Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.

Dynamic compressive characteristics of a green sandstone under coupled hydraulic-mechanical loading: Experiments and theoretical modeling

Deep rock is under a complex geological environment with high geo-stress, high pore pressure, and strong dynamic disturbance. Understanding the dynamic response of rocks under coupled hydraulic-mechanical loading is thus essential in evaluating the stability and safety of subterranean engineering structures. Nevertheless, the constraints in experimental techniques have led to limited prior investigations into the dynamic compression behavior of rocks subjected to simultaneous high in-situ stress and pore pressure conditions. This study utilizes a triaxial split Hopkinson pressure bar (SHPB) system in conjunction with a pore pressure loading cell to conduct dynamic experiments on rocks subjected to hydraulic-mechanical loading. A porous green sandstone (GS) was adopted as the testing rock material. The findings reveal that the dynamic behavior of rock specimens is significantly influenced by multiple factors, including the loading rate, confining stress, and pore pressure. Specifically, the dynamic compressive strength of GS exhibits an increase with higher loading rates and greater confining pressures, while it decreases with elevated pore pressure. Moreover, the classical Ashby-Sammis micromechanical model was augmented to account for dynamic loading and pore pressure considerations. By deducing the connection between crack length and damage evolution, the resulting law of crack expansion rate is related to the strain rate. In addition, the influence of hydraulic factors on the stress intensity factor at the crack tip is introduced. Thereby, a dynamic constitutive model for deep rocks under coupled hydraulic-mechanical loading was established and then validated against the experimental results. Subsequently, the characteristics of introduced parameter for quantifying the water-induced effects were carefully discussed.

Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review

Rock failure phenomena,such as rockburst,slabbing(or spalling) and zonal disintegration,related to deep underground excavation of hard rocks are frequently reported and pose a great threat to deep mining.Currently,the explanation for these failure phenomena using existing dynamic or static rock mechanics theory is not straightforward.In this study,new theory and testing method for deep underground rock mass under coupled static-dynamic loading are introduced.Two types of coupled loading modes,i.e.'critical static stress + slight disturbance' and 'elastic static stress + impact disturbance',are proposed,and associated test devices are developed.Rockburst phenomena of hard rocks under coupled static-dynamic loading are successfully reproduced in the laboratory,and the rockburst mechanism and related criteria are demonstrated.The results of true triaxial unloading compression tests on granite and red sandstone indicate that the unloading can induce slabbing when the confining pressure exceeds a certain threshold,and the slabbing failure strength is lower than the shear failure strength according to the conventional Mohr-Column criterion.Numerical results indicate that the rock unloading failure response under different in situ stresses and unloading rates can be characterized by an equivalent strain energy density.In addition,we present a new microseismic source location method without premeasuring the sound wave velocity in rock mass,which can efficiently and accurately locate the rock failure in hard rock mines.Also,a new idea for deep hard rock mining using a non-explosive continuous mining method is briefly introduced.

Dynamic tensile behaviour and crack propagation of coal under coupled static-dynamic loading

The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal.In this study,coupled static-dynamic loading tests are conducted on Brazilian disc(BD)coal specimens using a modified split Hopkinson pressure bar(SHPB).The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied.The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing.When no static axial pre-stress is applied,or the static axial pre-stress is 30%of the static tensile strength,the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases.When the static axial pre-stress is 60%of the static tensile strength,the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases.According to the crack propagation process of coal specimens recorded by high-speed camera,the impact velocity influences the mode of crack propagation,while the static axial pre-stress influences the direction of crack propagation.The failure of coal specimens is a coupled tensile-shear failure under high impact velocity.When there is no static axial pre-stress,tensile cracks occur in the vertical loading direction.When the static axial pre-stress is applied,the number of cracks perpendicular to the loading direction decreases,and more cracks occur in the parallel loading direction.

Mechanical properties of rock under coupled static-dynamic loads

Rock drilling machine,INSTRON testing system,and SHPB device are updated to investigate the characteristics of rocks at great depth,with high loads from overburden,tectonic stresses and dynamic impacts due to blasting and boring.It is verified that these testing systems can be used to study the mechanical properties of rock material under coupled static and dynamic loading condition and give useful guidance for the deep mining and underground cavern excavation.Various tests to determine the rock strength,fragmentation behavior,and energy absorption were conducted using the updated testing systems.It is shown that under coupled static-dynamic loads,if the axial prestress is lower than its elastic limit,the rock strength is higher than the individual static or dynamic strength.At the same axial prestress,rock strength under coupled loads rises with the increasing strain rates.Under coupled static and dynamic loads,rock is observed to fail with tensile mode.While shear failure may exist if axial prestress is high enough.In addition,it is shown that the percentage of small particles increases with the increasing axial prestress and impact load based on the analysis of the particle-size distribution of fragments.It is also suggested that the energy absorption ratio of a specimen varies with coupled loads,and the maximum energy absorption ratio for a rock can be obtained with an appropriate combination of static and dynamic loads.

Numerical analysis of deformation and failure characteristics of deep roadway surrounding rock under static-dynamic coupling stress

In actual production,deep coal mine roadways are often under typical static-dynamic coupling stress(SDCS)conditions with high ground stress and strong dynamic disturbances.With the increasing number of disasters and accidents induced by SDCS conditions,the safe and efficient production of coal mines is seriously threatened.Therefore,it is of great practical significance to study the deformation and failure characteristics of the roadway surrounding rock under SDCS.In this paper,the effects of different in-situ stress fields and dynamic load conditions on the surrounding rock are studied by numerical simulations,and the deformation and failure characteristics are obtained.According to the simulation results,the horizontal stress,vertical stress and dynamic disturbance have a positive correlation with the plastic failure of the surrounding rock.Among these factors,the influence of the dynamic disturbance is the most substantial.Under the same stress conditions,the extents of deformation and plastic failure of the roof and ribs are always greater than those of the floor.The effect of horizontal stresses on the roadway deformation is more notable than that of vertical stresses.The results indicate that for the roadway under high-stress conditions,the in-situ stress test must be strengthened first.After determining the magnitude of the in-situ stress,the location of the roadway should be reasonably arranged in the design to optimize the mining sequence.For roadways that are strongly disturbed by dynamic loads,rock supports(rebar/cable bolts,steel set etc.)that are capable of maintaining their effectiveness without failure after certain dynamic loads are required.The results of this study contribute to understanding the characteristics of the roadway deformation and failure under SDCS,and can be used to provide a basis for the support design and optimization under similar geological and geotechnical circumstances.

Supporting characteristics analysis of constant resistance bolts under coupled static-dynamic loading

To study the tensile mechanical properties of constant resistance bolts, the RFPA(Rock Failure Process Analysis) statics software is used to perform a uniaxial tensile test on a constant resistance bolt. The numerical test results show that the plastic strain value is 12 times the magnitude of the elastic strain. During plastic deformation, the fluctuation in the stress magnitude is relatively stable, indicating that the bolt has good constant resistance characteristics. The numerical test results are in good agreement with the laboratory test results of M.C. He, and the accuracy and reliability of the numerical test method are verified. Therefore, the RFPA software with coupled static-dynamic loading is further adopted to study the supporting effects of traditional bolts and constant resistance bolts under coupled staticdynamic loading. The numerical comparison of the test results show that the constant resistance bolts can effectively control the deformation amount and rate of the laneway surrounding rock, reduce the total and rate of increase in the accumulated acoustic emissions,decrease the stress on the units in the model and protect the stability of the laneway. This paper verifies that a constant resistance bolt has better impact resistance mechanical properties than those of a traditional bolt and provides an effective way to control rock burst and soft rock that is prone to large deformation damage.

Dynamic response and failure behavior of rock under static-dynamic loading

Dynamic response and failure behavior of rock under static-dynamic loading were studied. The effects of initial static load on the total energy dissipated during the failure process of specimen were analyzed. To simulate the engineering situation that in-situ rock experienced and obtain the dynamic loading with an intermediate strain rate, a low cycle fatigue load with the frequency from 0.5 to 5 Hz was adopted by servo-controlled Instron material testing system. The results show that the obtained strain rate increase with the increase of load frequency. The initial static load has great influence on both the energy and dynamic response of rock. Both the energy and the maximum failure load P_f decreases with the increase of initial static load. P_f under the static-dynamic loading is larger than that under only the static loading but less than that under only the dynamic loading. The load-displacement curves become nonlinear as the pre-added static load reaches the transition point which is about one third of static strength. With the increase of initial static load, Young’s modulus decreases and poisson ratio increases. It shows that rock has a lower strength and a tendency to soften under a higher initial static load. Rock may be broken more easily static-dynamic loading than under only the dynamic loading. The proposed method is useful in the investigation of constitutive relationship and failure behavior of rock under quasi-dynamic loading.

Mechanical behavior of sandstone during post-peak cyclic loading and unloading under hydromechanical coupling

This paper investigates mechanical behaviours of sandstone during post-peak cyclic loading and unloading subjected to hydromechanical coupling effect, confirming the peak and residual strengths reduction laws of sandstone with water pressure, and revealing the influence of water pressure on the upper limit stress and deformation characteristics of sandstone during post-peak cyclic loading and unloading.Regarding the rock strength, the experimental study confirms that the peak strength σ_(p) and residual strength σ_(r) decrease as water pressure P increases. Especially, the normalized strength parameters σ_(p)/σ_(pk) and σ_(r)/σ_(re) was negatively and linearly correlated with the P/σ_(3). Moreover, the Hoek-Brown strength criterion can be applied to describe the relationship between effective peak strength and effective confining stress. During post-peak cyclic loading and unloading, both the upper limit stress σ_(p(i)) and crack damage threshold stress σ_(cd(i)) of each cycle tend to decrease with the increasing cycle number. A hysteresis loop exists among the loading and unloading stress–strain curves, indicating the unloading deformation modulus E_(unload) is larger than the loading deformation modulus E_(load). Based on experimental results,a post-peak strength prediction model related to water pressure and plastic shear strain is established.

Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure

To reveal the water inrush mechanics of underground deep rock mass subjected to dynamic disturbance such as blasting, compression-shear rock crack initiation rule and the evolution of crack tip stress intensity factor are analyzed under static-dynamic loading and seepage water pressure on the basis of theoretical deduction and experimental research. It is shown that the major influence factors of the crack tip stress intensity factor are seepage pressure, dynamic load, static stress and crack angle. The existence of seepage water pressure aggravates propagation of branch cracks. With the seepage pressure increasing, the branch crack experiences unstable extension from stable propagation. The dynamic load in the direction of maximum main stress increases type I crack tip stress intensity factor and its influence on type II crack intensity factor is related with crack angle and material property. Crack initiation angle changes with the dynamic load. The initial crack initiation angle of type I dynamic crack fracture is 70.5°. The compression-shear crack initial strength is related to seepage pressure, confining pressure, and dynamic load. Experimental results verify that the initial crack strength increases with the confining pressure increasing, and decreases with the seepage pressure increasing.

Coupling Mechanism of Saturated Concrete Subjected to Simultaneous Fatigue Loading and Freeze-thaw Cycles

The coupling mechanism of saturated concrete subjected to simultaneous 4-point fatigue loading and freeze-thaw cycles was, for the first time, experimentally studied by strain technology. The coupling strain, temperature strain and fatigue strain of concrete specimens were measured at the same time from one sample with stain analysis method and the relationship among these three kinds of strains was studied by fitting data to present coupling mechanism at macro level. The results showed that there was no interaction between fatigue strain and temperature strain and the coupling strain could be written by linear superposition of temperature strain and fatigue strain.

Stress Path Analysis of Deep-Sea Sediments Under the Compression-Shear Coupling Load of Crawler Collectors

The mechanical properties of deep-sea sediments during the driving process of crawler collectors are essential factors in the design of mining systems.In this study,a crawler load is divided into a normal compression load and a horizontal shear load.Then,the internal stress state of sedimentary soil is examined through a theoretical calculation and finite element numerical simulation.Finally,the driving of crawlers is simulated by changing the relative spatial position between the load and stress unit,obtaining the stress path of the soil unit.Based on the calculation results,the effect of the horizontal shear load on the soil stress response is analyzed at different depths,and the spatial variation law of the soil stress path is examined.The results demonstrate that the horizontal shear load has a significant effect on the rotation of the principal stress,and the reverse rotation of the principal stress axis becomes obvious with the increase in the burial depth.The stress path curve of the soil is different at various depths.The spatial variation rule of the stress path of the shallow soil is complex,whereas the stress path curve of the deep soil tends to shrink as the depth increases.The stress path of the corresponding depth should be selected according to the actual research purpose and applied to the laboratory test.

Torsionally coupled dynamic performance analysis of asymmetric offshore platforms subjected to wave and earthquake loadings

The dynamic equations of motion of asymmetric offshore platforms under three different environmental conditions:seismic action,wave action and their combination are established in this paper. In establishing these motion equations,three typical eccentricity types including mass eccentricity,rigidity eccentricity and their combination were considered,as are eccentricities that occur un-idirectionally and bi-directionally. The effects of the eccentricity type,the dynamic characteristics and the environmental conditions on the torsional coupling response of platforms are investigated and compared. An effort has also been made to analyze the inffluence of accidental eccentricity on asymmetric platforms with different eccentricity in two horizontally orthogonal directions. The results are given in terms of non-dimensional parameters,accounting for the uncoupled torsional to lateral frequency ratio. Numerical results reveal that the eccentricity type has a great inffluence on the torsionally coupled response under different environmental conditions. Therefore,it is necessary to consider the combination of earthquake and wave action in the seismic response analysis of some offshore platforms.

THE COUPLING IMPEDANCE OF VANE-LOADED TAPE HELIX SLOW-WAVE STRUCTURE

Based on the actual vane-loaded tape helix slow wave structure, a new theoretical analytic model for calculating coupling impedance is proposed by Chen Qingyou, et al.(1999)with calculated values of dispersion in good agreement with measured ones. In this paper, it is continued to use this model to calculate the coupling impedance of such a structure, and analyze the effects of the propagation power within vane gaps and the helix gap on the coupling impedance.As a result, the theoretical values are found to be in good agreement with the measured ones,with the maximum difference less than ±18%.

Coupling Singular Spectrum Analysis with Artificial Neural Network to Improve Accuracy of Sediment Load Prediction

Sediment load estimation is generally required for study and development of water resources system. In this regard, artificial neural network (ANN) is the most widely used modeling tool especially in data-constraint regions. This research attempts to combine SSA (singular spectrum analysis) with ANN, hereafter called SSA-ANN model, with expectation to improve the accuracy of sediment load predicted by the existing ANN approach. Two different catchments located in the Lower Mekong Basin (LMB) were selected for the study and the model performance was measured by several statistical indices. In comparing with ANN, the proposed SSA-ANN model shows its better performance repeatedly in both catchments. In validation stage, SSA-ANN is superior for larger Nash-Sutcliffe Efficiency about 24% in Ban Nong Kiang catchment and 7% in Nam Mae Pun Luang catchment. Other statistical measures of SSA-ANN are better than those of ANN as well. This improvement reveals the importance of SSA which filters noise containing in the raw time series and transforms the original input data to be near normal distribution which is favorable to model simulation. This coupled model is also recommended for the prediction of other water resources variables because extra input data are not required. Only additional computation, time series decomposition, is needed. The proposed technique could be potentially used to minimize the costly operation of sediment measurement in the LMB which is relatively rich in hydrometeorological records.

ANALYSIS OF SHAKEDOWN OF FG BREE PLATE SUBJECTED TO COUPLED THERMAL-MECHANICAL LOADINGS

The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures.

Mechanical Behaviors of Silt Rock Subjected to Coupling Static and Impact Loads

Experiments of silt rock subjected to coupling loads were carried out on tailormade equipment. With a constant dynamic load, the behaviors of eight sets of siltite specimens were investigated with different axial static loads. The experimental results show that the modulus of the specimens under coupling loads increases at first and then decreases with the increase of axial static pressure. The failure model of the specimens also varies. Keeping the dynamic load constant, when the axial static pressure is low, the specimen breaks in two simply. With the increase of axial static pressure, the cone-shaped fragment appeares. When the axial static pressure reaches 90% of the static strength of rock, the specimen smashes into amount of small fragments.

A numerical simulation study on mechanical behaviour of coal with bedding planes under coupled static and dynamic load

To investigate the bedding influence on coal mechanical behaviour in underground environments such as coal or rock burst, simulations of dynamic SHPB tests of pre-stressed coal specimens with different bedding angles were carried out using a particle flow code 2-dimensional(PFC2D). Three impact velocities of 4, 8 and 12 m/s were selected to study dynamic behaviours of coal containing bedding planes under different dynamic loads. The simulation results showed that the existence of bedding planes leads to the degradation of the mechanical properties and their weakening effect significantly depends on the angle h between the bedding planes and load direction. With h increaseing from 0° to 90°, the strength first decreased and subsequently increased and specimens became most vulnerable when h was 30° or 45°.Five failure modes were observed in the specimens in the context of macro-cracks. Furthermore, energy characteristics combined with ultimate failure patterns revealed that maximum accumulated energy and failure intensity have a positive relation with the strength of specimen. When bedding planes were parallel or perpendicular to loading direction, specimens absorbed more energy and experienced more violent failure with increased number of cracks. In contrast, bedding planes with h of 30° or 45° reduced the specimens' ability of storing strain energy to the lowest with fewer cracks observed after failure.

Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads

The deep fissured rock mass is affected by coupled effects of initial ground stress and external dynamic disturbance.In order to study the effect of internal flaw on pre-stressed rock mechanical responses and failure behavior under impact loading,intact granite specimens and specimens with different flaw inclinations are tested by a modified split Hopkinson pressure bar(SHPB)and digital image correlation(DIC)method.The results show that peak strain and dynamic strength of intact specimens and specimens with different flaw angles(α)decrease with the increase of axial static pressure.The 90°flaw has weak reduction effect on peak strain,dynamic strength and combined strength,while 45°and 0°flaws have remarkable reduction effect.Specimens with 90°flaw are suffered combined shear and tensile failure under middle and low axial static pre-stresses,and suffered shear failure under high axial static pre-stresses.Specimens with 45°and 0°flaws are suffered oblique shear failure caused by pre-existing flaw under different axial static pre-stresses.Besides,based on digital image correlation method,it is found that micro-cracks before formation of macro fractures(include shear and tensile fractures)belong to tensile cracks.Tensile and shear strain localizations at pre-existing flaw tip for specimen with 45°and 0°flaws are produced much earlier than that at other positions.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.