Triaxial Loading Research Articles

Determination of Consolidation Parameters of Geomaterials Using Modified CRS Consolidation Testing System

Nowadays, the constant rate of strain (CRS) consolidation phenomenon has gained more attention as an alternate testing method to evaluate the consolidation characteristics of finegrained soils based on strain rate criterion. In the present study, a modified consolidation cell has been fabricated indigenously and carried out a series of CRS tests using a conventional triaxial loading frame at four different strain rates on reconstituted samples of marine clay at 0.002, 0.003, 0.004 and 0.005 mm/min, black cotton soil at 0.0025, 0.003, 0.005 and 0.0075 mm/min, red mud at 0.10, 0.125, 0.25 and 0.50 mm/min, and Varanasi local soil at 0.05, 0.075, 0.10 and 0.125 mm/min. Based on the pore pressure ratio (PPR) criterion, the best suitable strain rates for marine clay, black cotton soil, red mud, and Varanasi local soil were found to be 0.002, 0.0025, 0.1 and 0.05 mm/min, respectively. Further, the consolidation parameters namely primary compression index (cc), recompression index (cr), coefficient of consolidation (cv), coefficient of axial compressibility (av) and permeability (k) obtained through proposed CRS consolidation method are compared and validated successfully with the parameters obtained through Incremental Loading (IL) tests using both conventional and modified oedometer cells.

Effect of injection flow rate on fracture toughness during hydraulic fracturing of hot dry rock (HDR)

The fracture toughness of hot dry rock (HDR) is a test parameter affected by the injection flow rate and temperature in the hydraulic fracturing of enhanced geothermal systems (EGS), and it is crucial to the determination of fracture expansion criteria in artificial thermal reservoirs. To investigate the fracture toughness of hot dry rock during hydraulic fracturing as influenced by the injection flow rate and temperature, hydraulic fracturing tests were conducted using thick-walled hollow cubic granite specimens with pre-cracks at different specimen temperatures and injection flow rates on a self-developed real-time high-temperature true triaxial load hydraulic fracturing apparatus. The specimen's fracture toughness was calculated by plugging the breakdown pressure into the corresponding fracture mechanics equation. Additionally, the acoustic emission events of the specimens during fracturing were recorded. The test results show a 14.11%, 21.11%, 24.66%, 33.54%, 43.84%, and 57.89% decrease in fracture toughness for six temperature groups of specimens from 25 to 500 °C when the injection flow rate was varied from 10 ml/min to 1 ml/min, and the fracture toughness decreased by 45.45%, 56.99%, and 73.26% at the three injection flow rates of 10 ml/min, 5 ml/min, and 1 ml/min, respectively, when the specimen temperature was from 25 °C to 500 °C. This indicates that a reduction in the injection flow rate could lower the specimen's fracture toughness both independently and in a mutually reinforcing and controlled way together with the temperature factor. The independent effect of the injection flow rate was attributed to the mean fracture power, and the thermal shock excited by the rapid cooling of high-temperature specimens during hydraulic fracturing was believed to be the essential cause of its interaction with temperature to affect the fracture toughness. The test results were closer to the actual fracture toughness of high temperature rocks during hydraulic fracturing than the NSCB results, demonstrating the feasibility of this test method. To date, this work is the most reliable method for calculating the fracture toughness of hot dry rock during hydraulic fracturing.

Wellbore stability in high-temperature granite under true triaxial stress

Supercritical/superhot geothermal success depends on successful drilling. However, wellbore stability in supercritical environments has not been investigated because imposing sufficient stress on high-temperature granite with true triaxial loading is difficult. We conducted wellbore failure experiments on 200–450 °C granite under true triaxial stress, including deformation and acoustic emission measurements, and post-experiment thin section observations. Wellbore failure initiated at stress states consistent with existing brittle failure criterion at the studied temperatures. Using breakout geometry for in situ stress estimation may be difficult as shear failure propagation is suppressed at high temperatures; however, boreholes may be inherently stable in high-temperature environments.

Evaluation of plasticity‐based concrete constitutive models under monotonic and cyclic loadings

SummaryThis paper evaluates the applicability of several concrete models to simulate the behavior of concrete elements under monotonic and cyclic loadings. Several robust constitutive models based on the combination of plasticity and continuum damage or plasticity and smeared crack approach are selected. The behavior of one concrete element is evaluated under different uniaxial compression, uniaxial tension, biaxial compression, biaxial tension, biaxial compression–tension, and triaxial compression loads. Then, the applicability of the concrete models is investigated for two flexural beams under cyclic loading. Five concrete models available in the versatile finite element‐based software LS‐DYNA are selected, including Winfrith, CSCM, RHT, KCC, and CDPM. The prepeak, peak, and postpeak behaviors of all selected models are presented, including initial stiffness, peak strength, strain at peak strength, postpeak stiffness, and failure strain.

Large-Scale Triaxial Tests on Dilatancy Characteristics of Lean Cemented Sand and Gravel

The dilatancy equation, which describes the plastic strain increment ratio and its dependence on the stress state, is an important component of the elastoplastic constitutive model of geotechnical materials. In order to reveal their differences of the dilatancy value determined by the total volume strain increment ratio and the real value of lean cemented sand and gravel (LCSG) materials, in this study, a series of triaxial compression tests, equiaxial loading and unloading tests, and triaxial loading and unloading tests are conducted under different cement contents and confining pressures. The results reveal that hysteretic loops appear in the stress–strain curves of equiaxial loading and unloading tests, and triaxial loading and unloading tests and that the elastic strain is an important component of the total strain. The hysteretic loop size increases with an increase in the stress level or consolidation stress, whereas the shape remains unchanged. Furthermore, with an increase in the cement content, the dilatancy value determined by the total volume strain increment ratio becomes smaller than that determined by the plastic strain increment ratio, and the influence of the elastic deformation cannot be ignored. Thus, in practical engineering scenarios, especially in the calculation of LCSG dam structures, the dilatancy equation of LCSG materials should be expressed by the plastic strain increment ratio, rather than the total volume strain increment rati.

Progressive failure characteristics and energy accumulation of granite with a pre-fabricated fracture during conventional triaxial loading

Deformation and failure of rocks under the loading effect is an energy-driven progressive process of damage evolution, and the abrupt energy release from rocks storing strain energy under high geostress conditions is a determinant inducing catastrophic effects. Therefore, studying the progressive fracture mechanism of rocks from the perspectives of energy accumulation and dissipation contributes to prediction and evaluation of catastrophic effects such as a rockburst. Fractured samples with different fracture dip angles were prepared using granite collected from the underground powerhouse (under maximum geostress of about 37.82 MPa) in Shuangjiangkou Hydropower Station in Dadu River Basin in China. By using these samples, the progressive failure characteristics and energy accumulation and evolution in fractured rocks during triaxial loading were studied under different stress conditions. In addition, the functional relationships of the crack initiation strength, damage strength, and peak strength of the fractured granite with the confining pressure and fracture dip angle in the loading process were established. The evolution of volumetric strain upon cracking corresponding to the peak stress with the confining pressure and fracture dip angle was discussed. Furthermore, the research explored the intrinsic relationships between the acoustic emission (AE) events and mechanical characteristics of the fractured granite during fracturing thereof. The correspondence of the AE count rate and cumulative energy count with various stages in the progressive failure of the rock was studied, and the evolution of the elastic strain energy and dissipated energy in the rock can be predicted based on the strength, deformation, and AE characteristics. Besides, effects of the confining pressure and the dip angle on the AE characteristic signals were investigated. Finally, the accumulation and evolution of the input energy, elastic strain energy, and dissipated energy of fractured granite in the pre-peak stage during triaxial loading were revealed using an energy analysis. Moreover, the relationships of the eigenvalues of elastic strain energy and dissipated energy of fractured granite with the confining pressure and fracture dip angle were determined.

Experimental Study on the Anisotropy of Layered Rock Mass under Triaxial Conditions

Weak and hard inhomogeneous rock formations are typically encountered during tunnel excavations. The physical and mechanical properties and geological conditions of these rock formations vary significantly; thus, it is crucial to investigate the mechanical characteristics of deep bedded composite rock formations. Three-dimensional (3D) scanning and 3D printing were used to prepare composite rock specimens to simulate natural rock laminae. Triaxial compression tests were conducted to determine the influence of the bedding angle, rock composition, and confining pressure on the mechanical properties of the composite rock specimens. The anisotropic strength characteristics and the damage patterns of the composite rock specimens were analyzed under different confining pressures, and the failure mechanism during triaxial loading was revealed. The results show that the damage of the composite rock specimens with a bedding structure depends on the bedding dip angle and the rock formation. The stress-strain curves and peak strengths of the composite rock specimens have anisotropic characteristics corresponding to their failure modes. As the bedding dip angle increases, the peak strength of the three groups of specimens first decreases and then increases under different confining pressure levels. The compressive strength has a nonlinear relationship with the confining pressure, and the difference between the compressive strengths of specimens with different inclination angles decreases as the confining pressure increases. The Hoek–Brown strength criterion is a good predictor of the nonlinear increase in peak strength of the composite rock specimens under different confining pressures. The specimen with a β = 60°dip angle shows the most significant increase in the strength difference with increasing confining pressure. The results can be used as a reference for testing and analyzing the anisotropic mechanical properties of bedded rock masses.

A geomechanics classification for the rating of railroad subgrade performance

The type of subgrade of a railroad foundation is vital to the overall performance of the track structure. With the train speed and tonnage increase, as well as environmental changes, the evaluation and influence of subgrade are even more paramount in the railroad track structure performance. A geomechanics classification for subgrade is proposed coupling the stiffness (resilient modulus) and permanent deformation behaviour evaluated by means of repeated triaxial loading tests. This classification covers from fine- to coarse-grained soils, grouped by UIC and ASTM. For this achievement, we first summarize the main models for estimating resilient modulus and permanent deformation, including the evaluation of their robustness and their sensitivity to mechanical and environmental parameters. This is followed by the procedure required to arrive at the geomechanical classification and rating, as well as a discussion of the influence of environmental factors. This work is the first attempt to obtain a new geomechanical classification that can be a useful tool in the evaluation and modelling of the foundation of railway structures.

Investigation of the Energy Evolution of Tectonic Coal under Triaxial Cyclic Loading with Different Loading Rates and the Underlying Mechanism

It is of great significance to ascertain the mechanical characteristics and deformation laws of tectonic coal that is under complex stress conditions for safe production, but the targeted research in this area is still insufficient at present. This paper performed triaxial tests under cyclic multi-level loading at different rates by using an MTS-815 Rock Mechanics Testing System. The strain characteristics, elastic modulus and energy evolution were obtained in order to explore the effects of the mechanism of loading rate on the evolution of deformation and energy parameters of tectonic coal. The results showed that the irreversible strain and plastic energy increased exponentially with the increase in the deviatoric stress, but the growth rate decreased with the increase in loading rate. Furthermore, the elastic strain increased linearly and the growth rate was essentially unaffected by the loading rate. During the compaction stage, the variation of each parameter was not sensitive to the loading rate; during the elastic and damage stage, the rate increase inhibited secondary defect propagation and improved rock strength. In addition, the stepwise and cumulative energy ratio was defined in order to describe the energy distribution during cyclic loading and unloading. It was found that the decrease in the loading rate was beneficial to the transformation of the total energy into plastic energy. The elastic modulus was the most sensitive to sample damage, but the energy density evolution was able to be used to describe the deformation damage process of tectonic coal in more detail. These findings provide important theoretical support for the tectonic coal deformation law and action mechanism in the damage process that occurs under complex stress conditions.

The Role of Pore Pressure on the Mechanical Behavior of Coal Under Undrained Cyclic Triaxial Loading

The Role of Pore Pressure on the Mechanical Behavior of Coal Under Undrained Cyclic Triaxial Loading

An Integrated Study of Water Weakening and Fluid Rock Interaction Processes in Porous Rocks: Linking Mechanical Behavior to Surface Properties

We investigated the impact of water weakening on the mechanical behavior of Obourg Chalk and Ciply Chalk (Mons Basin, Belgium). Different mechanical tests were conducted to estimate the unconfined compressive strength (UCS), tensile strength, Young’s modulus, mechanical strength under triaxial loading, critical pressure, fracture toughness, cohesion, and internal friction coefficient on samples either dry or saturated with water or brine. This extensive dataset allowed us to calculate wet-to-dry ratios (WDR), i.e., the ratio between any property for a dry sample to that for the water-saturated sample. For both chalks, we found that water has a strong weakening effect with WDR ranging from 0.4 to 0.75. Ciply Chalk exhibits more water weakening than Obourg Chalk. The highest water weakening effect was obtained for UCS, critical pressure, and Young’s modulus. Weakening effects are still present in brine-saturated samples but their magnitude depends on the fluid composition. The mechanical data were correlated to variations in surface energy derived from three different methods: fracture mechanics, contact angle goniometry, and atomic force microscopy. Water weakening in the tested chalks can be explained by a clear reduction in surface energy and by the existence of repulsive forces which lower the cohesion.

Experimental study on the mechanical behavior and mesoscopic damage of Guiyang red clay during triaxial loading

Experimental study on the mechanical behavior and mesoscopic damage of Guiyang red clay during triaxial loading

Unique relation between pore water pressure generated at the first loading cycle and liquefaction resistance

Accurate evaluation of excess pore water pressure (EPWP) generated in earthquake vibration is a key important factor in seismic engineering against liquefaction. Most previous studies were focused on the relation between cyclic resistance and EPWP developed in the entire liquefaction process. Only a few researchers pointed out that the maximum EPWP ratio accumulated at the first loading cycle, represented by (Δu/p0)max−N1, was intimately related to the liquefaction resistance of sand. Based on this viewpoint, liquefaction resistance of sandy soils can be improved significantly by repressing EPWP at the first cycle by engineering countermeasures. The relationship between (Δu/p0)max−N1 and liquefaction resistance or the cyclic number to liquefaction Nf, however, has not been established quantitatively yet. Moreover, whether this relationship is influenced by stress states such as liquefaction-induced anisotropy, structure or fabric of soils, and loading conditions, is not clear yet. Therefore, a series of undrained cyclic triaxial loading tests were conducted on Toyoura sand, a clean sand famous in Japan, to identify the above-mentioned uncertainties. Based on the test results, a unique empirical (Δu/p0)max−N1-Nf relation was proposed to evaluate the liquefaction resistance. Finally, three typical samples were given to display the application of (Δu/p0)max−N1-Nf relation.

Experimental Test on Nonuniform Deformation in the Tilted Strata of a Deep Coal Mine

Taking a deep-mine horizontal roadway in inclined strata as our research object, the true triaxial simulation technique was used to establish a model of the inclined strata and carry out high-stress triaxial loading experiments. The experimental results show that the deformation of surrounding rock in the roadway presents heterogeneous deformation characteristics in time and space: the deformation of the surrounding rock at different positions of the roadway occurs at different times. In the process of deformation of the surrounding rock, deformation and failure occur at the floor of the roadway first, followed by the lower shoulder-angle of the roadway, and finally the rest of the roadway. The deformation amount in the various areas is different. The floor heave deformation of the roadway floor is the greatest and shows obvious left-right asymmetry. The deformation of the higher side is greater than that of the lower side. The model disassembly shows that the development of cracks in the surrounding rock is characterized by more cracks on the higher side and fewer cracks on the lower side but shows larger cracks across the width. The experimental results of high-stress deformation of the surrounding rock are helpful in the design of supports, the reinforcement scheme, and the parameter optimization of roadways in high-stress-inclined rock, and to improve the stability control of deep high-stress roadways.

Study on Damage Evolution Model of Sandstone under Triaxial Loading and Postpeak Unloading Considering Nonlinear Behaviors

Conventional triaxial loading and unloading tests were carried out on sandstone samples in the Zigong area, of Sichuan Province, China. The changes in the elastic modulus of the unloading curves under different confining pressures were calculated, and the evolution law of the nonlinear properties of rock was analyzed. The results show that the rock is subjected to nonlinear damage during initial compaction, the elastic phase, destruction, and postpeak unloading. Moreover, the nonlinear behaviors of rock are restrained by the confining pressures. On this basis, a nonlinear stress-strain relationship affected by the average stress is proposed to describe nonlinear behaviors in the initial compaction stage. According to the test data, the evolution laws of various energies inside the rock during loading and unloading cycles are obtained. The results show that the external work is transformed into elastic energy and damage dissipated energy. Based on the energy analysis, the energy balance equation is established according to the law of energy conservation. By deriving the energy balance equation, the damage evolution equation of sandstone under triaxial loading is solved to establish a continuous constitutive model. The calculation results of the model are compared with the test results from two aspects of loading and postpeak unloading. The comparison results show that the proposed model, which reflects the whole stress-strain process and nonlinear properties of rock, could also describe the stress-strain relationship at the postpeak unloading stage to some extent.

Study on three-dimensional immiscible water–Oil two-phase displacement and trapping in deformed pore structures subjected to varying geostress via in situ computed tomography scanning and additively printed models

Accurate understanding and quantitative characterization of the three-dimensional (3D) immiscible water–oil two-phase displacement process and of the factors that affect this process in porous reservoir rocks are prerequisites for the enhancement of petroleum recovery efficiency. To meet these prerequisites, it is crucial to directly visualize and quantify the pore scale physics and dynamic evolution of the water–oil two-phase displacement behavior. However, engineering activities, such as borehole drilling, reservoir fracturing, and oil recovery, can cause geostress redistribution in petroleum reservoirs and drastically change the 3D pore structures of reservoir rocks. This makes it difficult to apply conventional experimental techniques and analytical models to directly reveal and evaluate the 3D immiscible fluid displacement in reservoir rocks during pore structure deformation. In this study, we used X-ray computed tomography, integrated with triaxial loading techniques, to capture in situ the immiscible water–oil displacement and oil trapping inside 3D pore spaces during the deformation induced by various geostresses. An additive manufacturing or 3D printing (3DP) technology was applied to replicate the transparent models of actual porous rocks, facilitating the representation and quantification of pore space deformation and the dynamic process of water–oil displacement and oil trapping. Pore scale displacement behaviors (including water sweeping, fingering effects, preferential flow paths, and oil trapping) and their evolution and pore structure deformation with varying geostress were directly visualized and quantified. The relationships between the characteristics of the deformed structures, water–oil displacement efficiency, and effective geostress changes were formulated. The results indicate that stress-induced pore structure deformation has an evident impact on the 3D water–oil displacement behavior and efficiency. A comparison of the 2D and 3D water-oil displacement behaviors indicates that the 3D model predicts a more realistic displacement performance, whereas the residual oil saturation is overestimated in a 2D pore system owing to the truncation of pore connectivity in the third dimension. This study provides a method for directly visualizing and quantifying the effects of geostress-induced pore deformation on the 3D water–oil displacement in porous reservoirs; this method can help draft a strategy to enhance petroleum recovery.

An analytical model for the triaxial compressive Stress-strain relationships of Cemented Pasted Backfill (CPB) with different curing time

The strength of Cemented Pasted Backfill (CPB) is gradually enhanced with the increase of curing time. It is of great significance to study the stress-strain behaviors of CPB with different curing time under triaxial loading conditions. The triaxial compressive tests of CPB samples with 4 different curing time (1, 3, 7, and 28 days) were firstly conducted using GCTS (Geotechnical Consulting ＆ Testing System) loading system under 4 different lateral constraint ratios (σ3/UCS≈0%, 10%, 20%, and 30%). The experimental data were then used to develop a damage constitutive model in which the lateral constraint rations σ3/UCS plays a key role. The tested stress-strain curves from the experiments were used to verify the proposed damage constitutive model. The comparisons between the tests and the model prediction showed that the triaxial strength of CPB can be accurately predicted by the Mohr-Coulomb strength criterion. An obvious secondary elastic strengthening stage was identified in the stress-strain curves of CPB when σ3/UCS is high (≥20%). And the proposed damage constitutive model can accurately represent the stress-strain relationships of CPB with different curing time and σ3/UCS. The results presented in this study contribute to a better understanding of the triaxial mechanical behaviors of CPB.

Investigation on the relationship between CT numbers and marble failure under different confining pressures

Abstract Computed tomography (CT) scanning technology is helpful in investigating rock materials as it can demonstrate the micro structure of rock clearly. Conventional triaxial compression tests and the corresponding graded triaxial loading tests were carried out to investigate the complex failure mechanism of the marble at the Jinping Hydropower Station. After that CT-scanning tests were done on the loaded marble specimens. The test results show that (1) the CT numbers of the specimens have a certain statistical regularity, that is, the CT numbers of the specimens under different confining pressures satisfy the Weibull distribution, as the confining pressure increases, the mean values rise while variances decrease; (2) in the two groups of tests, the average CT numbers corresponding to the conventional triaxial tests are higher than those corresponding to the graded loading tests, but the CT number variances are lower than those of the graded loading tests; and (3) according to meso-damage mechanics, the damage variables of the rock specimens were established based on the definition of CT numbers. The calculation results show that the damage variables decrease with the increase in confining pressure, the damage variables of the rock specimens in the graded loading tests are higher than those in the conventional triaxial test, and the differences between the two loading tests have grown with the increase in confining pressure.

Experimental study on mechanical and damage characteristics of coal under true triaxial cyclic disturbance

A true triaxial test system was used to study the mechanical and damage characteristics of coal under tiered cyclic maximum principal stress (σ1), intermediate principal stress (σ2), and minimum principal stress (σ3). The influence of each principal stress cycle on the deformation, energy evolution and damage characteristics of coal was systematically analyzed, and the mechanical evolution characteristics of coal under the disturbance action of true triaxial excavation were revealed. In the process of true triaxial tiered cyclic loading, it is found that: the stress-strain curves of different principal stress cycles processes are quite different, but they will all cause plastic deformation or plastic hysteresis loop of principal strain in each principal stress directions of coal, and the principal strain corresponding to the cyclic principal stress direction is the dominant deformation, and its deformation is relatively large. According to the true triaxial strength curve and experimental results, the cyclic loading or unloading σ2 may cause instability and failure of coal. The variation trend of residual deformation caused by σ1 and σ3 is the same: with the increase of the amplitude of true triaxial tiered cyclic loading, the absolute value of the cumulative maximum and minimum residual principal strains increase exponentially and quadratic parabola, respectively. And the absolute value of the relative maximum and minimum residual principal strains decrease first and then increase, showing U-shaped and arch shaped changes, respectively. While the changes of cumulative and relative residual intermediate principal strains are all small. The total dissipation energy of coal increases exponentially with the increase of the amplitude of true triaxial tiered cyclic loading. Combined with the energy dissipation characteristics, the damage variable equation of coal under true triaxial cyclic loading is newly defined. With the increase of the amplitude of true triaxial tiered cyclic loading, the damage variable presents an obvious S-type change trend of deceleration acceleration re-deceleration.

Effects of Confining Pressure and Temperature on the Energy Evolution of Rocks Under Triaxial Cyclic Loading and Unloading Conditions

Effects of Confining Pressure and Temperature on the Energy Evolution of Rocks Under Triaxial Cyclic Loading and Unloading Conditions