Triaxial Model Research Articles

Review on Intrinsic Shape of Elliptical Galaxies

: Elliptical galaxies, as one of the fundamental types of galaxies, have attracted astronomers due to their intriguing properties. In this review, we explore the intrinsic shape of elliptical galaxies, a field that plays a pivotal role in understanding their formation, evolution, and interactions within the cosmos. Methods for intrinsic shape determination using photometric and kinematic methods are extensively discussed. The use of photometric data and surface brightness profiles to derive the intrinsic shapes of elliptical galaxies is examined and triaxial models are reviewed. Constraining the intrinsic shapes of elliptical galaxies is crucial to understanding their formation histories. Elliptical galaxies are characterized by their ellipsoidal, rather than disk-like, shapes, and understanding the underlying factors and their intrinsic shapes of elliptical galaxies determination provides valuable insights into their formation, evolution, and the broader context of galaxy morphology. One key aspect of studying the intrinsic shape of elliptical galaxies involves the analysis of their axial ratios, which describe the flattening of the galaxy along different axes. The axial ratio is defined as the ratio of the semi-minor axis to the semi-major axis of the ellipse representing the galaxy's cross-section. The intrinsic shape can vary from nearly spherical (axial ratio close to 1) to highly elongated (axial ratio significantly different from 1).

Galaxy shapes in Magneticum

Context. Despite being one of the most fundamental properties of galaxies that dictate the form of the potential, the 3D shapes are intrinsically difficult to determine from observations. The improving quality of triaxial modeling methods in recent years has made it possible to measure these shapes more accurately. Aims. This study provides a comprehensive understanding of the stellar and dark matter (DM) shapes of galaxies and the connection between them. As these shapes are the result of the formation history of a galaxy, we investigate which galaxy properties they are correlated with, which will be especially useful for interpreting the results from dynamical modeling. Methods. Using the hydrodynamical cosmological simulation Magneticum Pathfinder Box4 (uhr), we computed the stellar and DM intrinsic shapes of 690 simulated galaxies with stellar masses above 2 × 1010 M⊙ at three different radii with an iterative unweighted method. We also determined their morphologies, their projected morphological and kinematic parameters, and their fractions of in situ formed stars. Results. The DM follows the stellar component in shape and orientation at three half-mass radii, indicating that DM is heavily influenced by the baryonic potential in the inner parts of the halo. The outer DM halo is independent of the inner properties such as the DM shape or galaxy morphology, however, and is more closely related to the large-scale anisotropy of the gas inflow. Overall, DM halo shapes are prolate, consistent with previous literature. The stellar shapes of galaxies are correlated with their morphology, with early-type galaxies featuring more spherical and prolate shapes than late-type galaxies out to 3 R1/2. Galaxies with more rotational support are flatter, and the stellar shapes are connected to the mass distribution, though not to the mass itself. In particular, more extended early-type galaxies have larger triaxialities at a given mass. Finally, the shapes can be used to better constrain the in situ fraction of stars when combined with the stellar mass. Conclusions. The relations between shape, mass distribution, and in situ formed star fraction of galaxies show that the shapes depend on the details of the accretion history through which the galaxies are formed. The similarities between DM and stellar shapes in the inner regions of galaxy halos signal the importance of baryonic matter for the behavior of DM in galaxies and will be of use for improving the underlying assumptions of dynamical models for galaxies in the future. However, at large radii the shapes of the DM are completely decoupled from the central galaxy, and their shapes and spin are coupled more to the large scale inflow than to the galaxy in the center.

Gravitational lensing by an ellipsoidal Navarro–Frenk–White dark-matter halo: An analytic solution and its properties

Context. The analysis of gravitational lensing by galaxies and galaxy clusters typically relies on ellipsoidal lens models to describe the deflection of light by the involved dark-matter halos. These models are most often based on the isothermal density profile – not an optimal description of the halo, but easy to use because it leads to an analytic deflection-angle formula. Aims. Dark-matter halos are better described by the Navarro–Frenk–White (hereafter NFW) density profile. We set out to study lensing by a general triaxial ellipsoidal NFW halo, with the aim of providing an analytic model that would be more consistent with the current understanding of dark-matter halos. Methods. We computed the conversion between the properties of a triaxial ellipsoidal lens model and its elliptical surface-density profile. In the case of the NFW lens model, its angular scale is defined by the projected scale semi-major axis of the halo, while its lensing regime depends on two parameters: the projected eccentricity e and the convergence parameter κs. We employed the Bourassa & Kantowski formalism to compute the complex scattering function of the model, which yields the deflection-angle components when separated into its real and imaginary parts. Results. We present the obtained closed-form expressions for the deflection-angle components, valid for an arbitrary eccentricity of the surface-density profile. We use them to compute and describe the lensing properties of the model, including: the shear, its components, and the phase; the critical curves, caustics, and the parameter-space mapping of their different geometries; the deformations and orientations of images. Conclusions. The analytically solved ellipsoidal NFW lens model is available for implementation in gravitational lensing software. The techniques introduced here such as the image-plane analysis can prove to be useful for understanding the properties of other lens models as well.

Octupole correlations in stable nucleus 153Eu within reflection-asymmetric particle rotor model

Abstract The observed low-lying K=5/2± positive- and negative-parity bands in the stable nucleus 153Eu are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra, the energy staggering parameters, as well as the intraband E2 and M1 transition probabilities are well reproduced. It is found that the calculated interband B(E1) values depend sensitively on the octupole deformation parameter β30, although the energy spectra and intraband E2 and M1 transitions can be reproduced without the octupole degree of freedom. The observed enhanced E1 transition probabilities can be reproduced with β30=0.05. The detailed analysis of the intrinsic wave functions shows these nearly degenerate positive- and negative-parity bands are built on two individual proton configurations, i.e., dominated by πg9/2[Ω=5/2] and πh11/2[Ω=5/2], respectively, which differs from the parity doublet bands built on a single parity-mixed configuration.

True triaxial modeling test of high-sidewall underground caverns subjected to dynamic disturbances

Seismicity resulting from the near- or in-field fault activation significantly affects the stability of large-scale underground caverns that are operating under high-stress conditions. A comprehensive scientific assessment of the operational safety of such caverns requires an in-depth understanding of the response characteristics of the rock mass subjected to dynamic disturbances. To address this issue, we conducted true triaxial modeling tests and dynamic numerical simulations on large underground caverns to investigate the impact of static stress levels, dynamic load parameters, and input directions on the response characteristics of the surrounding rock mass. The findings reveal that: (1) When subjected to identical incident stress waves and static loads, the surrounding rock mass exhibits the greatest stress response during horizontal incidence. When the incident direction is fixed, the mechanical response is more pronounced at the cavern wall parallel to the direction of dynamic loading. (2) A high initial static stress level specifically enhances the impact of dynamic loading. (3) The response of the surrounding rock mass is directly linked to the amplitude of the incident stress wave. High amplitude results in tensile damage in regions experiencing tensile stress concentration under static loading and shear damage in regions experiencing compressive stress concentration. These results have significant implications for the evaluation and prevention of dynamic disasters in the surrounding rock of underground caverns experiencing dynamic disturbances.

Reevaluation of structures in Se70 from combined conversion-electron and γ -ray spectroscopy

In the selenium isotopes various shape phenomena are present, in particular, the emergence of a dominant oblate deformation in the most neutron-deficient isotopes has been observed. The scenario of shape coexisting oblate and prolate bands has been proposed across the isotopic chain, with the crossing point of such bands being located near Se70, where no coexistence has yet been identified. To determine the presence or absence of any low-lying 0+ state in Se70, confirm the level structure, and interpret the nuclear deformation with theoretical models. A combined internal-conversion-electron and γ-ray spectroscopy study was undertaken with the SPICE and TIGRESS spectrometers at the TRIUMF-ISAC-II facility. Nuclear models were provided by the generalized triaxial rotor model (GTRM) and the collective generalised Bohr Hamiltonian (GBH). Despite a comprehensive search, no evidence was found for the existence of a 0+ state below 2 MeV in Se70. Significant discrepancies to the previously established positive-parity-level scheme were found. GBH calculations using UNEDF1 mass parameters were found to reproduce the revised low-lying level structure well. Se70 does not have a well-defined axial shape. The 22+ state at 1601 keV resembles a quasi-γ excitation rather than a member of a shape coexisting band; the presence of such a band is all but ruled out.Published by the American Physical Society2024

A multiaxial thermo-mechanical damage model for concrete including Load Induced Thermal Strain (LITS)

In the current study, a multiaxial LITS model of concrete was innovatively developed. This model can predict the behavior of concrete subjected to wide applied load level ranges from 20 % to 80 % and temperatures up to 800 °C. A 3D LITS model is developed through a triaxial compression stress confinement implementation and Poisson's ratio. Considering the water evaporation of concrete under high temperature, a third order polynomial LITS derivative function and an exponential derivative function were proposed to characterize the effects of the stress confinement and thermal effect. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete is developed. The effect of LITS on the multiaxial stress-strain response was considered in the multiaxial model. The coupling thermo-mechanical contributions containing the development of LITS among thermal effect, stress confinement, damage and plastic hardening evolution were creatively considered in the potential function within thermodynamics framework. The numerical calculations of this proposed model were conducted for validation. The effect of LITS on the multiaxial stress-strain response was studied. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranges from 20 °C to 1000 °C through the comparative study with test results in literatures, which indicates the accuracy and applicability of the proposed model.

A 3D thermo-mechanical damage model for concrete including Short-Term Thermal Creep Strain (STTCS)

In the current study, a Short-Term Thermal Creep Strain (STTCS) model of concrete was innovatively developed. This model can predict the time-dependent deformation of concrete subjected to wide applied load level ranging from 20 % to 60 % and temperatures up to 900 °C. A creep compliance function was developed to study the nonlinear creep characteristics of concrete with creep parameters. The definition and sensitivity of the creep parameters were investigated. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete is developed. The influence of STTCS on the multiaxial stress-strain behaviors was taken into account in the multiaxial model. The coupling thermo-mechanical contributions containing the development of STTCS with thermal effect, stress confinement, plastic damage and hardening evolution were creatively considered in the potential function within thermodynamics framework. The sensitivity of yield surface was discussed. The numerical operations of this proposed model were conducted for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranging from 20 °C to 800 °C through the comparative study with test results in literatures, which indicates the accuracy and applicability of the proposed model.

Research on the bearing creep characteristics and constitutive model of gangue filling body

The creep characteristics and potential deformation patterns of gangue backfill material are crucial in backfill mining operations. This study utilizes crushed gangue from the Gangue Yard in Fuxin City as the research material. An in-house designed, large-scale, triaxial gangue compaction test system was used. Triaxial compaction creep tests were conducted on gangue materials with varying particle size distributions. Analysis was performed based on different particle sizes, stresses, and confinement pressures. The study investigates the creep characteristics of the gangue under different conditions and explores the underlying causes. It reveals the relationship between the creep deformation of gangue materials and the passage of time. Mathematical methods are applied to develop a triaxial compaction creep power law model for gangue backfill materials. Finally, the creep results are fitted using an empirical formula approach.

First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region

Excited states have been observed for the first time in the very neutron-deficient odd-odd nucleus 57120La63. The observed γ rays have been assigned based on coincidences with lanthanum X rays measured with the JUROGAM 3 array and with A=120 fusion-evaporation residues measured with the MARA separator. The observed γ rays form a rotational band which decays to the ground state via a cascade of four low-energy transitions. Based on the systematic comparisons with the heavier odd-odd La isotopes we assign spin-parity 4+ to the ground state and a πh11/2⊗νh11/2 configuration to the rotational band. The nuclear shape has been investigated by the cranked Nilsson-Strutinsky model. Two quasiparticle plus triaxial rotor model calculations including the np interaction nicely reproduce the spin of the inversion between the even- and odd-spin cascades of E2 transitions, giving credit to the np interaction as an important parameter responsible for the mechanism inducing the inversion. The position of the Fermi levels, in particular for neutrons, also has a strong impact on the observed inversion in the chain of lanthanum nuclei.

Study of the static mechanical properties of tailings under the influence of multiple lens types

There are many types of lenses in tailings ponds that have important influences on stability. Lens types of more than 150 tailings dams were analyzed in China’s severely cold regions, cold regions, hot summers and cold winters (the civil building thermal design code (GB50176-2016)). The mechanism of lens formation is discussed in this paper. Triaxial tests of tailings were carried out with fine mud tailing lenses, notched lenses, ice lenses and soft plastic soil lenses. Moreover, a three-dimensional triaxial test model with a flexible boundary is constructed to study the influence of different lenses on the mechanical properties of the tailings. The lens can change the failure mode of the tailings. These faults can change the dilatancy failure of tailings to failure along the “lens-tailings” interface. With increasing confining pressure, the ability of the lens to weaken the strength of the tailings increases. At 500 kPa, the strengths of the samples with fine mud tailing lenses, notched lenses, ice lenses and soft plastic soil lenses are 95.28%, 88.79%, 76.99% and 5.49%, respectively, of those of the sample without lenses. In addition to soft plastic soil lenses, other lenses provide space to accommodate the deformation of tailings, thereby reducing the bulk strain of tailings. The conclusions of this study can provide theoretical support for studying the failure mode of tailings dams under the influence of lenses and improving the local stability of tailings ponds.

Characteristics of sandstone unloading creep and modelling for safe tunnel construction under high perimeter pressure and high pore water pressure condition

Research on the properties of sandstone in the tunnel environment has been conducted due to the building industry’s rapid development, which is gradually involving underground water. Sandstone used in tunnel construction is susceptible to high perimeter and water pressures as a result of the abundance of sand and gravel close to groundwater, which might result in mishaps resembling collapses. The modified Burgers Model for the Malm dataset is the foundation of this study, which aims to reduce the internal crack extension caused by sandstone’s unloading creep. First, the study increased the material’s Poisson’s ratio in accordance with the Mohr–Coulomb strength criterion and builds a triaxial loading model on its foundation. Next, it analyzed the extension of the fracture surface of sandstone while taking high peripheral pressure and high hydraulic pressure into account. Finally, it discretized the unloading creep of sandstone using the improved Burgers model. On the basis of the model put forward in the study, experimental validation was then done on the Malm dataset. The sandstone would reach the final rupture area without any protection measures in just 10 days, but the model suggested in the study can delay this time to 200 days, while the effects of the other three models would delay this time by 75, 60, and 41 days, respectively. The model’s breadth was indicated by the linear fit value of 0.9827 for 36 experiments. The experimental findings demonstrated that the model suggested in the study can successfully lower the rate of sandstone unloading creep and increase worker safety.

Asteroid spin and shape properties from Gaia DR3 photometry

The third data release of in June 2022, included the first large sample of sparse photometric data for more than 150\,000 Solar System objects (SSOs), mainly asteroids. The SSO photometric data can be processed to derive information on the physical properties for a large number of objects, including spin properties, surface photometric behaviour in a variety of illumination conditions, and overall shape. After selecting a set of 22\,815 objects for which an adequate number of accurate photometric measurements had been obtained by we applied the 'genetic' algorithm of photometric inversion developed by the Data Processing and Analysis Consortium to process SSO photometric data. Given the need to minimise the required data processing time, the algorithm was set to adopt a simple triaxial ellipsoid shape model. Our results show that in spite of the limited variety of observing circumstances and the limited numbers of measurements per object at present (in the majority of cases no greater than $40$ and still far from the number expected at the end of the mission of about $60$ - $70$), the proportion of correct determinations for the spin period among the observed targets is about $85$<!PCT!>. This percentage is based on a comparison with reliable literature data following a moderate filtering procedure developed to remove dubious solutions. The analysis performed in this paper is important in the context of developing further improvements to the adopted data reduction procedure. This includes the possible development of better solution filtering procedures that take into account, for each object, the possible presence of multiple, equivalent spin period solutions that have not been systematically investigated in this preliminary application.

Permeability evolution of fractured coal subject to confining stress and true triaxial stress loading: experiment and mathematical model

The accurate elucidation and prediction of coal permeability evolution under stress loading conditions are crucial for coalbed methane production. In this study, flow experiments were conducted on six cylindrical coal samples and four cubic coal samples under both confining and true triaxial stress loading conditions, respectively. The structure and characteristic parameters of the fractures inside each coal sample were obtained using the computed tomography scanning system and image processing technologies. The coal permeability under both types of loading processes was calculated through the transient pulse method. A mathematical model was developed to assess the evolution of coal permeability under true triaxial loading based on the current true triaxial permeability model and fractal theory. The results revealed that during the confining pressure loading, the coal permeability decreased exponentially with effective stress and was effectively described using the SD model. Additionally, the coal permeability initially rapidly decreased, followed by a gradual decrease, and eventually stabilized at a constant value. Particularly, during the first three loading steps, the fracture aperture and corresponding permeability of the six cylindrical coal samples decreased by ∼51.79%–57.83% and ∼38.06%–42.12%, respectively. However, during the final three loading steps, the fracture aperture and corresponding permeability of the six coal samples decreased by ∼18.26%–23.08% and ∼22.15%–26.93%, respectively. Moreover, owing to the various crossing angles of complex fracture networks with each principal stress, the effect of each principal stress on the coal permeability evolution was highly anisotropic during triaxial stress loading. Particularly, the permeability of the ST1 sample decreased by 43.08%, 14.84%, and 42.08% during the loading of each principal stress. Similarly, the permeability of the ST2 sample decreased by ∼65.74%, 14.29%, and 19.97%. The permeability reductions for the ST3 sample were ∼34.03%, 55.85%, and 10.12%, while those for the ST4 sample were ∼35.97%, 46.51%, and 17.52%. The SD model failed to describe these anisotropic effects. Compared with the SD model, the improved model, based on the current true triaxial permeability model and fractal theory, effectively described the anisotropic effect of each principal stress on the permeability of coal samples with complex fracture networks under triaxial stress conditions.

A damage constitutive model of layered slate under the action of triaxial compression and water environment erosion

Based on the macroscopic structure control theory, The slate with a significant bedding plane is a composite rock mass composed of rock blocks containing microscopic defects, joint surface closure elements, and shear deformation elements. Considering the coupling damage effect of water erosion and triaxial compressive load on bedding structure plane, the transversely isotropic damage constitutive model of slate under triaxial compressive load is derived with the dip angle of bedding and confining pressure as the variable. Firstly, based on the statistical theory of continuous damage mechanics and the maximum tensile strain criterion, the transversely isotropic deformation constitutive model of rock block with micro-defects is given; Secondly, based on the phenomenological theory of closed deformation and shear-slip deformation mechanism of layered structural plane under the coupling action of water erosion and triaxial compression load, the calculation formula of axial deformation of layered structural plane under the coupling action is given; Finally, to verify the accuracy of the established constitutive model, triaxial compression tests are carried out to study the influence of dip angle and confining pressure on the macroscopic mechanical properties and mechanism of slate. The results show that: the established triaxial compression damage constitutive model of bedding slate can accurately describe the stress–strain relationship of bedding slate after water environment erosion. With the increase of bedding dip angle, the strength and deformation capacity of the bedding slate first decreases and then increases, showing a U-shaped distribution as a whole. There are three main types of failure: tension shear composite failure, shear slip failure, and splitting tension failure.

A new model for predicting the axial compression capacity of reinforced concrete cylinders strengthened with CFRP

Numerous scholars have identified the shortcomings of imprecise terminology and substantial computational inaccuracies in the current models for predicting the axial compression capacity of CFRPstrengthened reinforced concrete (RC) cylinders. To improve the prediction accuracy of the axial compressive capacity model for CFRP-strengthened RC cylinders, the present axial compressive capacity model for CFRP-strengthened RC cylinders was scrutinized and evaluated. Drawing on Mander’s constraint theory and the concrete triaxial strength model, a novel axial compressive capacity model for CFRP-strengthened RC cylinders was proposed. This study collected 116 experimental data on the axial compression of CFRP-strengthened RC cylinders and analyzed the accuracy of various models using the data. The findings indicate that the model proposed in this study outperforms other models in predicting axial compression capacity and demonstrates high prediction accuracy. Furthermore, an analysis is conducted on the variation law of the model’s predicted value with respect to the design parameters. The proposed model in this study identifies concrete strength, stirrup spacing, and elastic modulus of CFRP as the primary factors that influence the axial compression capacity of CFRP-strengthened RC cylinders.

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D). I. Gas analysis method using X-ray and Sunyaev–Zel’dovich effect data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method for investigating the three-dimensional triaxial shapes of galaxy clusters from the Cluster HEritage project with -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this paper, the first in a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from and Sunyaev-Zel'dovich (SZ) effect maps from and the Atacama Cosmology Telescope to obtain a three-dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure, to be compared directly with the observed two-dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we applied the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, PSZ2 G313.33+61.13 (Abell 1689), to illustrate the technique. The inferred parameters are in agreement with previous analyses for the cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With a much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

Triaxial Schwarzschild models of NGC 708: a 10-billion solar mass black hole in a low-dispersion galaxy with a Kroupa IMF

ABSTRACT We report the discovery of a (1.0 ± 0.28) × 1010 M⊙ supermassive black hole (BH) at the centre of NGC 708, the Brightest Cluster Galaxy of Abell 262. Such high BH masses are very rare and allow to investigate BH–host galaxy scaling relations at the high mass end, which in turn provide hints about the (co)evolution of such systems. NGC 708 is found to be an outlier in all the canonical scaling relations except for those linking the BH mass to the core properties. The galaxy mass-to-light ratio points to a Kroupa IMF rather than Salpeter, with this finding confirmed using photometry in two different bands. We perform this analysis using our novel triaxial Schwarzschild code to integrate orbits in a five-dimensional space, using a semiparametric deprojected light density to build the potential and non-parametric line-of-sight velocity distributions (LOSVDs) derived from long-slit spectra recently acquired at Large Binocular Telescope (LBT) to exploit the full information in the kinematic. We find that the galaxy geometry changes as a function of the radius going from prolate, nearly spherical in the central regions to triaxial at large radii, highlighting the need to go beyond constant shape profiles. Our analysis is only the second of its kind and will systematically be used in the future to hunt supermassive BH in giant ellipticals.

The Calibration Method of Magnetometer Based on a Triaxial Noncoincident Model

The Calibration Method of Magnetometer Based on a Triaxial Noncoincident Model

Experimental investigation on triaxial mechanical properties of coral coarse aggregate-sea sand seawater concrete

The application of coral coarse aggregate-sea sand seawater concrete (CSSC) in offshore engineering construction is one of the effective measures to realize the rational allocation of resources and alleviate the shortage of resources. In addition, considering that concrete structures in coastal areas may be under triaxial stress, it is necessary to study the triaxial mechanical properties of CSSC. To study the triaxial mechanical properties of CSSC, the effects of aggregate combination and lateral confining pressure on the failure mode, stress-strain curve, yield stress and yield strain of specimens were studied by conventional triaxial tests. The results show that CSSC is more susceptible to the influence of lateral confining pressure. Under the lateral confining pressure of 6 MPa, the crack form transformation and plastic flow appear on the surface of the specimen. Under the lateral confining pressure of 12 MPa, the stress-strain curve appears "stress platform", while the gravel coarse aggregate concrete shows the above changes under the lateral confining pressure of 15 MPa and 24 MPa, respectively. When the lateral confining pressure reaches 15 MPa, the stress-strain curve of CSSC presents a bilinear shape with a second linear branch. With the increase of confining pressure, the damage development rate gradually decreases, and the yield stress and yield strain gradually increase. Finally, the triaxial compression constitutive model of CSSC is established, which can effectively predict the bilinear behavior of the CSSC curve.