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.

Measuring the Flow Functions of Pharmaceutical Powders Using the Brookfield Powder Flow Tester and Freeman FT4

This study examined the feasibility of combining data from different powder flow testers to determine the flow function characteristics of pharmaceutical powders. The Brookfield PFT and Freeman FT4 can measure flow function over different scales of consolidation load but were found to be most complementary with CRM limestone powder and lactose. The brittle behaviour of Easytab particles at higher loads made obtaining repeatable results with the FT4 challenging. By using the method of Wang et al., where the flow function coefficient ffc is plotted against the dimensionless cohesion C* (measured cohesion Ta divided by the initial compaction I), a plot was formed which could be used to predict the behaviour of other systems, which compared well with previous studies.

Constitutive Model of Solid Backfill Materials and Numerical Simulation of Overburden Movement and Deformation in Backfill Mining

Solid backfill mining is an efficient and environmental-friendly coal mining technology, which can effectively solve the problems of coal gangue pollution, water resource loss, and surface subsidence. Based on the mechanical behavior of backfill materials in the compaction process, volume strain was used to express the deformation modulus, and a constitutive model of backfill materials was proposed in this study. The ABAQUS UMAT was used to develop the numerical calculation subroutine of the model. Finally, the rationality of the model was verified that simulated stress-strain curves of the backfill materials during the compaction process agree well with experiments. Based on the proposed constitutive model, the influence of three factors (the initial compaction rate of the filling body, the mining height, and the mining depth) on the key strata and surface subsidence was analyzed systematically. The results show that the initial compaction rate and the height of coal seams have significant influences on surface subsidence. When the thickness of topsoil is only changed and the structural composition and lithology of overburden are not changed, the mining depth has little influence on surface subsidence, but a significant influence on surface subsidence range. The influence of mining height and mining depth on the deformation of key strata of overburden and surface subsidence is approximately linear, while the influence of the initial compaction rate is nonlinear.

INVESTIGATION OF SINTERING FEATURES OF CERAMIC MATERIALS BASED ON HYDROXYAPATITE AND ITS SUBSTITUTED FORMS

Порошки стехиометрического и фторзамещенного гидроксиапатита с повышенной активностью к спеканию (температура начала уплотнения составляет 600°С) синтезированы методом осаждения из раствора. Исследованы свойства синтезированных порошков и керамики после обжига. Показано, что введение фторид-ионов позволяет термически стабилизировать фазу апатита до температуры 1000°С, повысить степень дисперсности и площадь удельной поверхности, почти в три раза увеличить микротвердость материала. Сопоставление распределения частиц по размерам в синтезированных порошках и распределения зерен в спеченной керамике подтвердили наследование керамикой наноструктуры исходных порошков. Stoichiometric and fluorsubstituted hydroxyapatite powders with increased sintering activity (the initial compaction temperature is 600°C) were synthesized by precipitation from solutions. Properties of synthesized powders and ceramics after firing were investigated. It is shown that the introduction of fluoride ions can thermally stabilize the apatite phase to a temperature of 1000 °C, increase the degree of dispersion and the specific surface area, and almost three times increase the microhardness of the material. Comparison of the particle size distribution in synthesized powders and the grain distribution in sintered ceramics confirmed that ceramics inherited the nanostructure of the original powders.

The Mechanical Response of Wet Volcanic Sand to Impact Loading, Effects of Water Content and Initial Compaction

The effects of water content and initial compaction on the dynamic response of volcanic sand from Mount Etna were investigated by a series of experiments on a long Split Hopkinson Pressure Bar apparatus capable of generating stress pulses of duration exceeding one millisecond. The dynamic stress–strain characteristics were determined until large final compressive strains were achieved. An experimental protocol for the preparation of samples characterised by different initial porosity and moisture content was defined in order to reproduce, in a laboratory environment, granular volcanic aggregates representative of naturally occurring soils in different initial density and water content states. It was found that, for limited amounts of water content, the dynamic response of the investigated volcanic wet sand is more compliant than in dry conditions. Conversely, highly saturated samples exhibit a steep increase in stiffness occurring at strains when the dynamic compressive behaviour becomes dominated by the response of the nearly incompressible water. The presence of water has negligible effect on the mechanical behaviour when the samples are loaded at quasi static strain rates. The grain size distribution and morphology of samples tested in different conditions were evaluated and compared by means of edge detection analysis techniques applied to high contrast images.

Statistical Constitutive Model of Thermal Damage for Deep Rock considering Initial Compaction Stage and Residual Strength

From the theory of damage mechanics, based on the Hoek-Brown strength criterion and Weibull distribution law of rock microelement strength, a statistical constitutive model of rock thermal damage is established by using equivalent strain hypothesis, and the theoretical model is modified by considering the compression coefficient and residual strength correction coefficient. The rationality of the modified model is verified by experimental data. The results show that the stress-strain curves of rock can be divided into four stages: initial compaction, stable damage propagation, damage strengthening expansion, and damage failure according to the characteristics of rock damage evolution. The peak stress of rock increases exponentially with the increase of confining pressure, and the maximum damage evolution rate decreases exponentially with the increase of confining pressure, which indicates that confining pressure delays the development of cumulative damage. The peak stress and maximum damage evolution rate of rock decrease exponentially with the increase of temperature, which accelerates the damage of rock. The initial damage of rock is thermal damage caused by temperature, and the damage value increases with the increase of temperature. The revised theoretical curve reflects the characteristics of rock compaction stage and residual strength and improves the coincidence with the experimental curve. The research results provide a reference for the establishment of thermal damage constitutive model of rock in deep engineering.

Prediction of Pre-Compression Stress of Soil with Uniaxial Test

The paper presents a concept of determination of pre-compression stress. It assumes that the stress value is close to the unit pressure value which is indispensable to increase the initial degree of soil compaction. Thus, an attempt was made to develop an empirical model for predicting the value of stress at which the initial compaction of a soil sample increases by a determined value. Samples with the so-called intact structure (NS) and soil material in the form of loose mass were collected from subsoil, and they were used to form model samples. Both types of samples were uniaxially compressed. For the study, data on moisture and dry bulk density of model samples were used, as well as determined ratios (conversion factors) that present relations between the results of compaction of model samples and samples with the intact structure. It was reported that the pressure necessary for the increase of the initial compaction of the model samples with the value of +0.05 or +0.10 g∙cm−3 were higher than the formation pressure respectively by 1.03-1.11 and 1.42-1.93 times. It was proved that for determination of the pre-compression stress of the NS samples models of linear regression for prediction the pressure needed to increase the initial compaction of the model sample by the value of +0.05 g∙cm−3, combined with a coefficient calculated for the present state of the soil properties, can be applied.

Statistical Damage Constitutive Model for Cemented Sand considering the Residual Strength and Initial Compaction Phase

Based on continuum damage mechanics and the assumption of volume invariance, a damage constitutive model of cemented sand under triaxial stress was established while considering residual strength. Statistical theory was then introduced into this model. Assuming that the microunit strength of cemented sand obeys a Weibull random distribution, an expression of microunit strength based on the Mohr–Coulomb criterion was derived. Additionally, a damage evolution equation and a statistical damage constitutive model of cemented sand under triaxial stress were established. In order to consider the nonlinear deformation and volume change in the initial pore compaction stage, the critical point reflecting the completion of the initial compaction stage was determined. This was done by applying the volume invariance assumption to the linear portion of the stress and strain curve and performing a coordinate transformation. The nonlinearity of the initial compaction stage was fitted by a quadratic function. A triaxial compression test of cemented sand was then carried out to verify this proposed method. The results show that the calculated values by the damage constitutive model fit well with the actual experimental values and that the calculated results can reflect the stress softening, residual strength, and initial compaction characteristics of cemented sand, which shows the rationality and feasibility of the model.