Characteristics of Rock Mechanics Response and Energy Evolution Regime of Deep Reservoirs in the Bozhong Sag,Bohai Bay Basin

Hydraulic fracturing is a mature and effectivemethod for deep oil and gas production,which provides a foundation for deep oil and gas production.One of the key aspects of implementing hydraulic fracturing technology lies in understanding mechanics response characteristics of rocks in deep reservoirs under complex stress conditions.In this work,based on outcrop core samples,high-stress triaxial compression tests were designed to simulate the rock mechanics behavior of deep reservoirs in Bozhong Sag.Additionally,this study analyzes the deformation and damage law for rock under different stress conditions.Wherein,with a particular focus on combining energy dissipation theory to further understand damage law for deep reservoirs.The experimental results show that regardless of stress conditions,the process of deformation/failure of deep-seated reservoirs goes through five stages:Fracture compaction,newfracture formation,stable fracture expansion,unstable fracture expansion,and post-peak residual deformation.Under different stress conditions,the energy change laws of specimens are similar.The energy dissipation process of rocks corresponds closely to the trend of deformation-failure curve,then displays distinctive stage characteristics.Wherein,in stage of rock fracture compaction,the input energy curve is approximately coincident with the elastic strain energy curve,while the dissipation energy curve remains near zero.With the increase of strain,the growth rate of elastic strain energy increases gradually,but with the deformation entering the crack propagation stage,the growth rate of elastic strain energy slows down and the dissipation energy increases gradually.Finally,in the post-peak stage,rock fracture releases a lot of energy,which leads to the sharp decline of elastic strain energy curve.In addition,the introduction of damage variable D quantifies the analysis of the extent of failure for rocks.During the process of increasing strain,rock damage exhibits nonlinear growth with increasing stress.

Relation of Damage Variable and Gas Permeability Coefficient of Concrete under Stress

Compressive stress and tensile stress were applied to concrete specimens using test rigs designed by RILEM TC 246-TDC. Ultrasonic wave velocity and autoclam permeability system were used to characterize the damage variable and gas permeability coefficient of concrete, respectively. The experimental results show that the strain value of concrete increases with the increasing of stress level and loading time. The damage variable and gas permeability coefficient of concrete under compressive stress decrease at first and increase after a threshold value between 0 and 0.6. When the concrete is under tensile load, the damage variable and gas permeability coefficient increase with tensile stress, with a significant increase from 0.3 to 0.6 tensile stress. There is a strong linear relationship between the damage variable and the gas permeability coefficient, suggesting both as good indicators to characterize the damage of concrete under stress.

FATIGUE RELIABILITY DESIGN AND ESTIMATION METHOD FOR VARIABLE LOADING

A method is presented for estimating fatigue reliability under variable loading, which isbased on load cycles-fatigue life interference theory as well as cumulative fatigue damageanalysis. The basic opinion is that for variable loading the increment of failure probability pro-duced by each load cycle is determined by the stress level as well as the damage state at whichthis load cycle applies Contrast to 'conditional reliability-equivalent life methodology'. this meth-od calculates the equivalent cycle numbers between different stress levels according to cumulativefatigue damage rule but not equivalent failure probability.

Mechanical properties and damage constitutive model of sandstone after acid corrosion and high temperature treatments

Aiming at the problem of temperature-mechanics-chemical(T-M-C)action encountered by rocks in underground engineering,sandstone was selected as the sample for acid corrosion treatment at pH 1,3,5 and 7,the acid corrosion treated samples were then subjected to high-temperature experiments at 25,300,600,and 900℃,and triaxial compression experiments were conducted in the laboratory.The experimental results show that the superposition of chemical damage and thermal damage has a significant impact on the quality,wave velocity,porosity and compression failure characteristics of the rock.Based on the Lemaitre strain equivalent hypothesis theory,the damage degree of rock material was described by introducing damage variables,and the spatial mobilized plane(SMP)criterion was adopted.The damage constitutive model can well reflect the stress-strain characteristics of the rock triaxial compression process,which verified the rationality and reliability of the model parameters.The experiment and constitutive model analyzed the change law of mechanical properties of rock after chemical corrosion and high temperature thermal damage,which had certain practical significance for rock engineering construction.

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens is derived based on the Lemaitre strain equivalence hypothesis,which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale,as a kind of brittle rock,often exhibits different nonlinear stress-strain behavior,failure and timedependent behavior under different strain rates.To capture these features,this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1.The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates.These strain rate-dependent mechanical behaviors of shale are originated from damage growth,which is described by a damage parameter.When axial strain is the same,the damage parameter is positively correlated with strain rate.When strain rate is the same,with an increase of axial strain,the damage parameter decreases firstly from an initial value(about 0.1 to 0.2),soon reaches its minimum(about 0.1),and then increases to an asymptotic value of 0.8.Based on the experimental results,taking yield stress as the cut-off point and considering damage variable evolution,a new measure of micro-mechanical strength is proposed.Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength,a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established.Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.

Tests and Simulation Analysis on Fracture Performance of Concrete

To obtain the fracture parameters of concrete, fracture tests were conducted with three-point bending beam method aiming at 30 concrete beams with different sizes and different intensity. The concrete specimen with prefabricated crack to determine the fracture parameters of concrete were conducted and the fracture performance of the specimen was analyzed. The test results show that, initial fracture toughness is unrelated to the size of specimens; while unstable fracture toughness is related to the size of specimens. As for specimens of bastard size, when concrete intensity is relatively low, unstable fracture toughness increases along with the increase of intensity; when concrete intensity is relatively high, unstable fracture toughness will decrease; when concrete intensity increases continuously, unstable fracture toughness will further increase somewhat. As for specimens of standard size, unstable fracture toughness will increase along with the increase of intensity. Aiming at concrete beam specimens, we conducted two-dimensional non-linear finite element analysis, obtained the stress intensity factor, and carried out contrastive analysis with the experimental results.

Mesomechanics coal experiment and an elastic-brittle damage model based on texture features

To accurately describe damage within coal, digital image processing technology was used to determine texture parameters and obtain quantitative information related to coal meso-cracks. The relationship between damage and mesoscopic information for coal under compression was then analysed. The shape and distribution of damage were comprehensively considered in a defined damage variable, which was based on the texture characteristic. An elastic-brittle damage model based on the mesostructure information of coal was established. As a result, the damage model can appropriately and reliably replicate the processes of initiation, expansion, cut-through and eventual destruction of microscopic damage to coal under compression. After comparison, it was proved that the predicted overall stress-strain response of the model was comparable to the experimental result.

Effect of Mineral on Metallurgical Coke Solution Loss Reaction in Blast Furnace

According to the principle of damage mechanics, the damage characteristics of ferrite nodular cast iron under uniaxial stress were studied by measuring electric resistance. The results show that the damage in nodular cast iron occurs when the applied stress is more than a certain extent, and the damage variable increases with stress. The evolutional law of damage variable as a function of stress was obtained. The damage threshold of nodular cast iron increases with nodularity, but it is below the yield strength, which provides reference significance to the design of machinery structure and the choice of materials. The critical damage variable is not related to the nodularity, which is about 0 060-0 068.

EXPERIMENTAL RESEARCH ON EFFECTS OF INITIAL JOINTS ON SURFACE DISPLACEMENT DUE TO COAL MINING

Surface displacement caused by underground coal mining is influenced by many factors such as the depth and thickness of the coal seam and joints in overburben rocks. Extensive efforts have been devoted to the ground surface displacement. Nevertheless, the joints have not been taken into consideration for a long time. In fact, there exist numerous joints and cracks in rocks.As a result, the joints in overburden rocks have to be taken into account. The joints in rocks can be treated as initial damage theoretically. In this paper, two kinds of physical model, one containing no initial joints and anotber containing some initial joints, are employed to systematically investigate effecs of initial joints on surface subsidence. Moreover, within the framework of damage mechanics, the statistical relationships between the characteristic value for surface displacement and damage variable are obtained.

A Study of the Structural Evolution and Strength Damage Mechanisms of PishaSandstone Cement Soil Modified with Fly Ash

In the present study,in order to investigate the effects of fly ash on the structural evolution and strength damage mechanism of Pisha-sandstone cement soil,unconfined compressive strength tests of Pisha-sandstone cement soil with different fly ash content levels and various ages were carried out.The apparent morphology,microstructures,and chemical compositions of the samples were observed and analyzed using ultra-depth three-dimensional microscopy,scanning electron microscopy,and XRD methods.The results revealed that the unconfined compressive strength levels of Pisha-sandstone cement soil samples displayed increasing trends with the increases in fly ash content and age.For example,when the fly ash content levels were increased from 12%to 15%,the strength of Pisha-sandstone cement soil had only slightly increased under the curing ages of 7,28,and 60 days.In addition,the unconfined compressive strength levels of the samples with 15%fly ash content only increased 0.02%,0.51%,and 0.54%,respectively,when compared with the samples containing 12%fly ash.It was observed that with the increases in the fly ash content,the number of pores on the outer surfaces of the samples were significantly reduced.Also,the height differences of cross-sectional gullies were reduced,and the apparent morphology was observed to be flatter.Since cement hydration creates a strong alkaline environment for reaction systems,the active degrees of the pozzolanic reactions of the fly ash were stimulated in this study.Moreover,a significant amount of the C-S-H gel phase and the stable five-membered ring structure of the mordenite and ettringite were generated,which connected the loose Pisha-sandstone particles to form a skeleton.The internal microstructures were then observed to be denser and more uniform.At the same time,the micro-pores were filled and refined by the unreacted micro-bead fly ash.Consequently,the defects in the internal microstructures were improved.Also,based on the Weibull distribution,a damage evolution model of the Pisha-sandstone cement soil was established.The analysis results of the damage variable D values during the initial damage stage,damage evolution stage,and residual damage stage of the damage process showed that the damage variables during all three stages displayed decreasing trends with the increases in the fly ash content levels and age.Therefore,based on this study’s findings,it was considered that the incorporation of fly ash could effectively improve the damage degrees of Pisha-sandstone cement soil under external force conditions.

Damage Mechanics of Ferrite Ductile Iron under Uniaxial Stress

According to the principle of damage mechanics,the damage characteristics of ferrite nodular cast iron under uniaxial stress were studied by measuring electric resistance. The results show that the damage in nodular cast iron occurs when the applied stress is more than a certain extent,and the damage variable increases with stress. The evolutional law of damage variable as a function of stress was obtained.The damage threshold of nodular cast iron increases with nodularity,but it is below the yield strength,which provides reference significance to the design of machinery structure and the choice of materials.The critical damage variable is not related to the nodularity,which is about 0. 060-0. 068.

Fuzzy stochastic damage mechanics(FSDM) based on fuzzy auto-adaptive control theory

In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

Damage Analysis of Circulating Soaked Rock Sample Based on Sonic-test Trials

Circulating soaked sandstone and mudstone samples sonic parameters were tested and analyzed, using RSM-SY5 sonic instrument, the variation between soaked times and the velocity of longitudinal wave and shear wave was studied, calculation and analysis of the damage variable of circulating soaked rock samples were taken, with sonic measurement results and the empirical formula, the damage variable formulas associated with cycle times was established. The results showed that： the attenuation of sonic velocity basically in line with the exponential relationship, with cycle times increasing; The results of the critical calculation of damage variables and the strength test are well matched, which further confirms that the occurrence and expansion of new crack inside the rock mass resulted from circulating soaked lead to the decrease of the rock strength; The trend of sonic parameters attenuation and damage variable growth are good correspondence.

APPLICABILITY OF DAMAGE DEFINITION BASED ON HYPOTHESIS OF STRAIN EQUIVALENCE

The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, i.e. the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials.

Creep damage evolution process of asphalt binder based on viscoelastic characteristics

The creep damage evolution of asphalt binder plays a significant role in investigating the formation mechanism of rutting.The rutting is the common distress at high temperatures for asphalt pavements.However,the reliability of existing creep damage parameters is under questioned,and these parameters cannot accurately illustrate the change of intrinsic microstructure for asphalt binder.In this paper,a new test protocol was given access to study the evolution of viscoelastic parameters during creep damage.It was completed by inserting the frequency sweep during creep test.The frequency sweep curve clusters were fitted by the generalized Kelvin-Voigt model for obtaining the change law of model parameters.Based on the change law and sensitivity analysis of model parameters,(E_(2)+E_(3))/2 was proposed as the creep damage variable.According to the curve of(E_(2)+E_(3))/2 versus loading time,two stages during the creep test could be identified:an approximate constant value in phase I and a linear decrease in phase II.Intrinsic differences about creep property of binders could be determined by this new proposed parameter.Above results not only ensure better understanding of the creep damage mechanism of binders,but also lay the theoretical foundation on predicting the anti-rutting performance of binders.

A plastic damage model for concrete structure cracks with two damage variables

Based on the concepts of continuum damage theory,a new plastic damage model for concrete crack failure is developed through studying the basic damage mechanics.Two damage variables,tensile damage variable for tensile damage and shear damage variable for compressive damage,are adopted to represent the influence of microscopic damage on material macromechanics properties under tensile and compressive loadings.The yield criteria and flow rule determining the plasticity of concrete are established in the effective stress space,which is convenient to decouple the damage process from the plastic process and calibrate material parameters with experimental results.Meanwhile,the plastic part of the proposed model can be implemented by back-Euler implicit algorithm,and the damage part is explicit.Consequently,there exist robust algorithms for integrating the constitutive relations using finite element method.Comparison with several experimental results shows that the model is capable of simulating the nonlinear performance of concrete under multiaxial stress state and can be applied to practical concrete structures.

Influence of freeze-thaw damage gradient on stress-strain relationship of stressed concrete

Freeze-thaw damage gradients lead to non-uniform degradation of concrete mechanical properties at different depths.A study was conducted on the stress-strain relationship of stressed concrete with focus on the freeze-thaw damage gradient.The effects of relative freeze-thaw depths,number of freeze-thaw cycles(FTCs)and stress ratios on the stress-strain curves of concrete were analyzed.The test results demonstrated that freeze-thaw damage was more severe in the surface layers of concrete than in the deeper layers.The relative peak stress and strain of concrete degraded bilinearly with increasing depth.The stress-strain relationship of stressed concrete under FTC was established,and it was found to agree with the experimental results.

A Constitutive Model of Granite Shear Creep under Moisture

Previous constitutive models of granite shear creep have two limitations：（1） although moisture greatly affects granite shear creep behavior, currently there are no constitutive models that include this factor;（2） there are also no models that include an acceleration stage. This paper presents an improved Burgers constitutive model with the addition of a damage parameter to characterize the moisture effect and uses a nonlinear relation equation between stress and strain for inclusion as the acceleration stage. The damage parameter is determined from granite creep experiment under four different moisture contents（0%, 0.22%, 0.49%, and 0.79%）. The nonlinear relation equation is obtained by fitting a dataset of stain versus time under five different loading stages. To verify the presented model, a creep experiment was conducted on other granite samples and the results show that the model agrees well with the experimental observation data.