Mechanisms of Energy Transfer and Failure Zoning in Rock Mass Blasting: A Mohr–Coulomb Theory and Numerical Simulation Study

Evaluating Mohr–Coulomb yield criterion for plastic flow in model metallic glasses

To solve the classical problem that the Mohr–Coulomb yield criterion overestimates the tensile properties of geotechnical materials, a modified Mohr–Coulomb yield criterion that includes both maximum tensile stress theory and smooth processing was established herein. The modified Mohr–Coulomb constitutive model is developed using the user‐defined material subroutine (UMAT) available in finite element software ABAQUS, and the modified Mohr–Coulomb yield criterion is applied to construct a numerical simulation of a shaking table model test. Compared with the measured data from the shaking table test, the accuracies of the classical Mohr–Coulomb yield criterion and the modified Mohr–Coulomb yield criterion are assessed. Compared to the shaking table test, the classical Mohr–Coulomb model has a relatively large average error (−6.98% in peak acceleration values, −8.47% in displacement values, −23.93% in axial forces), while the modified Mohr–Coulomb model has a smaller average error (+2.71% in peak accelerations value, +3.19% in displacements value, +7.56% in axial forces). The results of numerical simulation using the modified Mohr–Coulomb yield criterion are closer to the measured data.

Development of an analytical model based on Mohr–Coulomb criterion for cutting of metallic glasses

ABSTRACT: We present a numerical approach for the quantification of the energy transfer, storage, and dissipation mechanisms in fluid-driven fracturing. The analysis approach is motivated and originated in the energy statement describing continuum damage, poroelasticity, and the non-local effects in both of damage and transport. The thermodynamically consistent derivation leads to the definition of the state laws, as well the as analytical expressions of energy storage and dissipation in the porous media. The derivation leads to the identification of three major energy loss mechanisms: 1) viscous fluid-flow, 2) solid-damage effect due to the growth of voids and cracks in the solid skeleton, and 3) fluid-damage effect due to the accompanying changes in compressibility and permeability. The analysis model is implemented following the framework of mixed non-linear finite element; and the energy dissipation functions are calculated numerically within this framework. Several benchmark fluid-driven fracturing problems are modeled, and the results agree with the available data from experimental models in the literature. The model is then used to perform several parametric investigations to provide an engineering value of the proposed approach; for example, the analysis of different fluid-injection rates shows most of the additional energy input in higher injection rates is dissipated in viscous fluid flow rather than the sought solid damage. Moreover, the model is used in the analysis of the interaction between fluid-driven fracturing and pre-existing weak zones featuring combinations of reduced stiffness and permeability to represent natural and man-made fractures. 1 INTRODUCTION Hydraulic fracturing is a process in which a fracturing fluid is pumped at high rates in order to increase the permeability in a fracture zone, ultimately leading to more economical oil production. Energy used in the process is transferred into the porous domain in the form of: (a) elastic energy stored in a deformed domain; (b) energy used to generate new fracture surfaces, resulting in the dissipation of energy through solid skeleton decay (damage); and (c) energy used to transport the fluid through pores, resulting in dissipation via fluid viscosity. The goal of an optimized hydraulic fracturing approach would be to maximize the dissipation due to solid damage, as this would result in the stimulation of a larger reservoir volumeBunger and Lecampion (2017); Shlyapobersky (1985). This paper provides a quantitative evaluation of energy stored and dispersed throughout the process of hydraulic fracturing, based on an non-local damage and transport (NLDT) model modelMobasher et al. (2017); Mobasher (2017); Mobasher et al. (2018); Mobasher and Waisman (2021a,b).

Pile foundation is the most important foundation type of long-span bridges, of which the ultimate load-bearing capacity affects the safety and sustainable performance of bridges. When constructing large-span bridges, the bridge site may be close to the adjacent fault zones, which seriously affects the safety and long-term performance of pile foundations, causing the failure and unsustainability of long-span bridges in their life-cycle service life. At present, there are no engineering design rules or methods for assessing the load-bearing capacity of the pile foundation near the fault zones. To study the influence of the fault zone on the loading-bearing capacity and sustainable performance of pile foundations, triaxial compression tests were carried out on the mylonite at the Yanji suspension bridge site near the Xiangfan–Guangji fault zone in Hubei Province. The mechanical properties of mylonite were reflected by the Mohr–Coulomb yield criterion, and a topographic and geological modeling method based on the multi-platform was established. Then, the ABAQUS finite element software was used to study the deformation, stress, failure modes, and sustainable performance of the pile foundation under different bridge load levels, analyze the safety of the pile foundation in the fracture zone, and summarize the ultimate bearing characteristics of the pile foundation. The results show that the whole pile and surrounding rock are basically elastic under the pressure of the designed load, the plastic zone of the pile foundation is mainly concentrated at the pile bottom, and the shear stress concentration zone of the pile is mainly manifested in the joint of the cap and pile and the interface between soft and hard rock. When the load is increased to 4 times the designed load, the stress concentration area of the pile body gradually shifts upward from the pile bottom, and the surrounding rock at the bottom forms an “X-shaped” shear failure zone. After 100 years of operation, the maximum compressive stress of piles reaches 28.6 MPa, which is 120% higher than that at the beginning of the bridge construction, indicating that the sustainable performance of the piles can withstand the effect of the fault zone over the designed service years.

Practical application of failure criteria in determining safe mud weight windows in drilling operations

The mechanical characteristics and stress state caused by water jet loading are influenced by many factors that have restricted studies on the jet mechanism. Using the basic theory of elasticity and fluid dynamics, the mechanical effects of water jet loading are analyzed. Based on the simplified jet distribution pressure, the elastic analytical solution of the stress distribution in a semi-infinite plane under the jet distribution pressure is derived, and the stress distribution characteristics are discussed. In addition, the Mohr–Coulomb yield criterion served as a fracture criterion, enabling establishment of the relationship between jet pressure and rock strength. The results indicate that the compressive stress is symmetrically distributed around the jet axis with the maximum at the center. Conversely, the shear stress is Anti-symmetrically distributed around the jet axis with the maximum at the point (0.5r, ± 0.65r). The initial fracture of rock under the impact of water jet is mainly shear compression failure. The Mohr–Coulomb yield criterion is useful for estimating the relationships between the rock failure zone diameter with the water jet impact pressure.

Photosynthesis uses light energy from the sun to convert CO2 and water into carbohydrates and oxygen, thus sustaining all aerobic life forms on Earth. Energy conversion in photosynthesis is carried out by two large membrane-protein complexes: photosystemⅠ(PSⅠ) and photosystemⅡ(PSⅡ). In higher plants, the PSⅠcore is surrounded by a belt of 4 light-harvestingⅠsubunits (LHCⅠor Lhca), forming a PSⅠ-LHCⅠsupercomplex. The PSⅠ-LHCⅠsupercomplex is an extremely efficient solar energy converter with a quantum efficiency close to 100%. In order to reveal the mechanism of energy harvesting and transfer within this large pigment-protein complex, it is essential to solve its crystal structure. The structure of the PSⅠ-LHCⅠsupercomplex has been analyzed at a resolution up to 3.3 A previously. However, this resolution was not enough to elucidate the detailed mechanism of light-harvesting and energy transfer in this complex. Recently we succeeded in analyzing the structure of the PSⅠ-LHCⅠsupercomplex from pea at 2.8 A resolution (1). Our studies showed that the PSⅠ-LHCⅠsupercomplex contains 16 different subunits (including 12 core subunits PsaA-L and 4 LHCⅠsubunits Lhca1-4) and 205 cofactors (143 chlorophylls a, 12 chlorophylls b, 26 β -carotenes, 5 luteins, 4 violaxanthin, 10 lipids), with a total molecular mass of 600 kD. Our results identified chlorophyll a , chlorophyll b, and some carotenoids in the 4 LHCⅠsubunits for the first time, and revealed the differences in the structures of the 4 LHCⅠ subunits, their interactions, and the interactions between them and the PSⅠcore subunits. Comparison among the available six structures of the Lhc family members (Lhca1 to Lhca4, LHCⅡand CP29) revealed that, although all these Lhc proteins have a highly conserved second protein structure, notable differences were found in the two loop regions AC and BC as well as the N-terminal region. Most pigments are arranged at the same position except some distinct differences among different Lhc subunits in the position of several Chls bound at the interface between adjacent Lhca complexes, and between Lhca and PSⅠcore complex. Based on the structure resolved, 4 plausible energy transfer pathways (1Bs, 1Fl, 2Js, 3As/l) from LHCⅠto the PSⅠcore complex were deduced. Red forms of Chls were found to be involved in energy transfer from each Lhca to PSⅠcore. Our structure revealed that each Lhca binds a red chlorophyll dimer of Chl a 3-Chl a 9, which contribute to red-shifted spectra of Lhca complexes and have a pronounced effect on the energy transfer and trapping in the whole PSⅠ-LHCⅠcomplex. All the four red dimers locate at the interface between LHCⅠand PSⅠcore complex, which looks like four bridges connecting Lhca with the core. The Chl-Chl interactions between each Lhca and the core complex suggested that excitation energy from the LHCⅠbelt to the PSⅠcore would mainly flow via Lhca1 and Lhca3. In this review, we discuss the detailed structure of the PSⅠ-LHCⅠsupercomplex and the possible energy transfer mechanism within it. Taken together, this structure provides a solid structural basis for our understanding on energy transfer and photoprotection mechanisms within PSⅠ-LHCⅠsupercomplex, and thus will be a big step forward toward understanding the mechanisms of photosynthesis.

Energy transfer mechanisms in flow-like landslide processes in deep valleys

The mining of coal mines in western China needs to focus on protecting groundwater. A non-hydrophilic similar material for simulating the development and hydraulic conductivity of weakly cemented overlying strata fractures was developed. Fine sand, coarse sand, and gypsum are used as aggregates. Paraffin and Vaseline are used as binders. The non-hydrophilic material ratios of weakly cemented sandy mudstone and medium-grained sandstone were determined by orthogonal experiments, and used for similar simulation tests. The results show that the non-hydrophilicity of rock-like materials can be adjusted to prevent them from softening and collapsing under the action of water. Non-hydrophilic materials of higher strength and brittleness of rocks can be achieved by adjusting the content of paraffin, fine sand, and gypsum. The non-hydrophilic materials of soft and large particle rocks can be achieved by adjusting the content of paraffin, fine sand, and gypsum. After the coal seam in a similar simulation experiment was extracted, the large area of weakly cemented rock above it underwent overall settlement and fracture. Although this part was located within the failure zone, there was no macroscopic water-conducting cracks generated. The height of the water-conducting fracture zone was lower than the height of the fracture zone classified by the traditional ‘three zone’ theory, which is consistent with the on-site measurements. This indicates that the prepared non-hydrophilic material is reliable. The similarity simulation method based on non-hydrophilic materials can enrich the means for studying the fracture and permeability of weakly cemented overlying rocks in coal mines.

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr–Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

A closed-form solution for the problem of the plastic zone and stress distribution around a circular tunnel in an elastic–plastic half space, derived using bipolar coordinates, is the main scope of this paper. By assuming a uniformly applied surface loading, the whole semi-infinite space is under uniform pressure: thus the gravitational effect is neglected, while the plastic zone formation around the circular tunnel is controlled by the applied internal support pressure. The plastic behaviour of the half space is described by the Mohr–Coulomb yield criterion, and the soil is assumed to be homogeneous and isotropic with earth pressure coefficient K0 equal to unity. The critical internal pressure, where the initial yielding occurs at the tunnel wall, is derived, along with equations describing the plastic zone and plastic stresses. These equations are functions of the soil properties, which are cohesion and friction angle. This derived closed-form solution is validated through mathematical and computational analysis, and is also compared with numerical models under gravitational load, solved using the finite difference method. This innovative closed-form solution has a significant impact in practical problems by introducing a simple and effective method that allows the quick estimation of a shallow tunnel's behaviour, since it gives, in principle, the opportunity for quick and accurate calculation of the plastic zone and stress distribution around the circular tunnel. By applying different values of support pressure, the tunnel designer can easily evaluate the feasibility of different design alternatives, such as shotcrete shell and tunnel-boring machine support pressure. As a result, an efficient and innovative method of solving shallow tunnelling problems in cohesive-frictional soil is introduced.

The energy transfer (ET) mechanism of atomic recombination reactions, X+X=X2*, X2*+M→X2+M, where X2* is a classically unstable orbiting quasidimer consisting of two X atoms and M is a third body, has been commonly used for the past forty years. Presently it is studied in some detail using the 3-D trajectory calculation technique and the Monte Carlo method of sampling. Since this mechanism approximates a pure three body problem by considering two independent and consecutive two body collisions, it introduces an error in trajectory calculations. In order to improve upon this approximation, a more reasonable modified method of trajectory sampling is made. It is found that even in one of the most favorable cases where the ET mechanism is predominant, i.e., for the 2I+He=I2+He reaction, the error introduced by the ET mechanism is of the order of two in the rate constant. It is concluded, in light of the present findings, that earlier as well as present trajectory studies for halogen atom recombination in helium are consistent with experimental data. The existing discrepancy between computed and experimental results can be accounted for by the approximations used in trajectory calculations. On the other hand, the combined Monte Carlo sampling and experimental errors cannot account for the existing discrepancies.

Linings and anchor bolts, as common support structures, play a crucial role in ensuring the stability of tunnel surrounding rock. This study aims to investigate the elastic–plastic behavior of lining-anchor bolt support structures in deep circular tunnels under static water pressure. Based on the Mohr–Coulomb (M-C) criterion and equivalent substitution method, this study derives the solution process for the radius of the plastic zone and the elastic–plastic stress expressions under a given lining internal pressure. Furthermore, through examples, this study analyzes the radius of the plastic zone and the stress evolution curve of the lining-anchor bolt-supported surrounding rock system under three conditions: without anchoring, various elastic moduli, and different anchor bolt support angles. Finally, this study verifies the rationality of the elastic–plastic analytical solution for the lining-anchor bolt-supported surrounding rock structure through numerical simulation methods. The integrated lining-anchor bolt support is notably effective in inhibiting the expansion of the plastic zone, particularly in soft rock. Additionally, the elastic modulus and circumferential spacing of the anchor bolts significantly influence the plastic zone inhibition rate in soft rock.

Model calculations are presented for the condensation of gases on metal surfaces for several mechanisms of gas-surface energy transfer. The mechanisms considered are classical and quantum-mechanical momentum transfer to the substrate, excitation of substrate electrons, and coupling to internal degrees of freedom of the gas molecules. Sticking coefficients are computed as functions of the interaction potential, adsorbate and substrate mass, and gas and surface temperatures. The dependence of the sticking coefficient on these parameters may be different for different mechanisms of energy transfer.