Stress-displacement Relationship Research Articles

Failure characterization of Longmaxi shale under direct shear mode loadings

Insight into the shear failure of shale is significant for the analysis of hydraulic fracturing and wellbore stability in a shale gas reservoir. In this work, a series of direct shear tests is conducted on cubic Longmaxi shale samples with various bedding orientations, i.e., α = 0°, 30°, 60° and 90°, where the bedding orientation α is defined as the angle between the bedding and shearing direction. The anisotropies in the shear stress-displacement relation, failure pattern and shear strength are then analyzed and highlighted. Stress fluctuation is widely observed near the peak shear stress for most samples with α = 30° and 60°, and the shear displacement at the peak shear stress reaches its maximum and minimum values at α = 60° and α = 0°, respectively, for a given normal stress. The failure surface is formed by shear sliding along a weak bedding plane if α = 0°, resulting in a smooth failure surface with a much lower fractal dimension value; when α = 30°, 60° and 90°, some inclined cracks form across the failure surface during shearing, resulting in much rougher fracture surfaces. The shear strength and cohesion reach their minimum values at α = 0°, while the smallest internal friction angle is observed at α = 90°. Finally, by considering the anisotropies induced by the material microstructure and stress state, a new anisotropic shear failure criterion is presented and found to achieve good agreement with the test results. With the new criterion, the bedding angle corresponding to the maximum shear strength is found to vary with the applied normal stress.

Characterization of Discontinuity and Mechanical Anisotropy of Shale Based on Continuum Damage Mechanics

The effect of the bedding structure on the mechanical properties of layered shale was studied by means of experiment and numerical simulation. Based on continuum damage theory and discrete fracture network modeling method (D-DFN), a finite element model describing structural discontinuity and mechanical anisotropy of shale is established. In this model, the degradation process of stiffness and strength of shale after failure is described based on the stress-displacement relationship of elements. In order to distinguish the mechanical properties between the bedding and the matrix, a nonzero initial damage variable is set in bedding elements to show initial lower elastic modulus and strength of bedding elements compared with initially nondamaged matrix elements. The calibration of model parameters is discussed, and the simulation results are compared with the experimental results. The results show that the D-DFN method can effectively simulate the anisotropic characteristics of shale deformation and strength, which verifies the effectiveness of the method.

Preparation and characterization of ultra-high-strength and ultra-high-ductility cementitious composites incorporating waste clay brick powder

Large quantities of waste clay bricks from construction and demolition (C&D) waste are currently stockpiled in landfills, which is an environmentally, technically, and economically detrimental procedure. In this work, waste clay bricks powder (WCBP) was assessed to determine its feasibility as an alternative to cement for ultra-high-strength and ultra-high ductility cementitious composites (UHS-UHDCCs). The influences of WCBP on the fluidity, hydration, mechanical properties, fiber/matrix interface performances, autogenous shrinkage, and ecological overload capacity of UHS-UHDCC with different replacement levels ranging from 0 to 50% were investigated. The results indicate that WCBPs reduce the fluidity of the UHS-UHDCC matrix. WCBP content of 20% slightly accelerates the hydration process and exhibits the highest compressive and flexural strength in the specimens. Moreover, all UHS-UHDCCs achieve strain-hardening characteristics and exhibit a tensile strain capacity of 3.18–5.47%. UHS-UHDCC with 20% WCBP obtains excellent ultimate tensile stress and tensile strain capability, reaching around 9.34 MPa and 3.18%, respectively. The performance of the interface frictional bond (τ) with different WCBP content was obtained through single-fiber pullout tests, which reasonably explained the macroscopic tensile properties of UHS-UHDCC. The average interface frictional bond (τ) between the fiber and matrix of UHS-UHDCC reaches the maximum 1.72 MPa in the WCBP20 specimen. The average slip hardening coefficient (β) of UHS-UHDCC is distributed between 0.0031 and 0.0075 and tends to be excellent in the WCBP20 specimen. The theoretical fiber bridging stress vs crack displacement relationship of UHS-UHDCC was calculated through the limitation of interface parameters, which had an excellent correlation with the experimental results. Furthermore, the introduction of WCBP remarkably reduces the autogenous shrinkage of UHS-UHDCC. The ecological overload capacity of UHS-UHDCC is decreased by the introduction of WCBP, which provides an environmentally friendly solution for the C&D and cement industries.

A shear damage model of the interface between soil and sulfate-corroded concrete

In order to investigate the mechanical properties of the interface between sulfate-corroded concrete piles and soil, a corrosion shear damage model and a method to determine the model parameters were proposed based on statistical damage theory. Assuming that the corrosion damage of the interface obeys Weibull random distribution, a damage model is established, which contains only six parameters. By fitting curves, the model parameters are obtained from the interface direct shear test. The shear damage model can not only predict the shear deformation behaviors, but also consider the effects of normal stress and corrosion time on the shear properties of the interface after corrosion. The results show that the shear stress-displacement relationships are significantly affected by normal stress and corrosion time. The peak shear stress increases with normal stress, and the corresponding peak shear displacement also increases. The longer the corrosion time is, the less obvious the shear softening phenomenon of soil-concrete interface is, and as the corrosion time reaches a threshold level, the softening phenomenon of shear stress-displacement relationship changes into weak softening. Finally, the rationality and feasibility of the proposed model are verified by comparing the theoretical curves with the experimental curves.

Displacement Analyses for a Natural Slope Considering Post-Peak Strength of Soils

A natural slope undergoing recurrent movements caused by rainfall-induced groundwater table rises is studied using a novel method. The strength and displacement parameters are back-calculated using a force-equilibrium-based finite displacement method (FFDM) based on the first event of slope movement recorded in the monitoring period. Slope displacements in response to subsequent rainfall-induced groundwater table rises are predicted using FFDM based on the back-calculated material parameters. Important factors that may influence the accuracy of slope displacement predictions, namely, the curvature of the Mohr-Coulomb (M-C) failure envelope and post-peak strength softening, are investigated. It is found that the accuracy of slope displacement predictions can be improved by taking into account post-peak stress-displacement relationship in the analysis. The accuracy of slope displacement predictions is not influenced by the curvature of the M-C failure envelope in the displacement analysis.

Role of hydro-mechanical coupling in excavation-induced damage propagation, fracture deformation and microseismicity evolution in naturally fractured rocks

We present a numerical study of spatio-temporal damage evolution and fracture displacements around underground excavation in fractured rock masses. We conduct a comparative analysis of this problem based on a mechanical (M) model by assuming an invariant pore pressure and a hydro-mechanical (HM) model by solving the coupling between the fluid and solid fields. In both models, an elasto-brittle constitutive law is employed to mimic the deformational and failure behavior of intact rocks, while a non-linear stress-displacement relationship is used to account for the normal compression and shear dislocation of natural fractures. In the HM model, we simulate excavation-induced transient groundwater flow in fractured porous rocks based on Darcy's law. The hydraulic and mechanical fields are linked based on the coupling mechanisms of poroelasticity (direct HM coupling) and stress-dependent material properties (indirect HM coupling). Many important HM phenomena such as stress perturbation, pore pressure fluctuation, damage evolution and fracture deformation are realistically captured in our simulation. We find that both direct and indirect couplings play important roles, and the excavation-induced disturbance in rock varies with the coupling degree characterized by the Biot coefficient. One interesting observation is that excavation-induced stress redistribution around the tunnel instantly causes perturbed pore pressure in low-permeability matrix, which gradually becomes dissipated during the post-excavation drainage. We also highlight the role of natural fractures in the tunnel inflow process and elucidate the consequences of spatial and temporal pressure variations. In addition, we analyze the microseismicity occurrence during and after the excavation to gain insights into excavation and drainage-induced responses in the fractured rock. The results of our simulation and analysis have important implications for underground excavation involved in many geoengineering applications such as civil infrastructure, nuclear waste repository and oil/gas/geothermal wellbore systems.

Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

Particle shape effects on the cyclic shear behaviour of the soil–geogrid interface

The accurate determination of the interface shear strength is essential in the design of geosynthetic-reinforced soil structures. The particle geometries of three types of soil materials and a spherical granular medium are imaged and quantified using binary image-based methods and described in terms of regularity. Cyclic direct shear tests are conducted to investigate the effects of particle regularity on the interface shear strength, stress–displacement relationship, shear stiffness, and damping ratio. The results reveal that the interface shear strength and deformation strongly depend on particle regularity. The vertical displacement ratio is found to increase with particle regularity under the same cycle number. The interface stiffness is observed to increase with the cycle number for particle regularities of 0.453, 0.565, and 0.672 but decreases with the cycle number for a particle regularity of 0.971. For a given regularity, the trend of damping ratio with the increasing cycle number is contrary to the that of shear stiffness. Finally, it is observed that the cyclic friction angle decreases with increasing particle regularity, the relationship of which is determined using linear regression. Thus, the systematic quantification of particle shape characteristics can lead to a better understanding of soil–geogrid interface behaviour.

A model of the time-harmonic torsional response of piled plates using an IBEM-FEM coupling

This article presents a model of the response of rigid circular plates supported by embedded elastic pile foundations under time-harmonic torsional excitation. The contact tractions at the pile-soil and plate-soil interfaces are resolved into circumferential components, which are then approximated by piece-wise constant distributions. The dynamic stress-displacement relation for the soil part, here modeled as a homogeneous, transversely isotropic half-space, is obtained by numerical integration of that medium’s Green’s functions. The pile is modeled as a series of interconnected one-dimensional circular shafts, and the plate is modeled by imposing rigid-body rotation conditions throughout the portion of the surface of the soil that it occupies. A tangential Winkler-type layer is incorporated between the plate and the soil, in order to represent potential imperfect bonding contact that may occur in engineering practice. This article presents an analysis of the influence of geometric and constitutive parameters of the system in its time-harmonic torsional response, as well as a study on the wave propagation from the piled plate system through the soil.

Mechanical and thermal buckling analysis of laminated composite plates

The mechanical and thermal buckling analysis of laminated composite plates is presented in this document. Different theories of thick plates taking into account the parabolic distribution of transverse shear stresses and satisfying the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor are presented and a comparison between the results obtained by these theories is also illustrated. The high order nonlinear stress-displacement relation of the plates was taken into consideration. The principle of potential energy is used to obtain the equations of equilibrium. The closed-form solutions of symmetric and antisymmetric cross-ply are obtained using Navier solution. Using math software Maple, the temperatures and the critical loads of buckling are determined. Finally, a parametric study of the influence of the various parameters such as: mode of buckling, the geometrical ratios a / b and a / h, Young's modulus, Coefficient of thermal expansion, loading type, the orientation of the fibers and the number of layers on the critical buckling temperature and the critical buckling charge is shown and discussed. Numerical results indicate that deformation due to transverse shear has a significant effect on both mechanical and thermal behavior of buckling of laminated simply supported plates.

Effect of working temperature on the interfacial behavior of overmolded hybrid fiber reinforced polypropylene composites

In the present study, the interfacial behavior of overmolded hybrid fiber reinforced polypropylene composites (hybrid composites) in the working temperature range from 23 °C to 90 °C was studied by experimental and constitutive methods. Monotonic and cycle loading-unloading single-lap-shear tests were employed to determine the interfacial properties of hybrid composites. The experimental results show that both interfacial shear strength and shear stiffness decrease with increasing working temperature. A regression function was adopted to evaluate the decaying degree of interfacial properties with increasing working temperature. The shear stress-displacement relationship under monotonic loading exhibits nonlinear behavior after an initial elastic region. The envelope lines of shear stress-displacement of hybrid composites under cyclic loading indicate that the nonlinearity in the curve is caused by the plastic deformation of polypropylene in the interphase region. A constitutive model was built to describe the nonlinear shear stress-displacement relation of hybrid composites at different working temperatures. A full suite of temperature-dependent plastic parameters in the model was obtained from cyclic loading-unloading tensile tests. The predicted shear stress–displacement curves agreed well with experimental results from different working temperatures. In addition, the failure mode of hybrid composites varied with working temperature.

Reformulated fractional plasticity for soil-structure interface

Correct representation of the non-associated state-dependent behavior of the soil-structure interface is important for geotechnical applications. The original fractional plasticity is reformulated in this study, by exploring the stress-displacement relation of the soil-structure interface under plain strain condition. Without using additional plastic potentials, a state-dependent non-associated plastic flow vector is developed for the interface, where plastic flow direction is governed by the fractional gradient of yielding function. The developed interface model has eight constants, which can be all determined from laboratory tests. Further validation against a series of test results of different soil-structure interfaces shows that the developed model can well capture the constitutive behavior of the interface subjected to different boundary conditions. The typical normal-dilatancy and strain hardening/softening responses of the interface can be reasonably reproduced.

Nonlinear shear constitutive model for peak shear-type joints based on improved Harris damage function

The majority of jointed rock mass failures mainly occur along the joints in shear mode, which promotes a wide investigation on the proposal of a reasonable and reliable shear constitutive model of rock joints. In this paper, based on Improved Harris function and laboratory shear tests, a new constitutive model of saw-tooth joints was proposed. Firstly, a series of laboratory direct shear tests were carried out on saw-tooth joint specimens made of rock-like materials (cement mortar) to obtain the shear stress-displacement curves. Subsequently, the test results were divided into sliding failure type and peak shear type according to whether there is a significant stress drop between peak stress and residual stress. It is assumed that rock elements can be divided into undamaged parts and damaged parts during the shearing process. The stress-displacement relation of the undamaged part satisfies Hooke’s law, while the damaged part provides residual stress. Via the comparison with commonly used micro-element failure probability density functions, the Improved Harris distribution function was selected as the standard to characterize the strength of micro rock units. Finally, derived from the theory of damage statistical mechanics, a damage statistical constitutive model was proposed, which can reflect the deformation characteristics of rock joints. Compared with previous models and experimental data, the model proposed in this paper can represent the trend of peak shear curve variation with higher accuracy, the parameters are easy to be solved and have obvious physical significance, which verifies the advantages and applicability of this model.

Statistical Damage Shear Constitutive Model of Rock Joints Under Seepage Pressure

The constitutive relation of rock joints in the percolation environment has always been a frontier research topic in the field of geotechnical engineering, involving nuclear waste disposal, dam foundation construction, tunnel tunneling and other fields. In this paper, a shear statistical damage constitutive model of rock joints considering seepage pressure was proposed, which takes into account the statistical damage, phase deformation characteristics and seepage action in the process of joint shear deformation. By introducing the seepage pressure reduction coefficient and establishing the relationship between the model parameters and the seepage pressure, the prediction of joint shear stress-displacement curves under different seepage pressures was achieved. The comprehensive comparisons between the theoretical results and the experimental results shows that the model can accurately reflect the shear deformation law of joints and reasonably simulate the shear stress-displacement relationship of joints. And ultimately, the physical significance of the model parameters and their relationship with shear strength characteristics are discussed via the grey correlation method.

Experimental and numerical investigation on bond between steel rebar and high-strength Strain-Hardening Cementitious Composite (SHCC) under direct tension

Sufficient bonding between Strain-Hardening Cementitious Composites (SHCC) and steel rebars is required to guarantee the stress transfer in structural applications. Although the bond between medium-strength SHCC and rebars has been extensively studied, the present understanding of this property for high-strength SHCC is very limited. Moreover, the previous pullout or bending test methods have some limitations. This study investigates the bond between deformed steel rebars and high-strength SHCC with a new direct tension approach, which is able to determine the fundamental interfacial stress versus displacement relation under pure tension. The effects of concrete block material and cover thickness, rebar diameter and embedment length, as well as confinement condition on the bond behavior were experimentally evaluated. The test results showed that high-strength SHCC can bond much better with deformed steel rebars than ordinary concrete and high-strength SHCC matrix (without fibers) due to the well-controlled splitting cracks, and that the geometry has certain influences on the bond strength. A simple but reasonably accurate finite element model for engineering applications was also proposed to analyze the bond behavior in structural components. In this model, all the non-linear behaviors were integrated into rebar/SHCC interfacial elements, so that the complicated steel surface geometry and/or the local splitting of concrete do not need to be explicitly modelled. Through a coupled experimental-numerical approach, the bond stress-displacement relationship was extracted from a small number of test results. The derived relationship was then employed for the prediction of additional test results, with good agreement achieved. With its general applicability demonstrated, the proposed numerical approach can facilitate the design of reinforced SHCC elements and structures.

Dynamic modelling and motion control research on deep seabed miner

In this paper, the trafficability and motion performances of a seabed miner were obtained by the collaborative simulation between a multi-body dynamic (MBD) model and a motion control system model. For the development of the seabed sediment mechanical model, a numerical simulation by the discrete element method (DEM) and a laboratory physical experiment were performed to obtain the specific shear stress-displacement (S-D) and pressure-sinkage (P-S) relationship of the seabed sediment. Besides, the computational fluid dynamics (CFD) method was adopted to investigate the hydrodynamic loads acting on the miner under the linear motion and circular motion conditions. Moreover, the MBD model and motion control system model of the miner were respectively established in the simulation programs RecurDyn/Track and MATLAB/Simulink. Then, A fuzzy adaptive PID control was introduced to improve the motion accuracy, and the collaborative simulation results were discussed. This research can provide a theoretical basis and technical reference for the optimization design, operation control and performance prediction of the seabed miner.

3D analytical investigation on the overall pullout behavior of grouted anchorages in presence of shear failure of grout

Grouted anchorages have been extensively applied in practical projects like reinforcing steel anchors embedded into concrete or rock through cement grouting. The pullout behavior of the anchorages is generally a three-dimensional (3D) problem, whereas most existing analytical studies are based on a one-dimensional (1D) assumption such that the overall behavior of the anchorages has not been fully understood. In this paper, a 3D analytical solution is presented that is capable of predicting the overall pullout behavior of grouted anchorages in the presence of shear failure of grout, where the shear behavior of the grout is simulated by a bilinear shear stress-displacement relation. 3D closed-form solutions are deduced for the displacement field, the stress field and the load-displacement curve of both long and short anchorages for various loading phases. The analytical solution is validated by comparing the analytical results with the experimental and numerical results from the literature. The load-displacement characteristics of long and short anchorages are elaborated with the influence of the anchorage length on the load-displacement response evaluated. Comparative study is conducted to investigate the difference between 1D and 3D solutions on the global load-displacement response and the local shear stress distribution. The results show that there is no significant difference between 1D and 3D solutions in the case of very short anchorages. However, Poisson’s effect plays an increasing role in the stress transfer as the anchorage length increases, leading to an increasing discrepancy between the two solutions, which demonstrates that neglecting Poisson’s effect has an impact on the performance prediction of grouted anchorages. The present 3D analytical solution, with Poisson’s effect taken into consideration compared to 1D solution, can be expected to be better capable of evaluating the overall pullout behavior of grouted anchorages, especially for long anchorages. While the present study is conducted with reference to grouted anchorages, the analytical solution remains applicable to similar bonded structures such as reinforced composites and cylindrical adhesive joints.

Moisture content effect on the ring shear characteristics of slip zone loess at high shearing rates

The residual strength of slip zone loess is strongly affected by the moisture content. To explore such an effect, slip zone loess obtained from Baqiao landslide was used in ring shear tests under moisture content ranging from 6% to 29%. Laboratory tests were utilized for the determination of the stress–displacement relationship and residual strength parameters for the effect of moisture content in loess. The experimental results showed that the residual strength generally decreases with increasing moisture content. In addition, for a given shearing rate, the residual strength at any moisture content is approximately proportional to the normal stress. The stress fluctuation of shear stress was found to be greater with high shearing rates. Furthermore, the effect of moisture content on the residual strength parameters (cohesion and friction angle) was presented: the residual cohesion of slip zone loess was observed to increase with moisture content to a certain limit that approaches the plastic limit, above which it decreases. Also, the friction angle of slip zone loess was found to decrease with increasing moisture content. Additionally, due to the increase of the moisture content, the scratch color on the shear surface changed from the original color yellow to brown and the thickness of the shearing band of samples reduced. Finally, the mechanism of the influence of moisture content on the macroscopic morphology of the shear surface was also analyzed and illustrated. The study may provide a basis for understanding the shear behavior of slip zone loess under different moisture contents, as well as guidelines for loess landslide stability prevention and prediction.

A load-transfer function for the side resistance of drilled shafts in soft rock

The shear stress and shear displacement relationship for the rock socket sidewalls is required for the calculation of the drilled shaft butt settlement under the service loads. This paper first introduces a comprehensive database of in situ axial load tests on drilled shafts, anchors and plugs that are embedded in different soft rock formations. The database includes measurements of (i) the initial shear stiffness, (ii) the peak shear stress and (iii) the post-peak reduction in shear stresses for the socket sidewalls. In addition to the load test results, information on soft rock mass mechanical properties and rock socket geometry is also included. It is found that (i) the initial shear stiffness is directly related to the deformation modulus of the soft rock mass and inversely proportional to the rock socket diameter and length, (ii) the mobilized peak shear stress is related to the drained friction angle of the rock mass and normal stress on the socket sidewalls at failure. The rock mass friction angle is related to the rock type and the geological strength index, and the normal stress at failure is directly related to deformation modulus of rock mass and inversely to the product of rock socket length and diameter, and (iii) the post-peak brittleness is related to the soft rock type and the post-peak shear displacement. An empirical framework for the prediction of the load-transfer function for side resistance of sockets in soft sedimentary and fine-grained rock is developed using the load test database introduced herein. The proposed framework accounts for the socket geometrical characteristics, and the rock mass engineering properties. The pre-peak range in the load-transfer function is modeled using a hyperbolic function, and the post-peak range is modeled using a brittleness index to account for the reduction in shear stresses with post-peak displacement.

Improvement of the engineering behavior of sand-clay mixtures using kenaf fiber reinforcement

Abstract The reinforcement of structural elements and construction materials using natural fibers has gained popularity among researchers and industries due to environmental concerns and financial problems of synthetic fibers. The contribution of natural fibers as soil reinforcement elements enhances the shear strength properties as the stresses in the soil mobilize tensile resistance in the fibers. Despite the specific limitations of direct shear test, it is considered as one of the most commonly used techniques that gives the design engineers a quick measure of soil strength properties when a certain fine content exists in the soil mixture. Therefore, this study is intended to present the results of a series of large-scale direct shear tests on compaction characteristics and shear strength properties of kenaf fiber reinforced soil. A total number of 128 tests have been carried out to determine the compaction and shear strength characteristics of unreinforced and reinforced sand-clay mixtures. Subsequently, the influence of kenaf fiber reinforcement on the stress-displacement relationship, volume change, ductility and failure state of reinforced soil was evaluated. Based on the results, the addition of a certain amount of kenaf fiber to the sand-clay mixture enhances the mixture ductility, improves the shear strength parameters, and ultimately makes it an appropriate candidate to be used in construction projects such as pavement layers, slope protection, embankment, and building foundation.