Deformation Model Research Articles

Predictive Model for Deformation of Adjacent Pipelines Caused by Tunnel Boring in Twin-Lane Tunnels in Soft Ground Layers

To create a discretized prediction model for the deformation of an adjacent pipeline, the pipeline structure is discretized, the differential equations governing the longitudinal deformation of the pipeline are inferred, and the displacement expressions and the solution methods of the virtual nodes of each unit are provided after discretization. This approach is based on the Pasternak foundation beam theory. It aims to address the issue of the difficulty in predicting the deformation of the adjacent pipeline caused by shield tunneling in a saturated soft ground layer in the Yangtze River Delta. The deformation pattern of the surrounding soil is determined and confirmed through additional numerical simulation, and the discretized prediction model is contrasted with the conventional Winkler foundation beam model and the Pasternak foundation beam model. The findings demonstrate that the discrete prediction model is simpler to solve and more accurately describes the deformation characteristics of the adjacent pipeline as well as the deformation distribution law. The calculated deformation characteristics primarily appear as the adjacent pipeline’s deformation due to the double tunnel boring exhibiting a “mono-peak shape” with a large middle and small ends, which is consistent with the actual situation. The two main factors influencing the pipeline deformation are the shield tunneling distance and pipeline spacing; the former has a negative correlation with the pipeline deformation, while the latter has a positive correlation. This work can offer a straightforward deformation prediction technique for shield tunneling in the Yangtze River Delta’s saturated soft ground next to existing pipelines.

Subscale modeling of material flow in orthogonal metal cutting

Enhanced simulation capability for the cutting process is crucial to making quick evaluations of cutting forces and temperatures, which are significant for assessing the machinability of the workpiece material and predicting tool wear. In this paper, the material flow in orthogonal cutting, including primary and secondary shear zones, is represented by a viscous/viscoplastic model that includes the temperature-sensitive Johnson-Cook flow stress model. A stabilized staggered finite element procedure is developed to handle incompressible Navier-Stokes material flow in combination with convection-dominated hardening and thermomechanical interaction. To handle material flow at tool-workpiece contact, a mixed method is used to reduce spurious oscillations in contact stresses along with simplified heat transfer in the tool-workpiece interface. A novel feature is that the velocity field is resolved as a subscale field to the velocity field of the distributed primary zone deformation model. It appears that the finite element solution to the subscale material flow model is significantly more cost-effective in contrast to directly addressing the velocity field and compared to the chip-forming simulations (DEFORM 2D). The cutting forces, temperature, and stress-strain state of the material in the critical deformation regions can be accurately estimated using the subscale model. The results obtained show that the trend of the estimated forces and temperatures is consistent with our experimental measurements, the DEFORM 2D simulations, and the experimental data from the literature.

A shear deformable shell model for dynamic performance of light-weight and advanced sport balls

The present study investigates the oscillation characteristics of a sport ball that is modeled as a doubly curved shell that is made of a nanocomposite material consisting of functionally graded graphene platelets and metal foams. The shell is immersed on a Kerr basis, which is an elastic foundation with three parameters. The organization of the pores and the dispersion of the graphene platelets throughout the thickness of the model are considered based on the stated functionality. The Halpin-Tsai and expanded rule of mixture micromechanical models are employed to determine the effective mechanical property values. Once the motion equations are established, the frequencies are derived using the analytical method, which is especially efficient for shells with simply supported edges. The investigation takes into account and deals with the effects of different influences on the natural frequencies. The results could serve as a benchmark for future research. Given the absence of comparable research in the existing literature, the findings of this study can serve as a standard for future investigations.

Construction and application of a physically-based constitutive model for superplastic deformation of near-α TNW700 titanium alloy

Construction and application of a physically-based constitutive model for superplastic deformation of near-α TNW700 titanium alloy

Pulse-by-pulse transient thermal deformation in crystal optics under high-repetition-rate FEL.

Time-domain modeling of the thermal deformation of crystal optics can help define acceptable operational ranges across the pulse-energy repetition-rate phase space. In this paper, we have studied the transient thermal deformation of a water-cooled diamond crystal for a cavity-based X-ray free-electron laser (CBXFEL), either an X-ray free-electron laser oscillator (XFELO) or a regenerative amplifier X-ray free-electron laser (RAFEL), by numerical simulations including finite-element analysis and advanced data processing. Pulse-by-pulse transient thermal deformation of a 50 µm-thick diamond crystal has been performed with X-ray pulse repetition rates between 50 kHz and 1 MHz. Results for temperature and thermal deformation have been compared with the results of transient analysis using a continuous wave (CW) power loading. Temperature and thermal deformation results from pulse-by-pulse transient analysis vary with time about the results for the CW case for the same average power. The variation amplitude increases with pulse energy and decreases with repetition rate. When the repetition rate increases to infinity, both temperature and thermal deformation converge to the results for the CW case. Two critical time scales for the operation of crystal optics in a CBXFEL are (1) first-turn time, i.e. the time for the XFEL pulse to complete the first turn around the cavity so that the crystal sees the recirculated XFEL pulse, and (2) period-end time, i.e.the time that the next electron bunch arrives for the amplification, so that the crystal outcouples the amplified FEL power. For the same average power, simulation results show that the crystal thermal deformation seen by the XFEL beam decreases with repetition rate at the first-turn time of a 300 m-long cavity and increases with repetition rate at the period-end time. For the wavefront preservation requirement of the crystal optics, a pulse-energy versus repetition-rate phase space has been established. The upper bounds of the pulse energy at both first-turn and period-end times decreases with repetition rate, especially at the period-end time. The upper bound of the thermal deformation of the crystal at the period-end time for any repetition frequency can be estimated from the CW case. For a water-cooled diamond crystal of dimension 5 mm × 5 mm × 0.05 mm, the time to reach a quasi steady-state is about 50 ms for temperature and 50 µs for thermal deformation.

Structure failure and strength evaluation of honeycomb-based sandwich composites under variable hydro-thermal-mechanical load

The high-strength and lightweight sandwich structures have broad application prospect in aerospace, wind turbine generator, traffic and civil engineering. The sandwich structures usually service with severe environment and complicated mechanical load, structure failure and strength prediction are crucial issues. Under time-varying and optional position hydro-thermal–mechanical loading, this paper systematically analyzes strength failure, buckling and delamination of a sandwich beam with carbon fiber-reinforced polymer face sheet and aluminum honeycomb core. Effects of elastic boundary conditions, hydrothermal stress, configuration of honeycomb cell and thickness of face sheet on failure pattern and critical failure loading are evaluated. The theoretical deformation model is verified by performing a bending experiment of cantilever beam. For the honeycomb core with small re-entrant angle and shot horizontal cell wall, the sandwich cantilever beam occurs strength failure of face sheet and delamination is happened in simply supported beam. With increase of re-entrant angle and cell wall length, buckling of horizontal cell wall becomes the primary failure pattern of sandwich beam. With thickness increase of face sheet, the failure pattern switches from face sheet’s strength failure to delamination. The critical load for delamination decreases to a volley value and then increases with thickness of face sheet.

Monitoring surface deformation of the Qinghai–Tibet permafrost region using an improved MT-InSAR method based on spatial–temporal constraints

ABSTRACT Monitoring ongoing permafrost degradation on the Qinghai–Tibet Plateau is challenging because of its underground characteristics. Interferometric synthetic aperture radar (InSAR) technology, which can detect large-scale and high-precision surface deformation, has become an effective tool for indirect permafrost monitoring. Traditional InSAR methods usually solve permafrost deformation independently and on a point-by-point basis with high coherence, while existing permafrost deformation models ignore the interannual variation in deformation. This paper proposes an improved multi-temporal InSAR (MT-InSAR) method based on spatial–temporal constraints for monitoring permafrost deformation. The method establishes a segmented permafrost deformation model considering the interannual variation in deformation over time. The spatial similarity constraint is subsequently introduced to establish the relationship between deformations at neighboring points, improving the results of permafrost monitoring. Both simulated and real experiments confirmed the ability of the proposed method to capture interannual variations in permafrost deformation with higher accuracy and point density. A real experiment with Sentinel-1 data revealed significant interannual variations in surface deformation within the Wudaoliang-Tuotuohe permafrost region from 2018–2021, characterized by decreased linear deformation and slight seasonal deformation changes. Compared with the traditional methods and in-situ data, the deformation accuracy and point density can be improved by approximately 15.6% and 19.4%, respectively.

Recent ice melt above a mantle plume track is accelerating the uplift of Southeast Greenland

Around the periphery of the Greenland ice sheet, satellite-based observations of ground uplift record Earth’s response to past and recent unloading of Greenland’s ice mass. On the southeast coast, near the Kangerlussuaq glacier, rapid uplift exceeding 12 mm/yr cannot be explained using current layered Earth deformation models. Here we find that 3D models with a weakened Earth structure, consistent with the passage of Greenland over the Iceland plume, can explain the rapid uplift of Southeast Greenland. This uplift is dominated by a viscous response that is accelerated by the low viscosities of the hot plume track. Recent mass loss, occurring during the last millennium and especially within the past few decades, drives most of the uplift. Holocene indicators recorded similarly rapid uplift following deglaciation that ended the last ice age. Such rapid uplift, occurring beneath marine terminating glaciers, can affect the future stability of entire ice catchment areas and will become increasingly important in the near future as deglaciation accelerates.

Optimization design of stress relief coalbed methane surface well in a high-gas mine

Coalbed methane drainage through surface wells has become increasingly important in high-gas mines. Surface wells are prone to different types of deformations and failures owing to mining-induced effects. In this paper, a displacement and deformation model was established for the overlying strata. Three forms of deformation and failure of the surface well casing was proposed, namely shearing, stretching, and uneven extrusion. Moreover, the mathematical model functions for the S-type shear deformation, delamination tensile deformation, and non-uniform extrusion of the surface well were established. In the Shanxi Coal Group Yue Cheng Mine, coalbed methane drainage at the surface well was conducted on the mining-affected area to achieve good effects. The YCCD-04 well without a local protective device was deformed and damaged, and the dynamic deformation and failure of the surface well was detected using a well imager. The YCCD-02 surface well with a local protective device showed good mining and gas drainage, which verified the effectiveness of the local protective device; the coalbed methane drainage time of this surface well was 35 months, and the cumulative coalbed methane drainage volume extracted was 1.3 × 107 m3. Simultaneously, the problem of gas control in the working face was solved, thereby ensuring the safety of coal mining and achieving good social as well as economic benefits.

High-cycle constitutive model for traffic loading induced permanent deformation of coarse granular material incorporating particle breakage

Repetitive traffic loads lead to particle rearrangement and breakage in granular trackbeds and roadbeds, resulting in irreversible deformations that hinder normal operations. Current models for cyclic deformation primarily address rearrangement-induced densification but overlook breakage-induced degradation. Particle breakage disrupts inter-particle interlocking and creates finer debris, promoting volumetric contraction and weakening material stiffness. This study introduces a novel cyclic constitutive model for predicting plastic strain in coarse granular materials, emphasizing the role of particle breakage. The model extended from the existing cyclic densification model within the framework named “Shakedown Surface Model,” integrating breakage effects. In this model, shakedown thresholds, associated with material densification, are influenced by both plastic strain and breakage-induced loosening. Parameters for shearing contraction/dilation decrease with breakage, capturing breakage-induced contraction. Additionally, the model accounts for principal stress rotation from moving loads. Implemented via an implicit Euler-backward algorithm and Newton–Raphson iteration, the model was validated against cyclic triaxial and full-scale tests, demonstrating its accuracy in predicting the permanent deformation of granular materials under traffic loads.

MODELING OF HIGH-RATE HARDENING OF A POLYMER COMPOSITE MATERIAL UNDER LOADING ALONG THE REINFORCEMENT DIRECTION

Modeling the high-rate deformation of composite structures is of great interest in the industry. Moreover, some processes such as accidents, explosions and possible impact issues require analysis of composite materials at significantly high deformation rates. The paper considers the possibility of developing a model of deformation of a composite material based on a polymer matrix and carbon fiber taking into account high-rate hardening. A feature of the study is the development of a model that takes into account a wide range of deformation rates from static to several thousand reverse seconds. Thus, tests were carried out with special equipment and samples that allow us to obtain data with such high loading speeds. The model is based on an approach considering the use of damage parameters, the so-called class of models with progressive degradation. The main innovative part of the chosen model is the formalization of the rate of deformation on the material through the damage parameter, that is, the rate of change in damage values is considered. This approach makes it possible to make constitutive relations based only on the damage parameters, which modify the stiffness and strength characteristics of composites, which greatly simplifies the modeling and analysis of material deformation.

CALCULATION OF STATIC DEFORMATION OF AXISYMMETRIC SHELLS OF ROTATION WITH DIFFERENTIAL MODEL

In the paper differential equations of static geometrically nonlinear deformation of axisymmetric shell of rotation are obtained. The resolving functions are projections of vectors in the global coordinate system. The equations allow describing any geometry of meridian (breaks, curvature jumps), large deformations, changing of shell thicknesses during deformation, also cross shears characteristic for thick shells. For the numerical solution, the approach based on the finite difference method is applied, which is realized in the own software package for the calculation of the mechanics of spatial rod systems – DARSYS. The calculations of test problems of the internal pressure inflation of cylindrical, spherical, elliptical, conical shells, as well as a combined conicalcylindrical shell with a meridian break are presented. Graphs of convergence of displacements at the reference points as a function of mesh density and under load variation are given, and deformed meridian configurations are plotted. The solutions obtained in ANSYS by different finite elements of Shell type were used as a reference for comparison. APDL scripts for parametric calculations of the test problems are given in the text of the paper. The proposed approach to the calculation of static deformation of shells of rotation has shown good agreement with finite element modeling in ANSYS (including thick shells) and in the future will be extended to the modeling of dynamic deformation and the possibility of solving coupled problems of interaction with liquid or gas. The given equations of the axisymmetric shell are a special case of the general equations, the development and application of which are beyond the scope of this paper, and the obtained solution results are the first stage of testing the developed complex approach to the calculation of static and dynamic deformation of shells, alternative to finite-element modeling.

Multilevel Model for Describing Martensitic Transformation: Formation of the Polyhedral Martensite Structure

Multilevel models of inelastic deformation that take into account microstructure evolution are promising for technology development for creating functional material structures with optimal performance characteristics. The paper discusses the mathematical formulation of a direct multilevel model to describe the inelastic deformation of a polycrystal representative volume (analogous to a macrosample), taking into account the formation and the martensitic structure evolution during the transformation process. The model considers three structural-scale levels. At the macro level, the boundary value problem is solved, the fields of stresses, strains and other model variables are determined. At mesolevel-I, a homogeneous original austenite grain is considered, in which a martensitic transition occurs due to external influences. For a detailed description of the material response at the grain level, an auxiliary scale level is introduced into consideration, i.e. mesolevel-II. At this level, the geometric features of the martensite packet formation are explicitly studied. An original method has been developed to describe martensite polyhedral structure, the construction of which is carried out when the new phase volume fraction in the austenite grain reaches a critical value. A packet description as union of polyhedra consisting of thin plates allows one to introduce the geometric characteristics of the structural elements into the model, in particular, plates and packet boundaries, linear dimensions, volumes etc., and supplement them with crystallographic orientations. The resulting geometric characteristics of martensite package with subsequent processing is transferred to an individual grain level. This makes it possible to take into account the mechanisms of deformation and hardening that occur during the interaction of phases. The results are presented of polyhedral martensite packet structure formations in AISI 304 steel in numerical experiments on uniaxial deformation at room temperature and strain rate 10–5s–1.

VARIATIONAL-DIFFERENCE SOLUTION OF DEFORMATION AND BUCKLING PROBLEMS OF ELASTOPLASTIC SHELLS OF REVOLUTION WITH ELASTIC FILLER UNDER COMBINED QUASI-STATIC AND DYNAMIC AXISYMMETRIC LOADINGS

The paper suggests a formulation and method for a numerical solution of deformation and buckling of elastoplastic shells of revolution with elastic filler under quasi-static and dynamic loadings. The problem is solved in a two-dimensional plane or generalized axisymmetric formulation with torsion. The governing system of equations is written in a Cartesian or cylindrical coordinate system. Modeling of deformation of an elastic-plastic shell is carried out based on the hypotheses of the theory of shells of the Timoshenko type, taking into account geometric nonlinearities. Kinematic relations are written in velocities and formulated in the metric of the current state. The elastoplastic properties of the shell are described by the flow theory with nonlinear isotropic hardening. Filler modeling is based on continuum mechanics hypotheses. The filler material is assumed to be linearly elastic. The variational equations of motion of structural elements (both shells and filler) are reduced from the three-dimensional equation of the balance of virtual powers of the work of continuum mechanics taking into account the accepted hypotheses of the theory of shells or a flat deformed state or generalized axisymmetric deformation with torsion. The modeling of the contact interaction between the shell and the filler is based on the condition of nonpenetration along the normal and slippage along the tangential. The finite-difference method and an explicit time integration scheme of the cross type are used to solve the defining system of equations. Approbation of the technique was carried out on the problem of buckling of a steel cylindrical shell with an elastic filler under quasi-static and dynamic compression by an external pressure that linearly increases with time. The results of the numerical study are compared with calculations performed using two other approaches developed earlier by the authors. The first approach is based on full-scale modeling of the process of deformation of the shell and filler within the framework of continuum mechanics. In the second approach, a simplified formulation is used, in which the deformation of the shell is modeled according to the hypotheses of the theory of non-sloping shells of the Timoshenko type taking into account geometric nonlinearities, and the filler is modeled according to the Winkler foundation hypothesis. The developed approaches make it possible to model the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the ultimate (critical) loads in a wide range of loading rates taking into account geometric shape imperfections, to study buckling in axisymmetric and non-axisymmetric shapes under dynamic and quasi-static combined loadings in plane and axisymmetric deformations.

COMPUTATIONAL-EXPERIMENTAL METHOD FOR STRESS-STRAIN CURVE CONSTRUCTING UNDER CONDITIONS OF INHOMOGENEOUS STRESS FIELDS

In order to ensure reliability of structures, it is necessary to study equilibrium damage accumulation which initiates softening zones in solids. It is considered appropriate to use postcritical deformation models when conducting strength analysis of structures. However, obtaining complete stress-strain curves in standard tests is difficult due to the strain localization in the form of a neck. At the same time, the use of true stresses taking into account changes in a specimen cross section is incorrect due to the implementation of a complex stress state. In this regard, it is necessary to develop computational and experimental methods for constructing material stress-strain curves under conditions of inhomogeneous stress fields. In this case it seems reasonable to use data on strain fields on the body’s surface, which can be obtained, for example, using non-contact optical video systems. The paper presents the computational-experimental method for constructing a stress-strain curve under conditions of inhomogeneous stress fields. An elastoplastic model of an isotropic material is considered. The initial data of the method are two elastic constants, the yield stress value, the load diagram of a body with a stress concentrator, and the maximum values of strain intensity corresponding to various states. The developed method was tested by a numerical simulation of deforming an hourglass specimen and a plate with a stress concentrator. Stress-strain curves with and without a yield plateau are considered. The results demonstrate a high agreement between the initially specified and reconstructed stress-strain curves. A conclusion is made about the rationality of using the developed method when constructing stress-strain diagrams and necessity for its modernization to describe the postcritical deformation stage.

The Mechanical Properties and Energy Absorption of AuxHex Structures.

Based on a combination of hexagonal honeycomb and re-entrant honeycomb cells, the concept of novel hybrid cell structures was developed. Experimental studies and numerical analyses of the behaviour of the analysed structures under in-plane compression in two compression directions were carried out. Explicit finite element analyses with an explicit integration scheme, incorporating plastic deformation and ductile damage evolution models, were employed to analyse the entire deformation process, including plastic and damage stages. Good agreement was obtained between the results of the numerical analyses and the experimental studies.

Nonlinear deformation model in the analysis of eccentri-cally compressed concrete-filled steel tube elements

This paper discusses the applicability of a nonlinear deformation model for determining the parameters of the stress-strain state of eccentrically compressed concrete-filled steel tube elements. Adjustments to the deformation diagrams of the concrete core and the steel tube were introduced to account for the complex stress state of the materials. The cross-section of the concretefilled steel tube element is considered as a collection of elementary areas. As the criterion for calculating compressive resistance at the ultimate strength stage, it is proposed to use the maximum force calculated based on the compatibility condition of steel and concrete deformations. The advantage of this criterion is that it eliminates the need to normalize the ultimate compressibility of concrete and accounts for the high degree of force redistribution in cross-sections. The method was verified by comparing the calculated and experimentally obtained ultimate forces on a sample of experimental data. The applicability of the nonlinear deformation model based on deformation diagrams, considering the multiaxial stress state of concrete and the steel tube, was confirmed for the analysis of eccentrically compressed concrete-filled steel tube elements.

Guidelines for Nonlinear Finite Element Analysis of Reinforced Concrete Columns with Various Types of Degradation Subjected to Seismic Loading

Concrete columns are considered critical elements with respect to the stability of buildings during earthquakes. To improve the accuracy of column damage and collapse risk estimates using numerical simulations, it is important to develop a methodology to quantify the effect of displacement history on column force–deformation modeling parameters. Addressing this knowledge gap systematically and comprehensively through experimentation is difficult due to the prohibitive cost. The primary objective of this study was to develop guidelines to simulate the lateral cyclic behavior and axial collapse of concrete columns with different modes of failure using continuum finite element (FE) models, such that wider parametric studies can be conducted numerically to improve the accuracy of assessment methodologies for critical columns. This study expands on existing FEM research by addressing the complex behavior of columns that experience multiple failure modes, including axial collapse following flexure–shear, shear, and flexure degradation, a topic which has been underexplored in previous works. Nonlinear FE models were constructed and calibrated to experimental tests for 21 columns that sustained flexure, flexure–shear, and shear failures, followed by axial failure, when subjected to cyclic and monotonic lateral displacement protocols. The selected columns represented a range of axial loads, shear stresses, transverse reinforcement ratios, longitudinal reinforcement ratios, and shear span-to-depth ratios. Recommendations on optimal material model parameters obtained from a parametric study are presented. Metrics used for optimization include crack widths, damage in concrete and reinforcement, drift at initiation of axial and lateral strength degradation, and peak lateral strength. The capacities of shear–critical columns calculated with the optimized numerical models are compared with experimental results and standard equations from ASCE 41-17 and ACI 318-19. The optimized finite element models were found to reliably predict peak strength and deformation at the onset of both lateral and axial strength failure, independent of the mode of lateral strength degradation. Also, current standard shear capacity provisions were found to be conservative in most cases, while the FE models estimated shear strength with greater accuracy.

On the size‐dependent vibrations of doubly curved porous shear deformable FGM microshells

AbstractThis paper aims to analyse the free vibrations of doubly curved imperfect shear deformable functionally graded material microshells using a five‐parameter shear deformable model. Porosity is modeled via the modified power‐law rule by a logarithmic‐uneven variation along the thickness. Coupled axial, transverse, and rotational motion equations for general doubly curved microsystems are obtained by a virtual work/energy of Hamilton's principle using a modified first‐order shear deformable theory including small size dependence. The modal decomposition method is then used to obtain a solution for different geometries of microshells: spherical, elliptical, hyperbolic, and cylindrical. A detailed study on the influence of material gradation and porosity, small‐length scale coefficient, and geometrical parameters on the frequency characteristics of the microsystem is conducted for different shell geometries.

Blasting effects of cross‐fault deep‐buried excavation on adjacent existing tunnel stability

AbstractThe vibration caused by blasting excavation of rock mass frequently poses a threat to the stability of adjacent tunnels. Previous research is limited by the simplification of a rock mass as a homogeneous elastic medium, without considering the wave attenuation caused by viscoelasticity and wave separation induced by rock discontinuities, as well as plane waves while neglecting geometric attenuation of near‐field nonplane blast waves. This paper establishes a theoretical model of cylindrical P‐wave propagation across a fault to an adjacent existing tunnel. Based on the time‐domain recursive method, vibration equations and peak particle velocity on the adjacent existing tunnel wall caused by a cylindrical wave passing through a fault are derived. The rock mass and fault are assumed to satisfy Kelvin viscoelastic bodies, and contact interfaces between fault and rock mass follow a nonlinear hyperbolic deformation model in the normal direction and a linear model in the tangential direction. The results show that tunnel vibration caused by the blast cylindrical P‐wave is primarily induced by transmitted P‐waves. With the increase of the fault dip angle, vibration on the upper side of the adjacent existing tunnel gradually decreases, while vibration on the lower side increases. The closer the vibration to the upper and lower sides, the stronger the shear effect on the tunnel wall, and the closer the vibration to the middle, the stronger the pressure effect on the tunnel wall. Larger fault thickness and higher initial blast wave frequency result in weaker vibration of the adjacent tunnel. The deeper the burial depth, the stronger the vibration of the adjacent tunnel wall. Findings of this study provide insight into the dynamic response of rock construction and safety evaluation in engineering service.