Strange Nonchaotic Attractors in a Quasiperiodically Excited Slender Rigid Rocking Block with Two Frequencies

In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor,or between two chaotic attractors.In particular,we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors.This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems.The properties of SNAs are verified by the Lyapunov exponent,rational approximation,phase sensitivity,power spectrum,and separation of nearby trajectories.

Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

Automatic identification of rock discontinuity and stability analysis of tunnel rock blocks using terrestrial laser scanning

Local geometric information and discontinuity features are key aspects of the analysis of the evolution and failure mechanisms of unstable rock blocks in rock tunnels.This study demonstrates the integration of terrestrial laser scanning(TLS)with distinct element method for rock mass characterization and stability analysis in tunnels.TLS records detailed geometric information of the surrounding rock mass by scanning and collecting the positions of millions of rock surface points without contact.By conducting a fuzzy K-means method,a discontinuity automatic identification algorithm was developed,and a method for obtaining the geometric parameters of discontinuities was proposed.This method permits the user to visually identify each discontinuity and acquire its spatial distribution features(e.g.occurrences,spac-ings,trace lengths)in great detail.Compared with hand mapping in conventional geotechnical surveys,the geometric information of discontinuities obtained by this approach is more accurate and the iden-tification is more efficient.Then,a discrete fracture network with the same statistical characteristics as the actual discontinuities was generated with the distinct element method,and a representative nu-merical model of the jointed surrounding rock mass was established.By means of numerical simulation,potential unstable rock blocks were assessed,and failure mechanisms were analyzed.This method was applied to detection and assessment of unstable rock blocks in the spillway and sand flushing tunnel of the Hongshiyan hydropower project after a collapse.The results show that the noncontact detection of blocks was more labor-saving with lower safety risks compared with manual surveys,and the stability assessment was more reliable since the numerical model built by this method was more consistent with the distribution characteristics of actual joints.This study can provide a reference for geological survey and unstable rock block hazard mitigation in tunnels subjected to complex geology and active rockfalls.

Mechanism of Pendulum-type wave phenomenon in deep block rock mass

Pendulum-type ( μ wave) wave is a new type of elastic wave propagated with low frequency and low velocity in deep block rock masses. The μ wave is sharply different from the traditional longitudinal and transverse waves propagated in continuum media and is also a phenomenon of the sign-variable reaction of deep block rock masses to dynamic actions, besides the Anomalous Low Friction (ALF) phenomenon. In order to confirm the existence of the μ wave and study the rule of variation of this μ wave experimentally and theoretically, we first carried out one-dimensional low-speed impact experiments on granite and cement mortar blocks and continuum block models with different characteristic dimensions, based on the multipurpose testing system developed by us independently. The effects of model material and dimensions of models on the propagation properties of 1D stress wave in blocks medium are discussed. Based on a comparison and analysis of the propagation properties (acceleration amplitudes and Fourier spectra) of stress wave in these models, we conclude that the fractures in rock mass have considerable effect on the attenuation of the stress wave and retardarce of high frequency waves. We compared our model test data with the data of in-situ measurements from deep mines in Russia and their conclusions. The low-frequency waves occurring in blocks models were validated as Pendulum-type wave. The frequencies corresponding to local maxima of spectral density curves of three-directional acceleration satisfied several canonical sequences with the multiple of 2～(1/2), most of those frequencies satisfied the quantitative expression (2～(1/2))i V p/2△ .

Mechanism of anomalous low friction phenomenon in deep block rock mass

Deep rock mass has the unique ＂self-stressed＂ block-hierarchical structure, anomalous low friction （ALF） was one of the typical nonlinear get-mechanical and dynamic responses in deep block rock mass, which occurred as the result of movements of large-scale get-blocks under the impact of external pulses （such as a deep confined explosion, earthquakes, rock bursts and etc.）. ALF phenomenon obtained its name to describe the curious phenomenon that the friction between interacting get-blocks qua- si-periodically disappears at some discrete points in time along the direction orthogonal to the direction of the external pulse. With the objective to confirm the existence of the ALF phenomenon and study the get-mechanical conditions for its occurrence experi- mentally and theoretically, laboratory tests on granite and cement mortar block models were carried out on a multipurpose testing system developed independently. The ALF phenomenon was realized under two loading schemes, i.e., blocks model and a working block were acted upon jointly by the action of a vertical impact and a horizontal static force, as well as the joint action of both ver- tical and horizontal impacts with differently delayed time intervals. We obtained the rules on variation of horizontal displacements of working blocks when the ALF phenomenon was realized in two tests. The discrete time delay intervals, corresponding to local maxima and minima of the horizontal displacement amplitudes and residual horizontal displacements of the working block, satis- fied canonical sequences multiplied by （√2）＇. Some of these time intervals satisfied the quantitative expression （√2）＇ ,alva. At last, 1D dynamic theoretical model was established, the analytical results agreed better with the test data, while the quantitative expression drawn from test data was not validated well in theoretical analyses.

A calculation model to assess the crack propagation length of rock block in clastic flow

The primary cracks in the rock block undergo series of steps and finally disintegrate,during this procession,the radius affects the impact force of rock block in clastic flow.Therefore,it is essential to figure out the evolution mechanism of crack propagation for the design of engineering protection.In this study,based on fracture mechanics and Hertz contact theory,collision happened between rock block and slope surface is assumed to be elastic contact.Based on the above assumption,the critical impact force of crack propagation is obtained,and a model used to calculate the crack propagation length in a single collision is established.Besides,a rock fall site in Jiuzhai Valley was used to verify the calculation model.According to the model,several key factors were identified to influence crack propagation length including falling height,initial equivalent radius,and recovery coefficient of slope surface.Moreover,as a result of the orthogonal experiment,the influence of those factors on the crack propagation length was ranked,normal recovery coefficient>initial radius>initial falling height.In addition,the kinetic energy of the rock block in the compression stage is transformed into elastic deformation energy,angular kinetic energy,and dissipated energy of crack propagation.Due to the increase of collisions,the kinetic energy is gradually transformed into angular kinetic energy,and the dissipated energy of crack propagation weights is reduced.In conclusion,the crack propagation in rock block is a complicated progress,which is affected by multiple factors,especially falling height,initial equivalent radius,and recovery coefficient of slope surface.Our study may provide guidance for the design of protective structure of clastic flows.

An estimation model for the fragmentation properties of brittle rock block due to the impacts against an obstruction

Mountain hazards with large masses of rock blocks in motion – such as rock falls, avalanches and landslides – threaten human lives and structures. Dynamic fragmentation is a common phenomenon during the movement process of rock blocks in rock avalanche, due to the high velocity and impacts against obstructions. In view of the energy consumption theory for brittle rock fragmentation proposed by Bond, which relates energy to size reduction, a theoretical model is proposed to estimate the average fragment size for a moving rock block when it impacts against an obstruction. Then, different forms of motion are studied, with various drop heights and slope angles for the moving rock block. The calculated results reveal that the average fragment size decreases as the drop height increases, whether for free-fall or for a sliding or rolling rock block, and the decline in size is rapid for low heights and slow for increasing heights in the corresponding curves. Moreover, the average fragment size also decreases as the slope angle increases for a slidingrock block. In addition, a rolling rock block has a higher degree of fragmentation than a sliding rock block, even for the same slope angle and block volume. Finally, to compare with others' results, the approximate number of fragments is estimated for each calculated example, and the results show that the proposed model is applicable to a relatively isotropic moving rock block.

Mechanical properties of bimrocks with high rock block proportion

For the investigation of mechanical properties of the bimrocks with high rock block proportion,a series of laboratory experiments,including resonance frequency and uniaxial compressive tests,are conducted on the 64 fabricated bimrocks specimens.The results demonstrate that dynamic elastic modulus is strongly correlated with the uniaxial compressive strength,elastic modulus and block proportions of the bimrocks.In addition,the density of the bimrocks has a good correlation with the mechanical properties of cases with varying block proportions.Thus,three crucial indices(including matrix strength)are used as basic input parameters for the prediction of the mechanical properties of the bimrocks.Other than adopting the traditional simple regression and multi-regression analyses,a new prediction model based on the optimized general regression neural network(GRNN)algorithm is proposed.Note that,the performance of the multi-regression prediction model is better than that of the simple regression model,owing to the consideration of various influencing factors.However,the comparison between model predictions indicates that the optimized GRNN model performs better than the multi-regression model does.Model validation and verification based on fabricated data and experimental data from the literature are performed to verify the predictability and applicability of the proposed optimized GRNN model.

Influence of stress wave-induced disturbance on ultra-low friction in broken blocks

Deep rock mass tends to be broken into blocks when mining for materials deep below the surface.The rock layer of the roof of the mine can be regarded as a system of blocks of fractured rock mass.When subjected to high ground stress and mining-induced disturbance,the efect of the ultra-low friction of the block system easily becomes apparent,and can induce rock burst and other accidents.By taking the block of rock mass as research object,this study developed a test system for ultra-low friction to experimentally examine its efects on the broken blocks under stress wave-induced disturbance.We used the horizontal displacement of the working block as the characteristic parameter refecting the efect of ultra-low friction,and examine its characteristic laws of horizontal displacement,acceleration,and energy when subjected to the efects of ultra-low friction by changing the frequency and amplitude of the stress wave-induced disturbance.The results show that the frequency of stress wave-induced disturbance is related to the generation of ultra-low friction in the broken block.The frequency of disturbance of the stress wave is within 1–3 Hz,and signifcantly increases the maximum acceleration and horizontal displacement of the broken blocks.The greater the intensity of the stress wave-induced disturbance is,the higher is the degree of block fragmentation,and the more likely are efects of ultra-low friction to occur between the blocks.The greater the intensity of the horizontal impact load is,the higher is the degree of fragmentation of the rock mass,and the easier it is for the efects of ultra-low friction to occur.Stress wave-induced disturbance and horizontal impact are the main causes of sliding instability of the broken blocks.When the dominant frequency of the kinetic energy of the broken block is within 20 Hz,the efects of ultra-low friction are more likely.

Petrogenesis of Early and Late Carboniferous Volcanic Rocks in the Yining Block:Constraints from Sr-Nd Isotope

The Yining Block is located in the southwestern part of the Central Asian Orogenic Belt （CAOB）,which is characterized by widespread Carboniferous volcanic rocks.Recently,we carried out the National Nature Science Foundation of China （No.41273033） and Special Fund for Basic Scientific Research of Central Colleges （No.310827153407） project,and focused on two suits volcanic rocks from the Early Carboniferous Dahalajunshan Formation and the Late Carboniferous Yishijilike Formation.Field observations,zircon U-Pb dating,and Sr-Nd isotopic dating were conducted to evaluate the petrogenesis.

Development of 2D computer program to determine geometry of rock mass blocks

Due to various geological processes such as tectonic activities fractures might be created in rock mass body which causes creation of blocks with different shapes and sizes in the rock body. Exact understand- ing of these blocks geometry is an essential issue concerned in different domains of rock engineering such as support system of underground spaces built in jointed rock masses, design of blasting pattern, optimi- zation of fragmentation, determination of cube blocks in quarry mines, blocks stability, etc. The aim of this paper is to develop a computer program to determine geometry of rock mass blocks in two dimen- sional spaces. In this article, the eometrv of iointed rock mass is programmed in MATLABTM.

Heterogeneity induced strain localization in block-in-matrix-soils subjected to uniaxial loading using real-time CT scanning

Block-in-matrix-soils(bimsoils)are geological mixtures that have distinct structures consisting of relatively strong rock blocks and weak matrix soils.It is still a challenge to evaluate the mechanical behaviors of bimsoils because of the heterogeneity,chaotic structure,and lithological variability.As a result,only very limited laboratory studies have been reported on the evolution of their internal deformation.In this study,the deformation evolution of bimsoils under uniaxial loading is investigated using real-time X-ray computed tomography(CT)and image correlation algorithm(with a rock block percentage(RBP)of 40%).Three parameters,i.e.heterogeneity coefficient(K),correlation coefficient(CC),and standard deviation(STD)of displacement fields,are proposed to quantify the heterogeneity of the motion of the rock blocks and the progressive deformation of the bimsoils.Experimental results show that the rock blocks in bimsoils are prone to forming clusters with increasing loading,and the sliding surface goes around only one side of a cluster.Based on the movement of the rock blocks recorded by STD and CC,the progressive deformation of the bimsoils is quantitatively divided into three stages:initialization of the rotation of rock blocks,formation of rock block clusters,and formation of a shear band by rock blocks with significant rotation.Moreover,the experimental results demonstrate that the meso-motion of rock blocks controls the macroscopic mechanical properties of the samples.

Numerical analysis of soil-rock mixture's meso-mechanics based on biaxial test

Soil-rock mixture(S-RM)is a widely distributed geotechnical medium composed of "soil" and "rock block" different both in size and strength. Internal rock blocks form special and variable meso-structural characteristics of S-RM. The objective of this work was to study the control mechanism of meso-structural characteristics on mechanical properties of S-RM. For S-RM containing randomly generated polygonal rock blocks, a series of biaxial tests based on DEM were conducted. On the basis of research on the effects of rock blocks' breakability and sample lateral boundary type(rigid, flexible) on macroscopic mechanical behavior of S-RM, an expanded Mohr-Coulomb criterion in power function form was proposed to represent the strength envelop. At the mesoscopic level, the variations of meso-structure such as rotation of rock block, and the formation mechanism and evolution process of the shear band during tests were investigated. The results show that for S-RM with a high content of rock block, translation, rotating and breakage of rock blocks have crucial effects on mechanical behavior of S-RM. The formation and location of the shear band inside S-RM sample are also controlled by breakability and arrangement of rock blocks.

Experimental Study on Seepage Characteristics of a Soil-Rock Mixture in a Fault Zone

A mixture of fault gouge and rubble taken out from a fault zone is used to prepare a S-RM(Soil-Rock Mixture)sample with rock block proportions of 20%,30%,40%,50%,60%and 70%,respectively.A GDS triaxial test system is used accordingly to measure the seepage characteristics of such samples under different loading and unloading confining pressures in order to determine the variation law of the permeability coefficient.The test results show that:(1)The permeability coefficient of the S-RM samples decreases as the pressure increases,and the decrease rate of this coefficient in the initial stage of confining pressure loading is obviously higher than in the semi-late period;(2)The permeability coefficient at different confining pressure levels presents a common trend as the rock block proportion is increased,i.e.,it decreases first then it increases(the permeability coefficient of the sample with rock block proportion 40%being the smallest,70%the largest);(3)In the stage of confining pressure unloading,the recovery degree of the permeability coefficient grows with the increase of rock block proportion(the recovery rate of S-RM sample with rock block proportion 70%reaches 50.2%);(4)In the stage of confining pressure loading and unloading,the sensitivity of the permeability coefficient to the rock block proportion displays the inverse“Z”variation rule(when rock block proportion reaches 60%,the sensitivity is highest);(5)In the stage of confining pressure loading,the relationship between the permeability coefficient and confining pressure can be described by an exponential relationship.

Cyclic load testing of pre-stressed rock anchors for slope stabilization

The objective of this research was to assess the characteristics of seismic induced damage and the deformation patterns of pre-stressed cement-grouted cables that are used for rock slope stabilization projects subjected to quasi-static cyclic loading.The experimental configuration includes the installation of 15 pre-stressed cables in a slope model made of concrete blocks(theoretically rigid rock mass) on top of a pre-existing sliding surface.The study showed that:(i) The pre-stressed cables exhibited great seismic performance.Rapid displacement of the model blocks was observed after the complete loss of the initial pre-stress load under continued applied cyclic loads and exceedance of the state of equilibrium,which implies the higher the initial pre-stress load,the better the seismic performance of the rock anchor;(ii) The failure of the pre-stressed cables was due to fracture at the connection of the tendons and cable heads under cyclic loading.The sequence of failure had a distinct pattern.Failure was first observed at the upper row of cables,which experienced the most severe damage,including the ejection of cable heads.No evidence of de-bonding was observed during the cyclic loading;(iii) The stress distribution of the bond length for pre-stressed cables was highly non-uniform.High stress concentrations were observed at both the fixed end and the free end of the bond length both before and immediately after the state of equilibrium is exceeded.The results obtained can be used to evaluate the overall performance of pre-stressed rock anchors subject to seismic loading and their potential as rockfall prevention and stabilization measures.

Experimental Field Study of Movement Charateristics of Rock Blocks Falling down a Slope

The downslope movement of detached rock blocks along steep slopes is an important process endangering the safety of infrastructure along the foot of a slope and on the valley bottom,but only limited knowledge is available on the influence of various factors on the velocity and distance of movement of such blocks.We discuss the influence of the mass and shape of the rock blocks,the steepness of the slope,and the thickness of the overburden on the slope,on the distance of movement of rock blocks which was observed in 256 field experiments with differently shaped blocks from 3 different positions on the slope with a height of 176 m.The statistical evaluation of the results of the field tests shows that the slope condition of gradient and overburden is the main factor,the form of rock masses is the second factor,and the mass is the third of the influencing factors.It is the maximum average acceleration for movement of rock masses when the mass of rock masses is 15≤m27 kg,the form of rock masses is flake,the condition of gradient is on average 59.6° and the overburden is basic exposed bedrock and a small quantity of gravel-soil in the experiment condition.It is the minimum average acceleration for movement of rock masses when the mass of rock masses is 9.5≤m15 kg,the form of rock masses is rectangular,the condition of gradient is on average 39° and the overburden is gravel-soil and cinder.Then,the foundation for impact energy is provided and the new feasible methods to prevent potential unstable rock masses are put forward.

Experimental and numerical simulation on the sliding process of roof rock blocks triggered by dynamic disturbance

With the excavation of underground opening,the roof rock block may fall under external dynamic disturbance.In this paper,the roof rock mass was simplified as a rock block system composed of trapezoidal rock blocks.A series of experiments and numerical simulations were performed to study the sliding process of the key block under the horizontal static clamping load and vertical impact disturbance.The propagation of stress wave in the block system were captured and analyzed by using high-speed camera and digital image correlation technique.The results reveal that a pendulum-type wave was generated due to the propagation and superposition of stress waves in the block system.Therefore,the governing mechanism of the sliding displacement of the key block was clarified based on the propagation of incident stress waves or pendulum-type waves.Meanwhile,it is found that the sliding distance of the key block decreases in a power function with the increasing friction coefficient,or decreases in a parabolic function with the increasing trapezoid internal angle.Finally,a case study on the roof block sliding of the roadway at a gold mine was conducted,and it is concluded that the sliding of the key block resulted from the coupled effects of"shear driving"and"low friction"driven by stress wave propagation,regardless of a single or multi-layer rock block system.These results may provide technical guideline for preventing rock-falling accidents caused by blasting distur-bances in underground mining.

Latest advances in discontinuous deformation analysis method

Discontinuous deformation analysis （DDA） method, proposed firstly by Shi [1] in 1988, is a novel numerical approach to simulate the discontinuous deformation behaviors of blocky rock structures. In DDA, the domain of interest is represented as an assemblage of discrete blocks and the joints are treated as interfaces between blocks. The governing equations of DDA are derived from Newton’s Second Law of Motion and the Principle of Minimum Potential Energy.