −10, +20 °C). Therefore, an isothermal mathematical formulation in the framework of elastoplasticity is proposed for the analysis of both conventional and energy piles. The effectiveness of the interface model in reproducing the observed behaviour is confirmed via experimental tests. The proposed constitutive model is applicable in engineering practice via the finite-element or the load-transfer method. Additionally, its calibration requires exclusively conventional geotechnical testing.

Anchorage effect of bolt on en-echelon fractures: A comparison between energy-absorbing bolt and conventional rigid bolt

Widespread en-echelon fractures may induce some disasters such as landslides of rock slopes and destabilization of underground excavations. Bolt support has been widely used in various rock engineerings for many years, but the bolting behavior of en-echelon fractures has rarely been studied. In this study, the anchorage effect of conventional rigid bolt and energy-absorbing bolt was investigated by direct shear tests under constant normal stiffness conditions. The bolting performance of the two bolts was quantitatively evaluated based on shear strength and dilation indices. The test results show that the anchorage effect of bolt is closely related to the bolt material and fracture angle. This is essentially determined by the deformation mechanism of bolt in different shear failure structures. A bolt deformation factor was proposed to predict the breakage displacement of bolt at different fracture angles and a bolt contribution index was defined to comprehensively evaluate the bolting performance.

Enhancement of constant normal stiffness direct shear testing protocols for determining geomechanical properties of fractures

Discontinuity behaviour can have a large impact on geotechnical engineering design; therefore, it is essential to determine their geomechanical properties to predict rockmass behaviour and mitigate any potential failure that may affect personnel safety or damage property. Geotechnical numerical software programmes that discretely simulate discontinuities rely on direct shear laboratory tests to provide the properties needed as inputs to these tools. This study presents valuable direct shear laboratory test results for the mechanical properties and behaviours of fresh, unweathered, rough fractures in the Pointe du Bois granite. The testing programme considers three separate boundary conditions: constant normal stress (CNL*) and two variations of constant normal stiffness (CNS). A new machine stiffness model is proposed to estimate the machine stiffness for tunnelling applications. Measurements of shear strength and a proposed secant dilation angle are assessed and critically evaluated. It is found in this study that there is no significant difference between shear strength parameters determined from direct shear data from CNL* and CNS boundary conditions when comparing maximum strength and residual strength. In addition, it is found that the proposed secant dilation angle, critical shear displacement, and total dilation potential all have a negative relationship with increasing normal stress.

Influence of surface roughness on shear behaviors of rock joints under constant normal load and stiffness boundary conditions

Influence of surface roughness on shear behaviors of rock joints under constant normal load and stiffness boundary conditions

Influence of Microroughness on Stick–Slip Characteristics of Fault Under Constant Normal Stiffness

Influence of Microroughness on Stick–Slip Characteristics of Fault Under Constant Normal Stiffness

Numerical Simulation on Shear Behavior of Double Rough Parallel Joints Under Constant Normal Stiffness Boundary Condition

The shear characteristics of rock joints under constant normal stiffness (CNS) boundary condition are critical to the stability of underground engineering rock mass. Five different rock joint profiles with random morphology were constructed using the independent segmentation method of the Hurst exponent. Based on the continuously yielding joint model, the discrete element calculation models of double rough parallel joints with different joint surface roughness and spacing of joints under CNS boundary condition were established using UDEC software to investigate the shear effect of joints under CNS boundary condition. The results show that under CNS boundary condition, the shear stress, normal displacement, normal stress, and surface resistance index (SRI) all increase with the increase of joint surface roughness coefficient (JRC) for both single- and double-joint specimens, and these of the single-joint are greater than these of the double-joint. With the increase of the joint spacing d, the peak shear stress τy, and the peak surface resistance index (SRIp) show a gradually increasing trend, and the influence of d on τy and SRIp is greater with the increase of JRC, and both τy and SRIp show a linear increasing trend with the increase of JRC. With the increase of d for the same JRC, both normal displacement and normal stress show a gradually increasing trend, and also, the increased amplitudes gradually increase; with the increase of JRC for the same d, the two parameters also show an increasing trend.

Modelling the Constant Normal Stiffness Shear Strength of Rock Discontinuities Filled with Unsaturated Materials

Modelling the Constant Normal Stiffness Shear Strength of Rock Discontinuities Filled with Unsaturated Materials

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

Linear and nonlinear fluid flow responses of connected fractures subject to shearing under constant normal load and constant normal stiffness boundary conditions

Linear and nonlinear fluid flow behaviors of connected fractures during shearing under constant normal load and constant normal stiffness boundary conditions are numerically characterized solving the Navier-Stokes equations. The model consists of three fractures having an identical length of 200 mm and a width of 100 mm, among which the bridge fracture is sheared. Both smooth and rough-walled fracture surfaces are generated to investigate the effect of surface roughness on flow streamline distributions and the ratio of flow rate to hydraulic gradient. The results show that the permeability monotonically increases during shearing under constant normal load conditions, due to the shear-induced dilation of fractures. Under constant normal stiffness conditions, the permeability either increases or decreases during shearing, controlled by the competing role played by the shearing fracture and nearby fractures. As shear advances, the shearing fracture dilates and increases the permeability, whereas the surrounding fractures are compressed that decrease the permeability. The flow rate of rough-walled models is overestimated by approximately 45 ∼ 80% comparing to the smooth parallel plate model. For smooth models, the critical hydraulic gradient dramatically decreases with increasing the shear strain from 0.015 to 0.025 and then slightly fluctuates with the increment of shear strain from 0.025 to 0.05. The critical hydraulic gradient monotonically decreases during the shearing process for rough-walled models. The range of critical hydraulic gradient is between 0.001 and 0.02.

Impact of shear displacement on advective transport in a laboratory-scale fracture

The impact of shear displacement under different mechanical boundary conditions on fluid flow and advective transport in a single fracture at the laboratory scale is demonstrated in the present study. The shear-induced changes of fracture aperture structures are determined by using the measured normal displacements and digitalized fracture surfaces from laboratory shear tests. Five shear tests on concrete replicas of the same fracture under different mechanical boundary conditions, including constant normal loading (CNL) and constant normal stiffness (CNS), are conducted to analyse the influence of mechanical boundary conditions on the shear-flow-transport processes. Fluid flow in the fracture with different shear displacements are simulated by solving the Reynolds equation. The Lagrangian particle tracking method is applied to model the advective transport in the fracture after shearing. The results generally show that the shear displacements and the normal loading conditions can significantly affect flow patterns and advective travel time distributions in the fracture. For mated fractures, the flow and transport will be enhanced by the increasing shear displacement because of shear dilation. For cases with the same shear displacement, the median advective travel time increases with the increasing boundary normal stiffness. The median advective travel time under the CNS boundary condition is generally longer than that under the CNL boundary condition. The results from this study can help to improve our understanding of stress-dependent solute transport processes in natural rock fractures.

Large-scale characterisation of cemented rock fill performance for exposure stability analysis

A novel large-scale geomechanical laboratory testing program is developed to provide full characterization of the strength and deformational response of cemented rockfill (CRF) material for use in exposure stability analyses. Uniaxial compressive strength (UCS), direct shear, and three-point bending tensile tests are performed on large-scale samples that require the use of novel processes and laboratory equipment. For the first time, the shear properties of large-scale CRF samples have been investigated using direct shear tests under constant normal stiffness (CNS) boundary conditions. Large-scale three-point bending tests are also conducted to obtain true tensile strengths without having to infer them from UCS test results. For up to 28 days curing time, the effects of particle size distribution and binder quantity are experimentally examined for each compression, tension, and shear failure mode through a study of the full stress–strain response. In order to obtain accurate laboratory results, findings are compared against published large-scale tests from various mine sites. The results show that the large-scale samples completed herein provide a reliable UCS estimate with standard deviations of less than one. It is also found that the direct shear responses are substantially larger for simulated CRF: Sidewall contacts than CRF: CRF contacts, and tensile strength responses are higher than previously estimated at 10% of the UCS strength. The effect of particle size distribution on the geomechanical response of the CRF material is highlighted through the large-scale sample testing. The findings of this research study provide increased technical understanding for the development of CRF structures in underground mines that are cost-effective, safe, and durable. Additionally, this research study establishes a practical testing methodology that overcomes the challenges that occur in collecting quantitative geomechanical data from large-scale CRF samples for design purposes.

Research Progress on Shear Characteristics of Rock Joints under Constant Normal Stiffness Boundary Conditions

The constant normal stiffness (CNS) boundary condition is more representative for the underground engineering, in which the shear-induced dilation is restricted by surrounding rocks, resulting in an increase in the normal stress. Therefore, the use of CNS boundary conditions in the research of shear-slip failure of underground rock engineering is more in line with the actual situation. Taking the instability and failure of surrounding rock in underground engineering as the background, the present study introduces the engineering background of CNS boundary conditions and the research progress on shear characteristics of rock joints under CNS boundary conditions. Three key directions for future research are proposed based on the latest research results of shear characteristics of rock joint under CNS boundary conditions: ① developing a rock joint shear test system that can realize the function of “CNS boundary conditions + shear-seepage test + visualization”; ② carrying out the shear tests of real rock joints under CNS boundary conditions based on 3D scanning and 3D carving technology; and ③ carrying out the shear tests of rock joint network under CNS boundary conditions.