Deformation Analysis Method Research Articles

An improved 3D DDA method considering the unloading effect of tunnel excavation and its application

Tunnel excavation unloading is the primary factor in disasters such as collapse and large deformations of surrounding rock. Therefore, it is a key issue to study the deformation mechanism of the surrounding rock in the process of tunnel excavation unloading. However, the original three-dimensional discontinuous deformation analysis method (3D DDA) can only simulate the displacement of the surrounding rock after the completion of tunnel excavation, which is not suitable for studying the mechanism of the surrounding rock’s deformation caused by tunnel excavation. Therefore, this paper proposes a virtual block removal algorithm that moves the blocks out of the calculation area while ensuring the consistency of the array and develops an improved 3D DDA method (3D DDA_exc) by embedding the algorithm into the original 3D DDA program, which is suitable for the simulation of tunnel excavation. In addition, based on the free fall models of static and sliding blocks, we compare the results of the 3D DDA_exc simulation with theoretical calculation results, which are basically the same. Then, both the 3D DDA_exc method and the discrete element method (DEM) are used to simulate the excavation of the tunnel in a blocky rock mass, and the rock displacements around the tunnel hole are basically the same, which further illustrates the accuracy of the 3D DDA_exc method in simulating tunnel excavation. Finally, taking the Huangjiazhuang Tunnel of the Rizhao-Lankao high-speed railway as a case study, we simulated block collapse during the excavation process of the tunnel using the centre diaphragm method (CD method). Compared with the result of the 3D DDA method without the process of tunnel excavation, block collapse can be avoided if the dangerous blocks are supported and reinforced during the excavation of part ① and part ② of the tunnel, which was of guiding significance to the safe construction of the tunnel.

Analysis method of the water inrush and collapse in jointed rock mass tunnels: A case study

Water inrush disaster occurs easily when the tunnel is close to the water rich fault fracture zone. To clarify the disaster evolution process and the critical thickness of the water-resistant rock mass is the key problem of the prevention and control of water inrush disaster in jointed rock tunnel. However, the water inrush disaster in jointed rock tunnels involves solid-fluid interaction, and the conventional single-phase numerical method is difficult to realize the real simulation of the disaster. To solve this problem, we gave full play to the advantages of the discontinuous deformation analysis method (DDA) in simulating solid motion and the smoothed particle hydrodynamics method (SPH) in simulating fluid motion, and the two-dimensional DDA-SPH (2D DDA-SPH) method was used to simulation the solid-fluid interaction in the water inrush disasters. Firstly, the 2D DDA-SPH method was used to replicate the solitary wave experiment, named Scott Russell's wave generator, and the result of the simulation was almost the same with experiment, which verified the accuracy of 2D DDA-SPH method in simulating solid-fluid interaction dynamic problems. Secondly, taking the Yonglian Tunnel as the research object, we simulated the water inrush disaster in the F2 fault of Yonglian Tunnel under the condition of different thickness of water-resistant rock mass. Based on the results of the simulation, the critical thickness of water-resistant rock mass was determined, which was about 5m. Lastly, we analyzed the process of the water inrush disasters based on the movement state of the fluid near the water-resistant rock mass. And we divided the process of the water inrush disasters in the jointed rock mass into three stage, which were mutation stage, cataclysmic stage and stable stage, which provided a theoretical basis for the prevention and control of water inrush in jointed rock tunnel.

A new SDDA-based numerical approach for simulating rock cracking induced by temperature stresses

Temperature-induced rock failure occurs in geothermal exploitation, nuclear disposal, and other underground engineering scenarios. In this paper, the conventional spherical discontinuous deformation analysis (SDDA) method is extended to simulate the temperature-induced rock failure problems. Firstly, an improved bonded sphere algorithm is proposed to precisely modeling rock failure behavior in the SDDA framework. Secondly, a heat conduction model based on the thermal conductivity pipe between spheres is proposed and further implemented in the SDDA program through an explicit thermal–mechanical coupling procedure. Thirdly, three typical examples are selected to verify the accuracy of the heat conduction model by comparing the temperature evolution between numerical and analytical results. Finally, the improved SDDA model was applied to analyze several experimental cases involving thermal cracking, including lab-scale experiments and field-scale examples. The simulation results show that the improved SDDA approach is effective for the simulation of the temperature-induced crack propagation process.

A novel pre-processing modelling method for the finite element analysis of the thermal deformation of large structures in the erection stage

The manufacturing process of ships and offshore structures comprises several stages, which include plate cutting, sub-assembly, block assembly, pre-erection, and erection. Accuracy and quality control management are crucial issues in the manufacturing process. Welding-induced distortion and deformation complicate the assembly stage in shipyards. Through conventional finite element (FE) analysis, the manufacturing process can be predicted and controlled up to the sub-assembly stage; however, applying the FE method to the stages between block assembly and erection is difficult. In this study, a new FE analysis method for predicting welding-induced thermal deformation of large blocks, which was difficult to predict with traditional methods, was proposed. In addition, based on this result, we developed a novel pre-processing modelling system that can automatically extract the erection weld lines and automatically divide blocks, which are necessary for the thermal deformation analysis of large blocks. Validation experiments confirmed the applicability of the proposed method to the shaft alignment of a container ship and LNG carrier, with industrial accuracy and quality control in the manufacturing process. Compared with existing methods, the proposed method increases the accuracy of the analysis and reduces the total pre-processing time.

TLS and FEM combined methods for deformation analysis of tunnel structures

With the increasing of tunnel mileage, one of the most vital problems of broad-scale structures is the intelligent identification and location of structural defects, which require massive data storage capacity and high data processing efficiency. The full-field point cloud data collected by terrestrial laser scanning (TLS) can be extracted to construct three-dimensional measured models more accurately, therefore, the fusion of TLS and the finite element method (FEM) is particularly beneficial to the deformation analysis of tunnel structures. This paper combines numerical simulation and full-field measurement to interactively verify the reliability of deformation analysis based on FEM simulation and point cloud processing. The innovation of this paper is that a three-dimensional FEM is validated through the measured point cloud data of the tunnel structure. The result of this study indicated that FEM simulation and the structural health monitoring analysis are consistent.

Experimental study on the fracture closure law of fault-controlled reservoir

This paper presents the fracture closure law of fault-controlled reservoir under different pressures by means of a combination of laboratory tests and numerical calculation. Fractures are an important seepage channel for fault-controlled reservoirs. With the improvement of the recovery degree of fault-controlled oil and gas reservoirs, the formation pressure decreases, and the effective rock stress increases, which leads to the deformation and even closure of fractures. The dynamic opening and closure of fractures restricts the formation permeability and affects the production of oil and gas wells. In this paper, experimental methods are used to study the fracture closure law. First collect carbonate rock samples, prepare samples through Brazilian splitting experiment and linear cutting method. We establish fracture deformation analysis method based on CT scan gray image. Through pressurization and depressurization test, the closure law of fractures under different filling conditions and fracture extension length was studied. The research results show that as the confining pressure increases, the fracture width and permeability gradually decrease. The stronger the ductility of the filler is, the more obvious the fracture closure is under pressure, and the greater the permeability reduction is. For the same quartz filled fractures, fracture closure laws are different under different filling methods. For fracture support effect, the single layer fine sand > thick layer fine sand > medium-fine mixture sand. In general, the greater the fracture extension length, the higher the permeability, but the increase of permeability is different. The findings of this study can help for a better understanding of reasons for large differences in single well productivity and contribute to rational productivity optimization of fault-controlled reservoirs.

A complex variable EFG method for hyperelastic large deformation analysis under non-conservative loads

The finite element method is extremely popular in almost all fields of engineering and scientific research due to its powerful and accessible industrial software for computational modelling. However, alternatives including the meshless methods, have received increasing attention on the large deformation problems of hyperelastic materials that need to avoid mesh distortion. In this paper, based on the complex variable moving least-squares approximation, the complex variable element-free Galerkin (CVEFG) method for the large deformation problem of hyperelastic materials under non-conservative loads is established. In the present method, the Newton-Raphson method is used for solving the nonlinear equations. The algorithm for hyperelastic large deformation problems under non-conservative loads are established. Three numerical examples are used to verify the effectiveness of the CVEFG method in this paper. Numerical results show that the solution obtained using the CVEFG method is closer to that obtained by ABAQUS and is more efficient than the element-free Galerkin method.

A discontinuous deformation analysis of the internal shear restraint mechanism in the sliding instability process of compound slopes

Because of the geometric turning characteristics of its basal sliding surface, the compound slope will undergo internal shear deformation during the sliding process. However, few investigations have been conducted into the accurate location and formation process of the internal shear surface, as well as the internal shear restraint mechanism and its influence on slope stability. Therefore, relevant research was carried out based on the Vajont landslide, which is a typical representative of the compound slope. Firstly, the mechanical equilibrium on the internal shear fracture surface is further taken into account in the Rigid Limit Equilibrium Method (RLEM), and the accurate location of the shear surface was obtained by solving the equilibrium equations on the three sliding surfaces simultaneously. Additionally, a sensitivity analysis of the landslide's mechanical characteristics was conducted. Then, using the Discontinuous Deformation Analysis (DDA) method with hydraulic coupling, the entire instability process of the Vajont landslide generated by reservoir impoundment is simulated, as well as the formation process of the shear surface. The results reveal that the locations of the shear surface derived by the two methods agree well. Meanwhile, an objective shear restraint mechanism exists inside the compound slope, which contributes to its overall stability.

Parametric research on the time step and spring stiffness in three‐dimensional discontinuous deformation analysis method

AbstractThree‐dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.

Research on the Applicability of DInSAR, Stacking-InSAR and SBAS-InSAR for Mining Region Subsidence Detection in the Datong Coalfield

Intensive and large-scale underground coal mining has caused geological disasters such as local ground subsidence, cracks and collapse in the Datong coalfield, China, inducing serious threats to local residents. Interferometric synthetic aperture radar (InSAR) has the capability of surface deformation detection with high precision in vast mountainous areas. DInSAR, stacking-InSAR and SBAS-InSAR are commonly used InSAR-related deformation analysis methods. They can provide effective support for mine ecological security monitoring and prevent disasters. We use the three methods to conduct the deformation observation experiments in the Datong coalfield. Sentinel-1A data from November 2020 to October 2021 are used. As a result, a total of 256 deformations in the Datong coalfield were successfully detected by the three methods, of which 218 are mining deformations, accounting for 85% of the total deformations. By comparing the results of the three methods, we found that DInSAR, stacking-InSAR, and SBAS-InSAR detected 130, 256, and 226 deformations in the Datong coalfield, respectively, while the deformations caused by coal mining were 128, 218, and 190. DInSAR results with long spatiotemporal baselines are seriously incoherent. SBAS-InSAR results of displacement rate are more precise than stacking-InSAR, and the mean standard deviation is 1.0 mm/a. However, for areas with lush vegetation or low coherence, SBAS-InSAR has poor performance. The detection deformation area results of DInSAR and SBAS-InSAR are subsets of stacking-InSAR. The displacement rates obtained by stacking-InSAR and SBAS-InSAR are consistent; the mean difference in the displacement rate between the two methods is 2.7 mm/a, and the standard deviation is 5.1 mm/a. The mining deformation locations and their shapes in the study area can be identified with high efficiency and power by stacking-InSAR. Therefore, with a comprehensive understanding of the advantages and limitations of the three methods, stacking-InSAR can be an effective and fast method to identify the level, location and range of mining deformation in lush mountainous areas.

Prediction of In-plane Stiffness for the Cold-formed Steel Frame of the Wall Panel Structure

The purpose of this research was to study the lateral deformation behavior of cold-formed steel wall panel structures using experimental tests, finite element analysis and analytical methods to study the lateral stiffness of these structures. The wall panel structures were tested by full-scale experiments the experimental results of which were verified by a 3D-finite element model. The verification results showed a good correlation between the experimental tests and a finite element model. The single-column spring model was proposed for an elastic lateral stiffness analysis of the cold-formed steel wall panel structures that were formed by combinations of a guide cantilever beam and springs connection. The spring constants were defined by using the stiffness of the stub-chord connection and the bending stiffness of the chord. The experiments tests and finite element analysis were used to verify this single-column spring model. The comparison results showed good agreement between the analytical prediction, finite element analysis and experimental data in the case of the primary type of cold-formed wall structure. The proposed procedure was an efficient method for elastic lateral deformation analysis of cold-formed wall panel structures which can be used for such configurations.

A hybrid method for lattice image reconstruction and deformation analysis

Geometric phase analysis (GPA) is a powerful tool to investigate the deformation in nanoscale measurement, especially in dealing with high-resolution transmission electron microscopy images. The traditional GPA method using the fast Fourier transform is built on the relationship between the displacement and the phase difference. In this paper, a nano-grid method based on real-space lattice image processing was firstly proposed to enable the measurement of nanoscale interface flatness, and the thickness of different components. Then, a hybrid method for lattice image reconstruction and deformation analysis was developed. The hybrid method enables simultaneous real-space and frequency-domain processing, thus, compensating for the shortcomings of the GPA method when measuring samples with large deformations or containing cracks while retaining its measurement accuracy.

Stability analysis of Xiluodu Hydropower Station right bank slope based on discontinuous deformation analysis method

PurposeThe purpose of this study is to investigate the deformation characteristics and failure modes of the right bank slope of Xiluodu Hydropower Station after excavation.Design/methodology/approachMicro-seismic monitoring technology is applied to obtain the microfracture information and study the internal damage evolution law of the slope rock mass. A numerical model for discontinuous deformation analysis (DDA) is established to analyse the deformation characteristics and failure mode of the slope. Micro-seismic monitoring and DDA can verify and supplement each other's results in the investigation of slope failure.FindingsThe results show that the slope has a downhill displacement along the weathered zone under natural conditions; the maximum resultant displacement at the monitoring point is 380 mm. The micro-seismic events are concentrated in an area located 30–100 m horizontally away from the slope surface and at an elevation of 390–470 m. The distribution of these micro-seismic events is consistent with the location of the unloading and weathered zones; it is the same as the DDA simulation result.Originality/valueThe study is anticipated to be used as reference for the stability analysis of rock slopes. By combining the continuous (micro-seismic monitoring technology) and discontinuous (DDA) methods, the entire process starting from the gradual accumulation of internal rock micro-damage to the macroscopic discontinuous deformation and failure of the slope can be investigated.

A continuous-discontinuous deformation analysis method for simulating the progressive failure process of riverbanks

River scouring is the primary cause of impulsive riverbank failure. Its direct effect is to cause catastrophic changes in the structure of the riverbank slope, which then leads to riverbank collapse. However, its internal evolution mechanism is unclear. To solve this problem, a continuous-discontinuous deformation analysis method that can reveal the evolution mechanism has been developed based on the Discontinuous Deformation Analysis (DDA) method. It discretizes the soil into Voronoi-shaped sub-blocks, forces the displacement coordination of the continuous medium through the defined bar element between the sub-blocks, and simulates the evolution from continuum to discontinuum through the bar element failure. At the same time, the open-close iteration algorithm is still used to deal with the contact between the real block boundaries and there is no need to judge the contact between sub-blocks. Then, for the first time, a generalized model of riverbank collapse caused by flow erosion is built, the entire failure process is simulated, and the effects of different soil strengths and slope ratios on the failure mode are discussed. The results indicate that it is insufficient to explain the mechanism of riverbank collapse only by using the concept of circular slip failure of a traditional soil slope.

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering.

A compatible mixed finite element method for large deformation analysis of two‐dimensional compressible solids in spatial configuration

AbstractIn this article, a new mixed finite element formulation is presented for the analysis of two‐dimensional compressible solids in finite strain regime. A three‐field Hu–Washizu functional, with displacement, displacement gradient and stress tensor considered as independent fields, is utilized to develop the formulation in spatial configuration. Certain constraints are imposed on displacement gradient and stress tensor so that they satisfy the required continuity conditions across the boundary of elements. From theoretical standpoint, simplex elements are best suited for the application of continuity constraints. The techniques that are proposed to implement the constraints facilitate their automatic imposition and, hence, they can be regarded as an important feature of the work. Since the exterior calculus provides the basis for the developments presented herein, the relevant topics are discussed within the context of the work. Various technical aspects of the formulation are described in detail. These aspects help to illuminate the mathematical formulation that might seem vague in the first place and, more importantly, they help to provide an efficient implementation for ensuing developments. The performance of the mixed finite element method is studied through benchmark numerical examples and it is compared with other similar elements. It is shown that the element has excellent convergence properties and it is numerically stable, especially for problems where classical first order elements demonstrate stiff or unstable behavior.

Impact of Ambiguity of Physical Properties of Three-Dimensional Crustal Structure Model on Coseismic Slip and Interseismic Slip Deficit in the Nankai Trough Region

Since huge earthquakes are expected along plate subduction zones such as the Japan Trench and Nankai Trough, the estimation of coseismic slip and interseismic slip deficit is essential for immediate response and preliminary measures to reduce damage. Recently, analysis considering the complex topography and underground structure of the plate subduction zone has been performed for improving the estimation performance. However, the three-dimensional (3D) crustal structural model needs to be improved continuously. In this paper, we obtained Green’s functions for 3D crustal structural models with ambiguity by 3D crustal deformation analysis, and the coseismic slip and interseismic slip deficit were estimated. Here we enabled the calculation of many Green’s functions with different physical properties of the 3D crustal structure by utilizing a GPU-based 3D crustal deformation analysis method that significantly reduces the analysis cost. The physical properties on the upper plate’s side, which are located above the plate boundary fault, were changed. We found no significant difference in the estimation performance, except for the upper crust, which most of the fault slip area is in contact with, in the case of coseismic slip estimation. In contrast, the coseismic slip estimation when the properties of the upper crust was changed had a significant error, and a negative slip was estimated at the deep part of the plate boundary where no slip was originally given.

Extended DDA with rotation remedies and cohesive crack model for simulation of the dynamic seismic landslide

The failure of earthquake-induced landslides generally involves four stages: tensile cracking, breaking of the substrate, shearing failure, and deposition of the sliding mass, which poses a challenge for high-accuracy simulation of such landslides. To resolve this issue, this paper presents an integrated algorithm by introducing a bilinear cohesive contact model into the proposed discontinuous deformation analysis (DDA) method. In the proposed DDA, the displacement mode of the original DDA is replaced by the multiplicative decomposition of the displacement to improve the distortion and false volume expansion of blocks with large rotations. The timely introduction of the bilinear cohesive contact model can better describe the peak-post softening behavior of rocks consisting of blocks. Finally, the extended algorithm is formulated and implemented in the source program of the DDA and then verified through typical examples. The results indicate that the proposed method can facilitate the generation of tensile cracks and effectively eliminate distortion and false volume expansion of blocks, demonstrating consistent results with the test or field investigation.

Mixed Method for Isogeometric Analysis of Coupled Flow and Deformation in Poroelastic Media

Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi’s problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.

Effect of fillers on compression loading performance of modified re-entrant honeycomb auxetic sandwich structures

The auxetic sandwich panels for structures have been designed to provide impact protection. The aim of this work is to modify an auxetic (re-entrant) honeycomb cell to reduce the stress concentrations within the cell structure, and further enhancement of this design. The auxetic structure was filled to achieve a greater energy absorbance and enhance safety applications. Analytical and elastic three-dimensional finite element approaches were used to investigate the structural strength performance. The basic model (i.e. modified re-entrant strut cell design) consisted of the honeycomb auxetic polypropylene (PP) structure sandwiched between two steel plates (known as safety panels) which were placed under static compression loading. The cell geometry and size were then modified to reduce the stress concentration zones. The structure cells were filled with silly putty and polyvinyl chloride (PVC) foam. The effect of the filling the cells on the stress concentration and energy absorbance were analysed using elastic stress and deformation analysis methods. During the stress path analysis, it was found that an increase in Young’s modulus of the filling was directly proportional to a decrease in internal stresses. It was concluded that while filling the basic model with soft materials reduced the stress concentration, but it led to a reduction in the energy absorbance capability. Further on, the lower stress produced by the enhanced could be useful to prevent significant penetration of the protective panel. Compared to similar structures of steel, auxetic foam panels have the advantage of having only a fraction of the weight and being corrosion resistant at the same time as keeping impact strength. Graphical abstract [Formula: see text]