Damage Constitutive Equations Research Articles

Experimental study on mechanical properties of alkali activated concrete after freeze–thaw cycles

In order to study the frost resistance of alkali activated concrete (AAC), 15 AAC cube specimens and 15 cylindrical specimens were designed and manufactured. The frost thawing cycle test and mechanical performance test were used to study the frost resistance of AAC. The results showed that after freeze–thaw cycles, small pores appeared on the surface of the specimen, and the surface roughness increased, resulting in a darker appearance. As the number of freeze–thaw cycles increases, the highest mass loss rate of AAC reaches 1.88%. The cube compressive strength and axial compressive strength of AAC first increase and then decrease, while the elastic modulus gradually decreases. After 50 freeze–thaw cycles, the compressive strength of the specimen was greater than that of the normal temperature specimen. When the freeze–thaw cycles reached 200, the elastic modulus of the specimen degraded by 9.7%, the compressive strength decreased by 18.6%, and the axial compressive strength decreased by 31.2%. Based on the experimental results, a method for calculating the residual strength of AAC after freeze–thaw cycles and key parameters of the freeze–thaw damage constitutive equation were proposed.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process, nonlinear elements and creep damage are generally introduced in the model to resolve this issue. However, several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution. Nevertheless, the creep damage mechanism of rocks is still not clearly understood. In this study, a reasonable representation of the damage variables of solid materials is presented. Specifically, based on the Gurson damage model, the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established. Further, the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model. Finally, the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite. And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite. Overall, this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern, which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Mechanical behavior and damage constitutive relationship of basalt-brucite hybrid fiber reinforced low-heat cement concrete

In this study, the mechanical properties and microstructure of basalt-brucite hybrid fiber reinforced low heat cement concrete was explored. The results indicated that the mechanical properties of low heat cement concrete first increase and then decrease with the increase of hybrid fibers volume fraction, and the cubic compressive strength, splitting tensile strength, and axial compressive strength of the optimal strengthening group, that volume fraction is 0.20% for basalt fiber and 0.15% for brucite fiber, respectively, increased by 40.16%, 70.61%, and 56.16%, respectively. Under a reasonable volume fraction of hybrid fibers, the mechanical properties of concrete could be significantly improved. By comparing the bonding effect between fibers and concrete, fibers exhibited different distribution patterns in concrete matrix, that could improve the compactness of concrete matrix through filling effect, optimize internal structure, and delay the connection and expansion of microcracks. The causes of the bonding effect between fibers and concrete was discussed from the perspective of chemical bonding effects. Based on the above analysis, the reinforcement mechanism of hybrid fibers on concrete was explored. Based on statistical damage theory, a damage constitutive equation for hybrid fiber reinforced low heat cement concrete considering fiber volume fraction was established by modifying the model parameters, and the model curve fitted well with the experimental curve.

A damage constitutive model for concrete under uniaxial compression capturing strain localization

This paper presents a damage constitutive equation capturing the feature of strain localization and, on this basis, proposes a novel damage constitutive model for concrete under uniaxial compression. It is found that the proposed model can better simulate the stiffness degradation behavior of concrete under cyclic loading, well reproduce the dependency of the post-peak stress-strain curve on specimen or measuring length under monotonic loading, and provide FE simulation results that are insensitive to mesh size. Influence of the maximum aggregate size on the strain localization zone length is discussed.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters. Gypsum specimens containing non-penetrating crack(s) are used to study the damage evolution and characteristics under cyclic loading. The results show that under cyclic loading, the relationship between the number of non-penetrating crack(s) and the characteristic parameters (cyclic number, peak stress, peak strain, failure stress, and failure strain) of the pre-cracked specimens can be represented by a decreasing linear function. The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle, and the damage constitutive equation is proposed by the concept of effective stress. Additionally, non-penetrating cracks are more likely to cause uneven stress distribution, damage accumulation, and local failure of specimen. The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen. Therefore, the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst. These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

A coupled thermo-hydro-mechanical framework for simulating the failure response of asphalt concrete under freezing conditions

Freezing-induced damage occurs in extremely cold regions in the form of sudden and simultaneous formation of cracks in dry and wet asphalt concrete. This work investigates the mechanical response, up to and including final failure, of dry and partially saturated asphalt concrete at freezing temperatures as low as −30° (−22 °F). A coupled thermo-hydro-mechanical constitutive framework is proposed within the context of finite element simulation. The framework contains nonlinear viscoelastic-viscodamage constitutive equations, the swelling strain effect associated with the freezing of water content, and the moisture damage constitutive equation. The stress induced in dry and partially saturated asphalt concrete samples due to reducing temperatures is simulated and compared with those of a studied experiment, and an excellent agreement is achieved in terms of the critical features, including the final brittle failure and the swelling effect. A parametric study is then performed to discover the effects of the microstructural constituents of asphalt concrete on its mechanical response under freezing conditions. This work provides a reliable computational framework that can predict deterioration and damage in asphalt concrete structures in extremely cold weather and further leads to the development of novel construction materials that can resist the negative effects of cold temperatures, e.g., in the Arctic.

Study on properties of Portland cement-sulfoaluminate cement-based grouting materials modified by in-situ polymerization of calcium acrylate

To enchance the toughness of ordinary Portland cement-sulfoaluminate cement-based grouting material and minimize the secondary damage of road structure caused by stone body destruction under vehicle load. In this paper, the development laws of setting time, fluidity, and mechanical strength of grouting material, and the characteristics of stone damage under the action of calcium acrylate are systematically analyzed. The mechanism by which in-situ polymerization of improves the toughness improvement of ordinary Portland cement-sulfoaluminate cement-based grouting material is then revealed. In-situ polymerization of calcium acrylate delays the setting time, and an appropriate calcium acrylate content improves the flowability. The addition of calcium acrylate largely enhances the mechanical strength of the stone body, improving the 1-day compressive strength and flexural strength by 279.18% and 301.64%, respectively. Calcium acrylate also increases the flexural compression ratio of the stone body. The highest flexural compression ratio at 28d is 0.5592. The microscopic analysis reveals that calcium acrylate promotes hydration, and forms stable calcium polyacrylate in the stone body, which connects the hydration products into a more densely cement-calcium polyacrylate composite structure. Consequently, the toughness of the stone body improves. By analyzing the stress–strain curve, the stone body still exhibits a capacity to resist damage after the peak stress under the action of calcium acrylate. Finally, a damage constitutive equation of the stone body with different damage factors is established, which has excellent agreement with the test curve and can predict the mechanical properties of cement-based grouting material modified by in-situ polymerization of calcium acrylate. The findings provide a theoretical framework for designing the strength of grouting materials and evaluating road stability.

Study on Mechanical Properties of Deep Expansive Soil and Coupling Damage Model of Freeze–Thaw Action and Loading

This study is primarily intended to present a damage constitutive equation under the combined action of confining pressures and freeze–thaw cycles by subjecting deep expansive clay to the consolidated undrained triaxial tests. We study the influence of the numbers of freeze–thaw cycles on various mechanical indexes of soil by using the TSZ-2 instrument (fully automatic triaxial instrument). As the number of freeze–thaw cycles increases, the ultimate peak stress of the soil decreases, and then, the effect of the freeze–thaw effect on the shear strength gradually weakened. By combining the expression method of the damage variable under the action of loading alone with the expression method under the action of freeze–thaw cycles alone, we brought in the damage evolution equation to obtain the damage constitutive equation under the combined action of confining pressures and freeze–thaw cycles. The stress values under three confining pressures (100 kPa, 200 kPa, and 300 kPa) can be determined by using the final damage constitutive model. The measured data with a water content of 17% and six freeze–thaw cycles were compared with the theoretical data. The actual strength values were 118.4 kPa, 152.3 kPa, and 184.1 kPa, and the theoretical strength values were 120 kPa, 150 kPa, and 186 kPa. The fitting degree of the strength value was as high as 99%, which verifies the feasibility of this model. This study can serve as an available reference for well wall construction and disaster prediction in deep coal mining.

Resistivity and damage of coal under cyclic loading and unloading

The stability of the coal in underground coal mining can be reduced greatly by mining activities and seepage water. Studying the failure and damage evolution of water-saturated coal under cyclic loading is therefore of great importance. Conducting single-axis equal-amplitude cyclic loading and unloading tests of water-saturated coal, this paper studied the resistivity response and analyzed the relationship between resistivity and strain field with Digital Image Correlation (DIC) in coal cyclic loading. The damage in coal cyclic loading was quantitatively characterized by the damage variables and damage constitutive equations based on electrical resistivity. The results show that the response of resistivity and DIC is regular and complementary. In the loading stage, the strain field has an opposite trend to the resistivity, which decreases as the load force increases; In the unloading stage, the resistivity increases correspondingly, but the shearing strain decreases. The above responses correlate with the sample failure: as the number of cycles increases, the sample's internal damage accumulates, and the resistivity and strain increase accordingly. The two damage variables and the trend of plastic strain are in good agreement. The damage constitutive model's calculation agrees with the experimental results. The resistivity method is able to objectively describe the whole damage process of saturated water coal under constant amplitude cyclic loading, thus contributing to the understanding of the damage mechanism of coal and rock subjected to complex stresses, which is of great practical significance and value to the safe and efficient production of coal mines.

Atypical brittle failure and compression characteristics of polymer based on acoustic emission

Foamed polymer is frequently used for waterproofing repairs in underground engineering. Since the polymer acts as a plug in structure fractures, the mechanical characteristics of its foaming are essential. Its compressive damage constitutive equation is closely related to the engineering structure life. This study divides polymers into two types based on whether or not the molded skin is removed. Based on acoustic emission monitoring, quasi-static cyclic loading compression tests were conducted under a specific engineering background. Then, the failure modes were classified, and an energy-based constitutive analysis of two damage factors was conducted. The test results show that the presence of molded skin led to “atypical-brittle” failure characteristics, maintaining stepwise stress drop after yielding without densification. Acoustic emission energy-based damage factors can be incorporated into the constitutive model to reflect the damage process in advance. Furthermore, the conventional damage factor-based constitutive model was modified by a compaction factor to describe the characteristics from the elastic state to the atypical-brittle failure. From the perspective of the failure behavior of polymer materials, this work sheds light on grouting materials’ design.

Application of concrete and cement slurry based on waste recycling in fast consolidation of engineering rock mass

The cement-based rock materials and cement slurry used in the fast repair and reinforcement of engineering surrounding rock mass are generally not environmentally friendly and have a slow setting time. From the perspective of environmental protection and waste utilization, this study adopts a variety of domestic wastes, considers the fast condensation of materials, and comprehensively and systematically develops environmentally friendly high-similarity concrete and cement slurry through the Taguchi grey correlation analysis method. The damage constitutive equations, the constitutive equations after water saturation and after immersion in corrosive liquid are deduced. Combined with DIEM, VOCM and UDEC software, the effects BG and AG under various engineering site situation are analyzed. Research indicates that both rock-like materials and cement slurry have good performance. The research results are widely used in the rapid repair and reinforcement of damaged rock mass on the basis of environmental protection and waste recycling.

Complex fracture propagation model and plugging timing optimization for temporary plugging fracturing in naturally fractured shale

In this paper, a viscoelasticity-plastic damage constitutive equation for naturally fractured shale is deduced, coupling nonlinear tensile-shear mixed fracture mode. Dynamic perforation-erosion on fluid re-distribution among multi-clusters are considered as well. DFN-FEM (discrete fracture network combined with finite element method) was developed to simulate the multi-cluster complex fractures propagation within temporary plugging fracturing (TPF). Numerical results are matched with field injection and micro-seismic monitoring data. Based on geomechanical characteristics of Weiyuan deep shale gas reservoir in Sichuan Basin, SW China, a multi-cluster complex fractures propagation model is built for TPF. To study complex fractures propagation and the permeability-enhanced region evolution, intersecting and competition mechanisms between the fractures before and after TPF treatment are revealed. Simulation results show that: fracture from middle cluster is restricted by the fractures from side-clusters, and side-clusters plugging is benefit for multi fractures propagation in uniformity; optimized TPF timing should be delayed within a higher density or strike of natural fractures; Within a reservoir-featured natural fractures distribution, optimized TPF timing for most clustered method is 2/3 of total fluid injection time as the optimal plugging time under different clustering modes.

Study on the pore structure characteristics and damage constitutive model of sandstone under freeze-thaw conditions

Rocks in Northwest China are often affected by the combined action of freeze-thaw and load erosion. Therefore, in order to better understand the mechanical properties of rocks in seasonal frozen areas and the meso-damage caused by freeze-thaw erosion, uniaxial compression tests, electron microscope scanning tests, X-ray diffraction tests (XRD) and mercury intrusion tests (MIP) were carried out on five sandstone samples with different freeze-thaw times, and the mechanical parameters and meso-damage characteristics of sandstone samples with different freeze-thaw times were obtained. Fractal theory was used to analyze the change in pore volume of sandstone after freeze-thaw cycles. Finally, the damage constitutive equation under the coupling action of freeze-thaw damage and load was established based on Lemaitre’s equivalent effect variation criterion. The results showed that the type of sandstone is a porous coarse-grained sandstone. With the increased freeze-thaw times, the compressive strength and cohesion of sandstone gradually decreased, and the closed pores in sandstone gradually connected, leading to the visible internal macroscopic cracks. Affected by freeze-thaw times, the volume proportion of large pores (100–1,000 µm) in sandstone gradually increased, while the volume proportion of micropores (.05–100 µm) gradually decreased. With the increased freeze-thaw times, the fractal dimension of pore volume decreased from 1.94 to 1.59. The theoretical curve can better fit the characteristic points of the stress-strain curve, which can further reveal the damage mechanism of sandstone under the coupling effects of freeze-thaw and load. The minimum error between the peak point of the experimental curve and the theoretical curve is 3.3%.

Mechanical properties and damage constitutive model of coal specimen with different moisture under uniaxial loading

The moisture content has an important influence on the strength and stability of coal pillar dams in underground reservoirs. In this paper, the uniaxial compression test was performed on coal samples with three different moisture contents, to study the mechanical properties of them under water intrusion condition. The results show that, water has a significant damaging and softening effect on the mechanical properties of the samples. As the moisture content grows of coal samples, the peak strength and elastic modulus fall exponentially while the peak strain increases exponentially. In addition, the energy characteristics of coal samples with different moisture contents under uniaxial compression were analyzed. The releasable elastic strain energy, dissipated energy and total input energy all experience a decline with water content, and the proportion of the releasable strain energy in the total energy drops. The capacities of energy storage and strain energy release of coal samples both fall under influence of moisture, and more energy was transformed. Given this result, the damage variable on the basis of energy dissipation was introduced to explore the influence of moisture contents on the damage variable of coal samples and the damage evolution equations of coal samples with three different moisture contents were calculated from the results of uniaxial loading tests. Finally, the compaction coefficient considering the influence of immersion time was proposed to describe the compaction degree and being used to amend the damage constitutive model obtained, and the fitted results of the models were compared to experimental data. Results show that the values of damage variables increase exponentially with strains, and the modified damage constitutive equation can give a more accurate description of the compressive deformation of coal samples that contain varying contents of moisture.

Experimental Study on the Triaxial Compression Properties of Coarse-Grained Filling Soil under Drying–Wetting Cycles

To explore the mechanical properties of coarse-grained filling soil in the hydrofluctuation belt of the Baihetan reservoir, a fast drying–wetting cycle method for large-scale triaxial tests was developed and a series of large-scale triaxial compression tests of coarse-grained soil were conducted under drying–wetting cycles. The results show that the drying–wetting cycles and the confining pressure are both important factors affecting the mechanical properties of coarse-grained soil. The influences of the first and second cycles on the deviatoric stress–strain curve of the coarse-grained soil are the greatest, while the influences of the third to seventh cycles tend to be stable. The peak strain is not affected by the drying–wetting cycles but only increases with increasing confining pressure. The axial strain and volumetric strain at the volume expansion point decrease with increasing number of drying–wetting cycles but increase with increasing confining pressure. The secant modulus of the peak point decreases with increasing number of drying–wetting cycles, and the initial tangent modulus decreases slightly. The influence of the drying–wetting cycles on the cohesion of the coarse-grained soil is greater than that on the internal friction angle. The typical “bulging” phenomenon occurred after the specimens were destroyed. A damage constitutive equation was developed by introducing a damage variable into the hyperbolic model to reflect the influence of the number of drying–wetting cycles. The model parameters were obtained and the proposed model was verified by fitting the experimental results.

Integrity analysis of wellbores in the bedded salt cavern for energy storage

Salt cavern used for energy (natural gas, hydrogen) storage has a significant advantage in peak shaving of gas supply due to their high injection-production efficiency and fast gas injection-delivery switching speed. As the only channel for gas injection and delivery, the wellbore is easily damaged by the alternating gas pressure and is a weak component. For salt cavern underground gas storages (UGSs) in bedded rock salt, the roof collapse can also cause tensile damage to the wellbore. Long-running UGSs may suffer leakage accidents due to wellbore failures, and wellbore safety issues need to be fully considered. This paper proposes a coupled analysis of cement sheath fatigue damage and rock salt creep, and its applicability is proved by mechanical tests. A three-dimensional numerical model was established that includes a wellbore, open well section (cavern neck), and bedded salt cavern. The creep and damage constitutive equations were used to calculate rock salt creep and cement sheath damage. The results show that the creep ability of bedded rock salt is lower than that of high-purity rock salt, confirmed by the creep test results and can be described by the creep constitutive equation in this paper. The cavity shrinkage of the bedded UGSs is generally lower than expected, resulting in better wellbore integrity. The low creep capacity of the impurity-containing rock salt will reduce the cavity shrinkage and protect the airtightness of the wellbore. Based on the integrity of the wellbore, the working gas volume of the UGSs in the bedded formation can be increased. Taking the Jintan gas storage as an example, under the operating pressure of 7–17 MPa, the damaged area of the cement sheath is limited to within 0.5 m of the lower end of the wellbore. When the lower limit pressure is reduced to 6 MPa, the damaged area is limited to within 2 m of the lower end of the wellbore, and the wellbore still maintains sufficient airtightness.

Experiment and computation: A combined approach to characterize the constitutive and fracture behaviors of metallurgical bonding interface in bimetallic composites

This paper presents a novel experimental and computational approach to characterize fracture behavior of the intermetallic bonding layer (IMBL) in bimetallic bearing materials. The proposed methodology is applied to tin (Sn) based Babbitt alloy/mild steel bimetallic composite. In this study, macro stress–strain behavior of the bond under tensile-shear stress was calculated by considering the local shear surface geometry instead of the apparent bonding zone. The metallurgical bonding layer failure mechanism was identified from the scanning electron microscope (SEM) observations of the fractured IMBL of the bimetallic samples tested in tension-shear. It has been found that a damage mechanism of ductile nature was the cause of tearing of the IMBL. The coupled elasto-plasticity and damage constitutive equations for the IMBL were formulated and implemented based on SEM observations. Characterization of the shear fracture behavior of IMBL included FE numerical simulation of tensile-shear tests of the bimetallic composites. Consequently, a calibration methodology is proposed to estimate the IMBL fracture parameters. This proposed approach validation was based on a qualitative and quantitative confrontation between the experimentally measured shear force-displacement diagram and the numerically calculated diagrams obtained from the simulated IMBL. Commendable average quantitative errors of almost 1% are achieved in terms of yield strength, ultimate strength, and elongation at break between computed results obtained within sheared regions of the simulated Babbitt/steel (Sn – IMCs) BL and experience. The results of such a confrontation are promising for the application of the proposed approach to predict fracture during the forming of bimetallic composite materials.

Analysis of Damage Constitutive Model for Frozen Red Clay under Uniaxial Compression

At present, it is in the peak period of infrastructure construction in western China, and due to the natural climate, the soil has been frozen for a long time, but there is little research on frozen red clay at present. Therefore, it is necessary to further study the mechanical properties of frozen red clay. In this paper, taking the remolded red clay as the test material, the change characteristics of uniaxial compression and uniaxial creep of frozen soil under different test factors are studied by artificial freezing method, and the damage theory is introduced to analyze the test results. The results of uniaxial compression test of frozen soil show that temperature has a great influence on the uniaxial compressive strength, and the compressive strength increases with the decrease of temperature, and the damage theory is introduced. It is found that the initial damage stress increases with the decrease of temperature, while the initial strain changes little with temperature. A damage constitutive equation which can well reflect the whole damage process of frozen red clay is established. The experimental research results of this paper can provide some theoretical reference for the engineering of soil quality for freezing red clay.

Viscoelastic-viscoplastic damage analysis of transversely isotropic soft soils

Soft soils show noticeable creep, damage and transversely isotropic properties. An incremental three-dimensional Nishihara model is proposed to present the stress-strain relationship of soft soils in this paper. The Drucker-Prager yield criterion of the transversely isotropic media, the transversely isotropic flexibility matrix, and the damage law to Nishihara's constitutive model are applied to construct the transversely isotropic viscoelastic-viscoplastic damage constitutive equation of the soil. Afterwards, the constitutive model is implemented by applying a stress return mapping algorithm. We verified the proposed model by comparing the results calculated by ABAQUS with triaxial compression experimental data from Hong Kong marine deposits (HKMD) and Shanghai soft clay. Finally, based on the proposed model, we present several numerical examples to investigate the influences of damage parameters on the time-dependent behaviors of saturated soft clay.

Energy evolution and damage constitutive model of anchored jointed rock masses under static and fatigue loads

During propagation, cyclical impact loads transform into low-frequency fatigue loads, which induce the release of energy from far-field anchored jointed rock masses (AJRMs) under long-term disturbance loads. Shear tests of marble under static and fatigue loading rates were conducted using a servo-controlled compression shear test machine equipped with an improved specimen fixture system. The effects of static and fatigue loads on the mechanical behaviour of samples, for example, the stress–strain curve, peak stress, shear modulus, peak strain and failure strain, were explored. The energy evolution of different types of AJRMs was studied in detail. In addition, a damage constitutive model for AJRMs was developed based on the Weibull distribution under static loading and deformation characteristics under fatigue loading. The results showed that fatigue loading could reduce the strength and increase the deformation of specimens, while static loading had a cumulative effect on the deterioration of specimens, which could decrease the elasticity of AJRMs. In the energy transformation process, the total energy included elastic energy, which described the elastic deformation, and dissipated energy, which could be converted to describe the anchor deformation, fracture extension and plastic damage, depending on the application. The proposed damage constitutive model was established by considering the influence of static and fatigue loads, and a damage constitutive equation of AJRMs was derived. A comparison between the calculated and experimental data showed that the damage equation could accurately describe the effects of static and fatigue loading rates on the stress–strain responses of specimens, and its parameters had definite physical meanings. Thus, the proposed model is a very good tool for the analysis of load coupling problems involved in deep rock mass engineering.