Failure behavior and strength model of blocky rock mass with and without rockbolts

To better understand the failure behaviours and strength of bolt-reinforced blocky rocks,large scale extensive laboratory experiments are carried out on blocky rock-like specimens with and without rockbolt reinforcement.The results show that both shear failure and tensile failure along joint surfaces are observed but the shear failure is a main controlling factor for the peak strength of the rock mass with and without rockbolts.The rockbolts are necked and shear deformation simultaneously happens in bolt reinforced rock specimens.As the joint dip angle increases,the joint shear failure becomes more dominant.The number of rockbolts has a significant impact on the peak strain and uniaxial compressive strength(UCS),but little influence on the deformation modulus of the rock mass.Using the Winkler beam model to represent the rockbolt behaviours,an analytical model for the prediction of the strength of boltreinforced blocky rocks is proposed.Good agreement between the UCS values predicted by proposed model and obtained from experiments suggest an encouraging performance of the proposed model.In addition,the performance of the proposed model is further assessed using published results in the literature,indicating the proposed model can be used effectively in the prediction of UCS of bolt-reinforced blocky rocks.

Study on time effect and prediction model of shear strength of root-soil complex under dry-wet cycle

Triaxial compression tests were conducted on the alfalfa root-loess complex at different growthperiods obtained through artificial planting.The research focused on analyzing the time variation law of the shear strength index and deformation index of the alfalfa root-loess complex under dry-wet cycles.Additionally,the time effect of the shear strength index of the alfalfa root-loess complex under dry-wet cycles was analyzed and its prediction model was proposed.The results show that the PG-DWC(dry-wet cycle caused by plant water management during plant growth period)causes the peak strength of plain soil to change in a"V"shape with the increase of growth period,and the peak strength of alfalfa root-loess complex is higher than that of plain soil at the same growth period.The deterioration of the peak strength of alfalfa root-loess complex in the same growth period is aggravated with the increase of drying and wetting cycles.Compared with the 0 days growth period,the effective cohesion of alfalfa root-loess complex under different dry-wet cycles maximum increase rate is at the 180 days,which are 33.88%,46.05%,30.12%and 216.02%,respectively.When the number of dry-wet cycles is constant,the effective cohesion of the alfalfa root-loess complex overall increases with the growth period.However,it gradually decreases comparedwith the previous growth period,and the minimum increase rate are all at the 180 days.For the same growth period,the effective cohesion of the alfalfa root-loess complex decreases with the increase of the number of dry-wet cycles.This indicates that EC-DWC(the dry-wet cycles caused by extreme natural conditions such as continuous rain)have a detrimental effect on the time effect of the shear strength of the alfalfa root-loess complex.Finally,based on the formula of total deterioration,a prediction model for the shear strength of the alfalfa root-loess complex under dry-wet cycles was proposed,which exhibits high prediction accuracy.The research results provide useful guidance for the understanding of mechanical behavior and structural damage evolution of root-soil composite.

Application of the Sub-Model Method in the Engine Strength Analysis

On the basis of introducing the fundamental theory and the basic analysis steps of the sub model method, the strength of the new engine complex assembly structure was analyzed according to the properties of the engine structures, some of the key parts of the engine were analyzed with refined mesh by sub model method and the error of the FEM solution was estimated by the extrapolation method. The example showed that the sub model can not only analyze the comlex structures without the restriction of the software and hardware of the computers, but get the more precise analysis result also. This method is more suitable for the strength analysis of the complex assembly structure.

Failure characteristics of three-body model composed of rock and coal with different strength and stiffness

Four different types of three-body model composed of rock and coal with different strength and stiffness were established in order to study the failure characteristics of compound model such as roof-coal-floor. Through stress analysis of the element with variable strength and stiffness extracted from the strong-weak interface, the tri-axial compressive strength of the weak body and strong body near the interface as well as the areas away from the contact surface was found. Then, on the basis of three-dimensional fast Lagrangian method of continua and strain softening constitutive model composed of Coulomb-Mohr shear failure with tensile cut-off, stress and strain relationship of the four three-body combined models were analyzed under different confining pressures by numerical simulation. Finally, the different features of local shear zones and plastic failure areas of the four different models and their development trend with increasing confining pressure were discussed. The results show that additional stresses are derived due to the lateral deformation constraints near the strong-weak interface area, which results in the strength increasing in weak body and strength decreasing in strong body. The weakly consolidated soft rock and coal cementation exhibit significant strain softening behavior and bear compound tension-shear failure under uni-axial compression. With the increase of confining pressure, the tensile failure disappears from the model, and the failure type of composed model changes to local shear failure with different number of shearing bands and plastic failure zones. This work shows important guiding significance for the mechanism study of seismic, rock burst, and coal bump.

An elasto-plastic constitutive model for soft rock considering mobilization of strength

A new elasto-plastic constitutive model is presented in the framework of plasticity theory. The strength characteristics of a diatomaceous soft rock is investigated. The friction angle and cohesion of soft rock are mobilized as a function of plastic strain. A hyperbolic hardening function for the mobilized friction and a mixed parabolic and exponential equation for the mobilized cohesion are proposed. In view of the unified strength theory and the mobilizations of strength components, a yield function is given. A plastic potential function is determined by using the non-associated plastic flow rule. An elasto-plastic constitutive model is developed and verified. The results indicate that the proposed model can predict the behavior of soft rock accurately. The advantages of the proposed constitutive model are analyzed. The evidences support that the proposed constitutive model is a mixed hardening/softening model. A hump hardening/softening function for mobilized friction is extended to a more generalized condition.

An analytical model for estimating rock strength parameters from small-scale drilling data

The small-scale drilling technique can be a fast and reliable method to estimate rock strength parameters. It needs to link the operational drilling parameters and strength properties of rock. The parameters such as bit geometry, bit movement, contact frictions and crushed zone affect the estimated parameters.An analytical model considering operational drilling data and effective parameters can be used for these purposes. In this research, an analytical model was developed based on limit equilibrium of forces in a Tshaped drag bit considering the effective parameters such as bit geometry, crushed zone and contact frictions in drilling process. Based on the model, a method was used to estimate rock strength parameters such as cohesion, internal friction angle and uniaxial compressive strength of different rock types from operational drilling data. Some drilling tests were conducted by a portable and powerful drilling machine which was developed for this work. The obtained results for strength properties of different rock types from the drilling experiments based on the proposed model are in good agreement with the results of standard tests. Experimental results show that the contact friction between the cutting face and rock is close to that between bit end wearing face and rock due to the same bit material. In this case,the strength parameters, especially internal friction angle and cohesion, are estimated only by using a blunt bit drilling data and the bit bluntness does not affect the estimated results.

Study on Strength and Life of Anisotropic Single Crystal Blade - Part I: Crystallographic Constitutive Models and Applications

The single crystal blade is one of the key technologies for improving the performance, durability and reliability of aero-engines and ground gas-turbine engines. However, the anisotropic mechanical properties of the single crystal material makes a great deal of difficulties on the development and the application of the single crystal blade, which is a challenge for the engineering application of the single crystal superalloy and the theoretic bases of the application. Some researches on the strength analysis and the life prediction of the anisotropic single crystal blade were carried out by the authors' research team. They are as follows. The crystallographic constitutive models for the plastic and the creep behaviors and the method of the rupture life prediction were established and verified. The tensile or the creep experiments for DD3 single crystal alloy with different orientations under different temperatures and different tensile rates or under different temperatures and different stress levels were carried out. The experimental data and the anisotropic properties at intermediate and high temperatures revealed by the experiments are significant for the application of the single crystal alloy. In addition, the experimental research for a kind of single crystal blade was also made. As the application of the researches the strength analysis and the life prediction were carried out for the single crystal blade of a certain aero-engine. In this part, the constitutive models and their applications are described, and the experimental research work will be described in part II.

Discrete Stress-strength Interference Model of Reliability Analysis under Multi-operating Conditions

The conventional stress-strength interference（SSI） model is a basic model for reliability analysis of mechanical components. In this model, the component reliability is defined as the probability of the strength being larger than the stress, where the component stress is generally represented by a single random variable（RV）. But for a component under multi-operating conditions, its reliability can not be calculated directly by using the SSI model. The problem arises from that the stress on a component under multi-operating conditions can not be described by a single RV properly. Current research concerning the SSI model mainly focuses on the calculation of the static or dynamic reliability of the component under single operation condition. To evaluate the component reliability under multi-operating conditions, this paper uses multiple discrete RVs based on the actual stress range of the component firstly. These discrete RVs have identical possible values and different corresponding probability value, which are used to represent the multi-operating conditions of the component. Then the component reliability under each operating condition is calculated, respectively, by employing the discrete SSI model and the universal generating function technique, and from this the discrete SSI model under multi-operating conditions is proposed. Finally the proposed model is applied to evaluate the reliability of a transmission component of the decelerator installed in an aeroengine. The reliability of this component during taking-off, cruising and landing phases of an aircraft are calculated, respectively. With this model, a basic method for reliability analysis of the component under complex load condition is provided, and the application range of the conventional SSI model is extended.

Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth,resource exploitation continues to move deeper into the earth,it becomes a hot topic to simulate the whole process of rock strain softening,deformation and failure in deep environment,especially under high temperature and high pressure.On the basis of Lemaitre’s strain-equivalent principle,combined with statistics and damage theory,a statistical constitutive model of rock thermal damage under triaxial compression condition is established.At the same time,taking into account the existing damage model is difficult to reflect residual strength after rock failure,the residual strength is considered in this paper by introducing correction factor of damage variable,the model rationality is also verified by experiments.Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure,initiation,expansion,penetration,and the formation of macro-cracks under coupled effect of temperature and confining pressure.Rock thermal damage shows logistic growth function with the increase of temperature.Under the same strain condition,rock total damage decreases with the rise of confining pressure.By studying the electron microscope images(SEM)of rock fracture,it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite.The model parameter F reflects the average strength of rock,and M reflects the morphological characteristics of rock stress–strain curves.The physical meanings of model parameters are clear and the model is suitable for complex stress states,which provides valuable references for the study of rock deformation and stability in deep engineering.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

A new model for evaluating the dynamic shear strength of rocks based on laboratory test data for earthquake-resistant design

The dynamic shear strength of rocks is required for the earthquake-resistant design of nuclear power plants in Japan.This research aims to propose a mathematical model for estimating the dynamic strength and to validate the model.Two different types of specimens were prepared for the model validation,and the monotonic and cyclic loading tests were conducted to obtain the mathematical model parameters.Subsequently,multistep cyclic loading tests were performed,followed by simulations using the mathematical model.The test results demonstrated that the dynamic shear strength exceeded the static shear strength,which agreed with previous researches.Furthermore,the dynamic shear strength calculated using the mathematical model was generally consistent with that obtained from the experimental data.

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

Unified strength model based on the Hoek-Brown failure criterion for fibre-reinforced polymer-confined pre-damaged concrete columns with circular and square cross sections

Fibre-reinforced polymer(FRP)has the advantages of high strength,light weight,corrosion resistance and convenient construction and is widely used in repairing and strengthening damaged concrete columns.Most of the existing strength models were built by regression analysis of experimental data;however,in this article,a new unified strength model is proposed using the Hoek-Brown failure criterion.To study the strength of FRP-confined damaged and undamaged concrete columns,900 test data were collected from the published literature and a large database that contains the cross-sectional shape of each specimen,the damage type,the damage level and the FRP-confined stiffness was established.A new strength model using the Hoek-Brown failure criterion was established and is suitable for both circular and square columns that are undamaged,load-damaged and fire-damaged.Based on the database,most of the existing strength models from the published literature and the model proposed in this paper were evaluated.The evaluation shows that the proposed model can predict the compressive strength for FRP-confined pre-damaged and undamaged concrete columns with good accuracy.

THE AVALANCHE DYNAMICS IN RANDOM NEAREST NEIGHBOR MODELS OF EVOLUTION WITH INTERACTION STRENGTH

A generalized Bak-Sneppen model （BS model） of biological evolution with intcraction strength θ is introduced in d-dimensional space, where the “nearest neighbors” are chosen among the 2d neighbors of the extremal site, with the probabilities rebated to the sizes of the fitnesses. Simulations of one- and two-dimensional models arc given.For given θ 〉 0, the model can self-organize, to a critical state, and the critical threshold fc（θ） decreases as θ increases. The exact gap equation depending on θ is presented, which reduces to the gap equation of BS model as θ tends to infinity. An exact cquation for the critical exponent γ（θ） is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.

Strength softening models of soil and its application in rainfall-induced landslide simulation

In this study, strength softening models are developed for exploring rainfall-induced landslide mechanism based on Mohr Coulomb strength theory with both saturation degree and temporal evolution into consideration. According to the ratio of two time scales available, the model can be classified into three categories, i.e., instant softening model, delay softening model, and coupling softening model. Corresponding evolution functions are specified to represent these kinds of softening processes and then applied to simulate landslide of homogeneous slopes triggered by rainfall, therefrom, useful conclusions can be drawn in the end.

Influence of grain size on strength of polymineralic crystalline rock: New insights from DEM grain-based modeling

Grain size effect on rock strength is a topic of great interest in geotechnical engineering.A consensus obtained from earlier laboratory tests is that rock strength generally decreases with the increase of grain size for both silicate and carbonate rocks;however,some recent numerical results conflict with such laboratory test results.To address this intriguing issue,the effect of grain size on strength of polymineralic crystalline rock with low porosity is investigated numerically using the grain-based modeling(GBM)approach in discrete element method(DEM)by interpreting micro-cracking process in response to loading.In agreement with some previous DEM simulation results,the simulated rock strength is found to increase with increasing grain size for both homogeneous and heterogeneous models,even when the number of assembled disks in one mineral grain changes.The mechanism of strength increase with increasing grain size is mainly associated with the number of assembled smooth-joint contacts along grain interfaces and the generation of grain boundary cracks in response to loading.The grain interfaces significantly weaken the integrity of the rock model,which is similar to effects of inherent defects in real rock.As the grain size increases,fewer grain interfaces are built in the model and the rock strength becomes much higher.Hence,by solely changing the mineral grain size in a model,the mechanism of grain size effect as observed in laboratory tests cannot be replicated.To address this issue,a method of degradation of grain boundary strength parameters is used to mimic the possible mechanism of grain size effect.The simulated strength using the method becomes comparable with those obtained from laboratory tests when the heterogeneity in the rock is considered.Degradation of grain boundary parameters with increasing grain size provides a plausible explanation for the grain size effect on rock strength.

The temperature-dependent fracture strength model for ultra-high temperature ceramics

Breaking down the entire structure of a material implies severing all the bonds between its atoms either by applying work or by heat transfer. Because bond-breaking is indifferent to either means, there is a kind of equivalence between heat energy and strain energy. Based on this equivalence, we assume the existence of a constant maximum storage of energy that includes both the strain energy and the corresponding equivalent heat energy. A temperaturedependent fracture strength model is then developed for ultrahigh temperature ceramics （UHTCs）. Model predictions for UHTCs, HfB2, TiC and ZrB2, are presented and compared with the experimental results. These predictions are found to be largely consistent with experimental results.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.

Selection of regression models for predicting strength and deformability properties of rocks using GA

Recently,many regression models have been presented for prediction of mechanical parameters of rocks regarding to rock index properties.Although statistical analysis is a common method for developing regression models,but still selection of suitable transformation of the independent variables in a regression model is diffcult.In this paper,a genetic algorithm(GA)has been employed as a heuristic search method for selection of best transformation of the independent variables(some index properties of rocks)in regression models for prediction of uniaxial compressive strength(UCS)and modulus of elasticity(E).Firstly,multiple linear regression(MLR)analysis was performed on a data set to establish predictive models.Then,two GA models were developed in which root mean squared error(RMSE)was defned as ftness function.Results have shown that GA models are more precise than MLR models and are able to explain the relation between the intrinsic strength/elasticity properties and index properties of rocks by simple formulation and accepted accuracy.