Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

A thermodynamics-based three-scale constitutive model for partially saturated granular materials

A three-scale constitutive model for unsaturated granular materials based on thermodynamic theory is presented.The three-scale yield locus,derived from the explicit yield criterion for solid matrix,is developed from a series of discrete interparticle contact planes.The three-scale yield locus is sensitive to porosity changes;therefore,it is reinterpreted as a corresponding constitutive model without phenomenological parameters.Furthermore,a water retention curve is proposed based on special pore morphology and experimental observations.The features of the partially saturated granular materials are well captured by the model.Under wetting and isotropic compression,volumetric compaction occurs,and the degree of saturation increases.Moreover,the higher the matric suction,the greater the strength,and the smaller the volumetric compaction.Compared with the phenomenological Barcelona basic model,the proposed three-scale constitutive model has fewer parameters;virtually all parameters have clear physical meanings.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Ground settlement and tunnel response due to twin-curved shield tunnelling in soft ground with small clear distance

Twin curved tunnels are often encountered in shield tunnelling,where significant complexities in densely exploited underground space are observed.In this study,the ground settlement and tunnel deformation due to twin-curved shield tunnelling in soft ground were investigated using numerical simulation and field monitoring.Different curvature radii of twin curved tunnels and subsequent effects of tunnel construction were considered to reveal the tunnelling effect on ground surface settlement and tunnel deformation.The results show that the settlement trough yields one offset towards inside of curved shield tunnelling.The location of settlement trough and maximum settlement were affected by curvature radius but except for the shape and width of settlement trough.Adjacent parallel twin-curved shield tunnelling could increase the offset of existing settlement trough and maximum settlement.Then,an empirical prediction of surface settlement trough due to twin-curved shield tunnelling with same tunnel diameters in soft clay was proposed,which was applicable to curvature radius less than 800 m.Finally,a minimum radius of 600 m of curvature tunnel was proposed in terms of allowable convergence deformation of tunnel.The result could provide guidance on safety evaluation for twin curved shield tunnelling construction.

Thornthwaite moisture index and depth of suction change under current and future climate‒An Australian study

Climate change is one of the major global challenges and it can have a significant influence on the behaviour and resilience of geotechnical structures.The changes in moisture content in soil lead to effective stress changes and can be accompanied by significant volume changes in reactive/expansive soils.The volume change leads to ground movement and can exert additional stresses on structures founded on or within a shallow depth of such soils.Climate change is likely to amplify the ground movement potential and the associated problems are likely to worsen.The effect of atmospheric boundary interaction on soil behaviour has often been correlated to Thornthwaite moisture index(TMI).In this study,the long-term weather data and anticipated future projections for various emission scenarios were used to generate a series of TMI maps for Australia.The changes in TMI were then correlated to the depth of suction change(H s),an important input in ground movement calculation.Under all climate scenarios considered,reductions in TMI and increases in H s values were observed.A hypothetical design scenario of a footing on expansive soil under current and future climate is discussed.It is observed that a design that might be considered adequate under the current climate scenario,may fail under future scenarios and accommodations should be made in the design for such events.

复杂环境下基于CPTU的深基坑土压力模型与工程应用

土压力计算是深基坑围护结构设计的重要组成部分,但现有土压力模型难以合理地考虑开挖扰动诱发土体工程性质演化影响。孔压静力触探(piezocone penetration test,CPTU)能够有效避免取样扰动,并快速提供连续的原位土测试参数(锥尖阻力、侧壁摩阻力、孔隙水压力)。基于CPTU原位测试和位移相关土压力模型,结合库仑土压力框架,综合考虑开挖诱发土体工程性质演化、邻近地下结构(受限空间)、土拱效应、地基土强度参数和土-结构界面摩擦角等影响因素,构建了复杂环境下深基坑土压力统一计算模型(主动状态至被动状态)。分别通过与室内1g模型试验和离心机试验结果对比,验证了所构建模型的准确性与合理性。进一步将所构建模型应用至太湖冲湖积相软土地区某邻近地铁车站的深基坑工程。现场分别在基坑开挖前后对围护结构的两侧(基坑内外)开展了CPTU原位测试,并监测得到了围护结构侧向变形与土压力变化。原位测试解译结果表明,基坑开挖显著地改变了周边土体状态参数,但对于有效内摩擦角的影响甚微。与现场所测土压力对比指出,基于CPTU的土压力模型能够较好地反映复杂环境下基坑土压力变化,成功实现了工程应用。

Agricultural intensity for sustainable regional development:A case study in peri-urban areas of Karawang Regency,Indonesia

Peri-urban areas are playing an increasingly crucial role in the agricultural development and intensification in Indonesia.Peri-urban agriculture is highly vulnerable to change compared with urban and rural agriculture,due to its location in transitional areas.Indicators of peri-urban agricultural intensity can help guide regional development.In this study,we assessed the sustainability of peri-urban areas based on agricultural intensity in Karawang Regency,Indonesia.We developed a village-based index to assess the region’s agricultural intensity by rescaling the village agriculture index(VAI)and combining the local sustainability index(LSI)with factor analysis.Since the unit of analysis is the village,we modified the LSI to the village sustainability index(VSI).In addition,we also developed a logical matrix analysis to determine the level of agricultural sustainability(LoAS)of each village.The combined results of the three indices(VAI,VSI,and LoAS)generated information about agricultural sustainability.The results indicated that peri-urban villages with high agricultural intensity tended to exhibit low levels of social welfare,economic development,and disaster risk.Moreover,high agricultural intensity did not necessarily ensure the prosperity of the people.Instead,there was the economic disparity among the villages in the study area.Encouraging diversity of agricultural intensity seems to be more critical than promoting agricultural intensity itself.Overall,this study highlights the distinctive characteristics and dynamic of peri-urban areas.New approaches,variables,and information regarding the combination of agricultural intensity and sustainability need to be developed as valuable tools for regional planning.

Effect of fracture fluid flowback on shale microfractures using CT scanning

The field data of shale fracturing demonstrate that the flowback performance of fracturing fluid is different from that of conventional reservoirs,where the flowback rate of shale fracturing fluid is lower than that of conventional reservoirs.At the early stage of flowback,there is no single-phase flow of the liquid phase in shale,but rather a gas-water two-phase flow,such that the single-phase flow model for tight oil and gas reservoirs is not applicable.In this study,pores and microfractures are extracted based on the experimental results of computed tomography(CT)scanning,and a spatial model of microfractures is established.Then,the influence of rough microfracture surfaces on the flow is corrected using the modified cubic law,which was modified by introducing the average deviation of the microfracture height as a roughness factor to consider the influence of microfracture surface roughness.The flow in the fracture network is simulated using the modified cubic law and the lattice Boltzmann method(LBM).The results obtained demonstrate that most of the fracturing fluid is retained in the shale microfractures,which explains the low fracturing fluid flowback rate in shale hydraulic fracturing.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Impact of effective stress on permeability for carbonate fractured-vuggy rocks

To gain insight into the flow mechanisms and stress sensitivity for fractured-vuggy reservoirs,several core models with different structural characteristics were designed and fabricated to investigate the impact of effective stress on permeability for carbonate fractured-vuggy rocks(CFVR).It shows that the permeability performance curves under different pore and confining pressures(i.e.altered stress conditions)for the fractured core models and the vuggy core models have similar change patterns.The ranges of permeability variation are significantly wider at high pore pressures,indicating that permeability reduction is the most significant during the early stage of development for fractured-vuggy reservoirs.Since each obtained effective stress coefficient for permeability(ESCP)varies with the changes in confining pressure and pore pressure,the effective stresses for permeability of four representative CFVR show obvious nonlinear characteristics,and the variation ranges of ESCP are all between 0 and 1.Meanwhile,a comprehensive ESCP mathematical model considering triple media,including matrix pores,fractures,and dissolved vugs,was proposed.It is proved theoretically that the ESCP of CFVR generally varies between 0 and 1.Additionally,the regression results showed that the power model ranked highest among the four empirical models mainly applied in stress sensitivity characterization,followed by the logarithmic model,exponential model,and binomial model.The concept of“permeability decline rate”was introduced to better evaluate the stress sensitivity performance for CFVR,in which the one-fracture rock is the strongest,followed by the fracture-vug rock and two-horizontalfracture rock;the through-hole rock is the weakest.In general,this study provides a theoretical basis to guide the design of development and adjustment programs for carbonate fractured-vuggy reservoirs.

Effects of thawing-induced softening on fracture behaviors of frozen rock

Due to the presence of ice and unfrozen water in pores of frozen rock,the rock fracture behaviors are susceptible to temperature.In this study,the potential thawing-induced softening effects on the fracture behaviors of frozen rock is evaluated by testing the tension fracture toughness(KIC)of frozen rock at different temperatures(i.e.-20℃,-15℃,-12℃,-10℃,-8℃,-6℃,-4℃,-2℃,and 0℃).Acoustic emission(AE)and digital image correlation(DIC)methods are utilized to analyze the microcrack propagation during fracturing.The melting of pore ice is measured using nuclear magnetic resonance(NMR)method.The results indicate that:(1)The KIC of frozen rock decreases moderately between-20℃ and-4℃,and rapidly between-4℃ and 0℃.(2)At-20℃ to-4℃,the fracturing process,deduced from the DIC results at the notch tip,exhibits three stages:elastic deformation,microcrack propagation and microcrack coalescence.However,at-4℃e0℃,only the latter two stages are observed.(3)At-4℃e0℃,the AE activities during fracturing are less than that at-20℃ to-4℃,while more small events are reported.(4)The NMR results demonstrate a reverse variation trend in pore ice content with increasing temperature,that is,a moderate decrease is followed by a sharp decrease and-4℃ is exactly the critical temperature.Next,we interpret the thawing-induced softening effect by linking the evolution in microscopic structure of frozen rock with its macroscopic fracture behaviors as follow:from-20℃ to-4℃,the thickening of the unfrozen water film diminishes the cementation strength between ice and rock skeleton,leading to the decrease in fracture parameters.From-4℃ to 0℃,the cementation effect of ice almost vanishes,and the filling effect of pore ice is reduced significantly,which facilitates microcrack propagation and thus the easier fracture of frozen rocks.

Seismic response of a mid-story isolated structure considering SSI in mountainous areas under long-period earthquakes

At present,there is not much research on mid-story isolated structures in mountainous areas.In this study,a model of a mid-story isolated structure considering soil-structure interaction(SSI)in mountainous areas is established along with a model that does not consider SSI.Eight long-period earthquake waves and two ordinary earthquake waves are selected as inputs for the dynamic time history analysis of the structure.The results show that the seismic response of a mid-story isolated structure considering SSI in mountainous areas can be amplified when compared with a structure that does not consider SSI.The structure response under long-period earthquakes is larger than that of ordinary earthquakes.The structure response under far-field harmonic-like earthquakes is larger than that of near-fault pulse-type earthquakes.The structure response under near-fault pulse-type earthquakes is larger than that of far-field non-harmonic earthquakes.When subjected to long-period earthquakes,the displacement of the isolated bearings exceeded the limit value,which led to instability and overturning of the structure.The structure with dampers in the isolated story could adequately control the nonlinear response of the structure,effectively reduce the displacement of the isolated bearings,and provide a convenient,efficient and economic method not only for new construction but also to retrofit existing structures.

Advanced Sheet Pile Curtain Design: Case Study of Cotonou East Corniche

This paper delves into the critical aspects of sheet pile walls in civil engineering, highlighting their versatility in soil protection, retention, and waterproofing, all while emphasizing sustainability and efficient construction practices. The paper explores two fundamental approaches to sheet pile design: limit equilibrium methods and numerical techniques, with a particular focus on finite element analysis. Utilizing the robust PLAXIS 2016 calculation code based on the finite element method and employing a simplified elastoplastic model (Mohr-Coulomb), this study meticulously models the interaction between sheet pile walls and surrounding soil. The research offers valuable insights into settlement and deformation patterns that adjacent buildings may experience during various construction phases. The central objective of this paper is to present the study’s findings and recommend potential mitigation measures for settlement effects on nearby structures. By unraveling the intricate interplay between sheet pile wall construction and neighboring buildings, the paper equips engineers and practitioners to make informed decisions that ensure the safety and integrity of the built environment. In the context of the Cotonou East Corniche development, the study addresses the limitations of existing software, such as RIDO, in predicting settlements and deformations affecting nearby buildings due to the substantial load supported by sheet pile walls. This information gap necessitates a comprehensive study to assess potential impacts on adjacent structures and propose suitable mitigation measures. The research underscores the intricate dynamics between sheet pile wall construction and its influence on the local environment. It emphasizes the critical importance of proactive engineering and vigilant monitoring in managing and mitigating potential hazards to nearby buildings. To mitigate these risks, the paper recommends measures such as deep foundations, ground improvement techniques, and retrofitting. The findings presented in this study contribute significantly to the field of civil engineering and offer invaluable insights into the multifaceted dynamics of construction-induced settlement. The study underscores the importance of continuous evaluation and coordination between construction teams and building owners to effectively manage the impacts of sheet pile wall construction on adjacent structures.

Physics-based seismic analysis of ancient wood structure:fault-to-structure simulation

Based on the domain reduction method,this study employs an SEM-FEM hybrid workflow which integrates the advantages of the spectral element method(SEM)for flexible and highly efficient simulation of seismic wave propagation in a three-dimensional(3D)regional-scale geophysics model and the finite element method(FEM)for fine simulation of structural response including soil-structure interaction,and performs a physics-based simulation from initial fault rupture on an ancient wood structure.After verification of the hybrid workflow,a large-scale model of an ancient wood structure in the Beijing area,The Tower of Buddhist Incense,is established and its responses under the 1665 Tongxian earthquake and the 1730 Yiheyuan earthquake are simulated.The results from the simulated ground motion and seismic response of the wood structure under the two earthquakes demonstrate that this hybrid workflow can be employed to efficiently provide insight into the relationships between geophysical parameters and the structural response,and is of great significance toward accurate input for seismic simulation of structures under specific site and fault conditions.

Dynamic thermo-mechanical responses of road-soft ground system under vehicle load and daily temperature variation

A complete road-soft ground model is established in this paper to study the dynamic responses caused by vehicle loads and/or daily temperature variation.A dynamic thermo-elastic model is applied to capturing the behavior of the rigid pavement,the base course,and the subgrade,while the soft ground is characterized using a dynamic thermo-poroelastic model.Solutions to the road-soft ground system are derived in the Laplace-Hankel transform domain.The time domain solutions are obtained using an integration approach.The temperature,thermal stress,pore water pressure,and displacement responses caused by the vehicle load and the daily temperature variation are presented.Results show that obvious temperature change mainly exists within 0.3 m of the road when subjected to the daily temperature variation,whereas the stress responses can still be found in deeper places because of the thermal swelling/shrinkage deformation within the upper road structures.Moreover,it is important to consider the coupling effects of the vehicle load and the daily temperature variation when calculating the dynamic responses inside the road-soft ground system.

Performances of fissured red sandstone after thermal treatment with constant-amplitude and low-cycle impacts

In the engineering practices,it is increasingly common to encounter fractured rocks perturbed by temperatures and frequent dynamic loads.In this paper,the dynamic behaviors and fracture characteristics of red sandstone considering temperatures(25℃,200℃,400℃,600℃,and 800℃)and fissure angles(0°,30°,60°,and 90°)were evaluated under constant-amplitude and low-cycle(CALC)impacts actuated by a modified split Hopkinson pressure bar(SHPB)system.Subsequently,fracture morphology and second-order statistics within the grey-level co-occurrence matrix(GLCM)were examined using scanning electron microscopy(SEM).Meanwhile,the deep analysis and discussion of the mechanical response were conducted through the synchronous thermal analyzer(STA)test,numerical simulations,one-dimensional stress wave theory,and material structure.The multiple regression models between response variables and interactive effects of independent variables were established using the response surface method(RSM).The results demonstrate the fatigue strength and life diminish as temperatures rise and increase with increasing fissure angles,while the strain rate exhibits an inverse behavior.Furthermore,the peak stress intensification and strain rate softening observed during CALC impact exhibit greater prominence at increased fissure angles.The failure is dominated by tensile damage with concise evolution paths and intergranular cracks as well as the compressor-crushed zone which may affect the failure mode after 400℃.The second-order statistics of GLCM in SEM images exhibit a considerable dependence on the temperatures.Also,thermal damage dominated by thermal properties controls the material structure and wave impedance and eventually affects the incident wave intensity.The tensile wave reflected from the fissure surface is the inherent mechanism responsible for the angle effect exhibited by the fatigue strength and life.Ultimately,the peak stress intensification and strain rate softening during impact are determined by both the material structure and compaction governed by thermal damage and tensile wave.

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Numerical investigation of the effects of soil-structure and granular material-structure interaction on the seismic response of a flat-bottom reinforced concrete silo

In this work,a numerical study of the effects of soil-structure interaction(SSI)and granular material-structure interaction(GSI)on the nonlinear response and seismic capacity of flat-bottomed storage silos is conducted.A series of incremental dynamic analyses(IDA)are performed on a case of large reinforced concrete silo using 10 seismic recordings.The IDA results are given by two average IDA capacity curves,which are represented,as well as the seismic capacity of the studied structure,with and without a consideration of the SSI while accounting for the effect of GSI.These curves are used to quantify and evaluate the damage of the studied silo by utilizing two damage indices,one based on dissipated energy and the other on displacement and dissipated energy.The cumulative energy dissipation curves obtained by the average IDA capacity curves with and without SSI are presented as a function of the base shear,and these curves allow one to obtain the two critical points and the different limit states of the structure.It is observed that the SSI and GSI significantly influence the seismic response and capacity of the studied structure,particularly at higher levels of PGA.Moreover,the effect of the SSI reduces the damage index of the studied structure by 4%.