Study on the Meso-Energy Damage Evolution Mechanism of Single-Joint Sandstone under Uniaxial and Biaxial Compression

Energy conversion and release occur through the entire deformation and failure process in jointed rock masses, and the accumulation and dissipation of rock mass energy in engineering can reveal the entire process of deformation and instability. This study uses PFC2D to carry out numerical simulation tests on single-joint sandstone under uniaxial compression and biaxial compression, respectively, and analyse the influence of joint inclination, length, and confining pressure on the meso-energy conversion process and phase evolution of jointed sandstone. Through analysis, it is found that the input meso total strain energy is transformed into meso dissipated energy and meso-elastic strain energy. Macroscopic and microscopic joint sandstone law is consistent with the overall energy evolution; and the difference is reflected in two aspects: (1) the microlevel energy evolution has no initial compaction energy consumption section and (2) the linear energy storage section before the macroenergy evolution peak can be subdivided into two sections in the meso-level energy evolution. Under uniaxial compression, the energy values at the characteristic points of the meso-level energy evolution phases first asymmetrically decrease and then increase with the increase of the joint inclination. The initiation point of jointed sandstone is significantly affected by the length of the joint, and the degradation effect of the meso-energy at the damage point and peak point weakens with the increase of the joint length. Comparing the data obtained from the PFC numerical simulation with the experimental data, it is found that the error is small, which shows the feasibility of the numerical model in this paper. Under biaxial compression, the accumulation rate of meso-elastic strain at the peak point of the jointed sandstone first decreases and then increases with the joint inclination angle. After the peak of jointed sandstone, the rate of sudden change of meso-energy change decreases with the increase of joint length. The conditions of high confining pressure will promote the meso-accumulated damage degree of the jointed sandstone before the peak, while inhibiting the meso-energy and the mutation degree of the damage after the peak. The higher the confining pressure, the more obvious the joint length and inclination effect characteristics of the elastic strain energy at the peak point of the jointed sandstone.

Numerical Analysis for the Caving Characteristics of Rock Mass with Inclined Joints in Caving Mining

In caving mining, the successful initiation and propagation of caving require one low-dip joint set. However, not every mine has a low-dip joint set. The Hemushan Iron Mine in China was taken as the engineering background, and the caving characteristics of rock mass with inclined joints were analyzed based on the synthetic rock mass (SRM) model. First, the inclined joints were investigated in the Hemushan Iron Mine. Second, model parameters were determined based on the geological conditions of the mine, and seven models were established. Third, the caving process was simulated, and caving characteristics were monitored. For rock mass with inclined joints after undercutting, the research showed that the crack zone was significant, and the crack zone existed not only around the undercut area but also further away in the model. The stress concentration areas dispersed in the model except for the top of the undercut area. The caving line was not a standard arch, and the highest point of the caving line was biased towards the direction of the undercut. Under the same undercut width, with the decrease of joint length in the joint system, the number of cracks decreased, the degree of stress concentration became weaker, and the height of the caving line decreased.

Improved Continuum Joint Configuration Estimation Using a Linear Combination of Length Measurements and Optimization of Sensor Placement

This paper presents methods for placing length sensors on a soft continuum robot joint as well as a novel configuration estimation method that drastically minimizes configuration estimation error. The methods utilized for placing sensors along the length of the joint include a single joint length sensor, sensors lined end-to-end, sensors that overlap according to a heuristic, and sensors that are placed by an optimization that we describe in this paper. The methods of configuration estimation include directly relating sensor length to a segment of the joint's angle, using an equal weighting of overlapping sensors that cover a joint segment, and using a weighted linear combination of all sensors on the continuum joint. The weights for the linear combination method are determined using robust linear regression. Using a kinematic simulation we show that placing three or more overlapping sensors and estimating the configuration with a linear combination of sensors resulted in a median error of 0.026% of the max range of motion or less. This is over a 500 times improvement as compared to using a single sensor to estimate the joint configuration. This error was computed across 80 simulated robots of different lengths and ranges of motion. We also found that the fully optimized sensor placement performed only marginally better than the placement of sensors according to the heuristic. This suggests that the use of a linear combination of sensors, with weights found using linear regression is more important than the placement of the overlapping sensors. Further, using the heuristic significantly simplifies the application of these techniques when designing for hardware.

Time-dependent behavior of rock-like specimen containing multiple discontinuous joints under uniaxial step-loading compression

Rock with multiple discontinuous joints widely exists in rock engineering, and its mechanical properties are complex, which greatly increases the difficulty of engineering design and construction. Time-dependent deformation characteristics and long-term strength evaluation of jointed rock masses remain poorly understood. In this work, the creep experiments of rock-like specimens with multiple discontinuous joints under uniaxial step-loading compression are carried out to explore the influence of joint geometry (rock bridge length, joint length, joint angle, and joint spacing) on creep strain, long-term strength, and failure pattern of specimens with multiple discontinuous joints. The following conclusions are drawn from the test results: 1) The deformation of jointed rock specimens has evident time-dependent effect, and the cumulative creep deformation increases as creep load increases; 2) The strength of jointed rock specimens under loading changes with time, and the ratio of long-term strength and creep peak strength ( σ∞/ σc) of the tested specimens ranges from 41% to 96%; 3) The distribution of initial joints affects the creep fracture modes of rock-like specimens. The rupture of rock-like specimens with different joints distribution is mainly caused by the growth of wing cracks and quasi-coplanar secondary cracks. Three different failure modes are observed from these specimens: i) tensile failure with cracks across the joint plane; ii) shear failure with cracks along the joint plane; and iii) tensile failure with cracks along the joint plane. Based on the principles of damage mechanics and fracture mechanics, a theoretical mechanistic model considering both the closure stage of pre-existing open joints and time-dependent propagation stage of new cracks is established. Considering the influence of joint length, joint angle and joint density, the evolution of creep strain of rock-like specimen with multiple discontinuous joints is analyzed. The theoretical model results agree well with the experimental results, which indicates that the established model can replicate the creep failure process of jointed rock mass. These theoretical and test results help us better understand the effect of multiple joints on the long-term behavior of rock mass.

Spatiotemporal Evolution Characteristics of Fluid Flow through Large-Scale 3D Rock Mass Containing Filling Joints: An Experimental and Numerical Study

This study analyzes the spatiotemporal evolution characteristics of seepage through a large-scale rock mass containing a filling joint. Firstly, a conceptual model was established to characterize the geomechanical occurrence of a typical water-resistant slab adjacent to a water-bearing structure. Then, a special apparatus was developed to conduct a hydromechanical test of a 3D large-scale rock mass. For a certain boundary stress and inlet water pressure, the pore water pressure in the joint first experiences a dramatic increase before approaching a constant value, and the steady pore water pressure presents a linear decrease along the joint length. A water inrush phenomenon happens as a result of connected flowing channels induced by migration of fillings. Using the finite element of COMSOL multiphysics, the influences of filling joint permeability, matrix permeability, and joint thickness as well as the inlet water pressure on seepage evolution in the jointed rock mass were, respectively, investigated. The pore water pressure increases with all these factors, and the stable pressure values increase with the inlet water pressure but decrease along the joint length. The flow velocity undergoes an increase with both the joint permeability and inlet water pressure but presents constant values independent on the matrix permeability or joint thickness. The water pressure contour planes distributed along the flowing path generally transfer from a “long funnel” shape to a “short funnel” shape before reaching a series of parallel pressure planes perpendicular to the joint direction. By using the genetic algorithm, the coupling influences of these factors on the pore water pressure and flow velocity were investigated, and the decision parameters were optimized. The calculated values show a good agreement with the numerical results, indicating a good prediction of the seepage evolution through the filling joint.

Experimental Study on the Fracture Evolution Processof Rock-like Specimens Containing a Closed RoughJoint Based on 3D-Printing Technology

In order to overcome the disadvantage of traditional joint fabrication method—inability to reproduce the rough surfaces of practical rock joints—3D-printing technology was applied to restructure five kinds of rough joint according to the failure surface formed by the triaxial prepeak unloading test in this study. And uniaxial compression test was carried out on the rock-like specimens containing closed 3D-printing rough joint to study the effects of joint inclination and joint length on the mechanical properties (peak strength, peak strain, elastic modulus, and secant modulus), cracking process, and failure modes. Besides, digital image correlation (DIC) method and acoustic emission (AE) system are used to investigate the whole evolution process of strain fields and crack propagation during loading. It is found that the mechanical parameters decrease first and then go up as the joint inclination increases, while presenting a continuous downward trend with the increase of joint length. Inclination of 45° and the larger joint length bring more extensive reduction to mechanical properties of specimens. Specimens exhibit typical brittle failure characteristics. The failure mode of specimens affected by different joint inclination is tension-shear failure. And the joint scale rises; the failure mode of specimens changes from tensile failure to shear failure. Larger joint scale results in the longer prepeak fluctuation phase on axial stress-strain curves and more dispersed distribution of high-value AE counts.

Numerical Shear Tests on the Scale Effect of Rock Joints under CNL and CND Conditions

The scale effect of rock joint shear behavior is an important subject in the field of rock mechanics. There is yet a lack of consensus regarding whether the shear strength of rock joints increases, decreases, or remains unchanged as the joint size increases. To explore this issue, a series of repeated and enlarged numerical joint models were established in this study using the particle flow code (PFC2D). The microparameters were calibrated by uniaxial compression tests and shear tests on the concrete material under the constant normal loading (CNL) condition. Three different normal stresses were adopted in numerical shear tests with joint specimen lengths ranging from 100 mm to 800 mm. In addition to the commonly used CNL, the constant normal displacement (CND) condition was established for the purposes of this study; the CND can be considered an extreme case of the constant normal stiffness (CNS) condition. The shear stress-shear displacement curves changed from brittle failure to ductile failure alongside a gradual decrease in peak shear strength as joint length increased. That is, an overall negative scale effect was observed. Positive scale effect or no scale effect is also possible within a limited joint length range. A positive correlation was also observed between the peak shear displacement and joint length, and a negative correlation between shear stiffness and joint length. These above statements are applicable to both repeated and enlarged joints under either CNL or CND conditions. When the normal stress is sufficiently high and shear dilatancy displacement is very small, the shear behavior of rock joints under CNL and CND conditions seems to be consistent. However, for shear tests under low initial normal stress, the peak shear strength achieved under the CND condition is much higher than that under the CNL condition, as the normal stresses of enlarged joints increase to greater extent than the repeated ones during shearing.

Task space-based orientability analysis and optimization of a wire-driven continuum robot

Compared to traditional rigid robots, continuum robots have intrinsic compliance and therefore behave dexterously when performing tasks in restricted environments. Although there have been many researches on the design and application of continuum robots, a theoretical investigation of their dexterity is still lacking. In this paper, a two-joint wire-driven continuum robot is utilized to demonstrate dexterity by introducing the concept of orientability taking into account two indices, the accessible ratio and angle of the robot, when its tip reaches a certain task space inside the workspace. Based on the kinematic model, the accessible ratio and angle of the continuum robot are calculated using the Monte-Carlo method. From this, the influence of individual joint lengths on the proposed orientability indices and the optimal joint length are then investigated via an improved particle swarm optimization algorithm. Finally, the presented methods were validated through experiments showing that the use of optimal joint length can increase the accessible ratio and reduce the minimum accessible angle by more than 10° in the task space.

Seismic Performance of Damaged Dovetail Joints with Different Damaged Degrees in Timber Frames

The mortise and tenon joints are the main connection forms used in ancient timber buildings, and damaged joints have a critical effect on the safety of a timber structure. There are three main damaged cases of dovetail joints which are pulling, contraction, and mixing damages. In this study, using a theoretical analysis of the stress distribution in a mortise and tenon joint resulted from the pullout damage, a theoretical equation for the resisting moment of the joint was proposed. A finite element model was used to simulate the cyclic displacement loading of a frame with intact joints and with different levels of pulling and contraction damaged joints. The results show that the moment capacities both for the test and the simulation were in good agreement with each other. The simulation results also indicated that there are no changes in the capacity and energy dissipation of the pulling damaged joint compared to that of the intact joint, and good seismic performance still was provided when the pulling damage was less than 2/5 of the joint length. However, the capacity of the contraction damaged joint was significantly reduced, and its seismic performance was tolerably lost. The seismic performance of a mixing damaged tenon with the same degree of pulling damage was between that of the pulling damaged tenon and the contraction damaged tenon, and generally, it was controlled by the contraction damage. The friction between the tenon and the mortise is the main source of resisting moment and energy dissipation ability.