Lateral Pressure Coefficient Research Articles

Effect of rock nonlinear mechanical behavior on plastic zone around deeply buried tunnel: a numerical investigation

Rock shows a significant nonlinear mechanical behavior in the deeply buried tunnel, and it could affect the stress redistribution and the magnitude of the plastic zone (PZ) around the tunnel. Therefore, a series of numerical simulations were performed to highlight the effect of rock nonlinear behavior on PZ with the implementation of a novel proposed unified strain-hardening and strain-softening (UHS) constitutive model. UHS model can well describe the nonlinearity of stress–strain curves, peak strength and residual strength. The numerical model was first validated via the experimental results of one model test, followed by the parameter sensitivity of UHS model and initial stress field. The effect of strain-hardening, strain-softening, the nonlinearity of peak and residual strengths of rock, buried depth of tunnel and the lateral pressure coefficient were discussed. A detailed description method of the PZ was finally proposed considering the nonlinearity of rock. The results reveal that (i) PZ can be divided into the residual zone, strain-softening zone and strain-hardening zone; (ii) the maximum tangential stress stays in the strain-hardening zone; (iii) the initial stress state can change the shape of PZ. Moreover, for the deeply buried tunnel, the pre-stressing measures show a good potential to control PZ, and the support should be applied as early as possible to reduce the relief of initial stress.

Numerical Evaluation of Dynamic Earth Lateral Pressure on Basement Walls in Cohesionless Soils (A Case Study of Iranian Earthquakes)

Various earth-retaining structures are extensively used in different civil engineering projects. Using the results of experimental and numerical modeling, the effect of the earthquake loading on the distribution of the earth lateral pressures on basement walls was investigated. The UBCHYST constitutive model was used in the performed numerical simulations, and using the results of 12 centrifuge dynamic model tests, a calibration process was conducted to obtain the proper input parameters for numerical models. Based on the results, some correlations between the dynamic increment coefficient of earth lateral pressure (ΔKae) and the free-field peak ground acceleration (PGAff) were established. The correlations are different for stiff and flexible basement walls. In the end, the results of the model calibration process were verified by the examination of 12 major earthquakes that occurred in the Iran plateau. The results showed that the proposed ΔKae-PGAff correlations are precise enough for the applied design projects.

Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel

To study the stress distribution characteristics of surrounding rock and the spalling mechanism of deep hard rock tunnels with different arch heights, the complex variable function and angle-preserving transformation method in elasticity theory were applied to the analytic solution of tangential stress distribution of arch tunnels during stress adjustment. In addition, true triaxial tests were conducted on granite cube specimens (100 mm × 100 mm × 100 mm) containing holes with three arch heights (including the 25 mm semi-circular arch, 16.7 mm three-centered arch, 12.5 mm three-centered arch) to simulate the spalling process under different initial ground stresses. The stress distribution solution and experimental results show that the initial failure stress of arch holes is 0.39–0.48 times the uniaxial compressive strength (UCS) of the rock. The initial failure location occurs at the arch foot, where tangential stress maximizes. When the lateral pressure coefficient is in the range of 0.38–0.50, the tangential stress is 3.2–3.5 times the UCS. The rock debris of the hole wall are in thin flake shapes. Symmetrical V-shaped or curved failure zones occurred on hole sidewalls. The stress distribution resolution of the surrounding rock of tunnels with different arch heights shows that with the increasing burial depth, the bearing performance of the semi-circular arch tunnel is optimal. In addition, the maximum tangential stress increases as the height of the arch decreases or the lateral stress increases, making it easier for the initial failure to occur at the foot of the arch.

A Study of the Deformation Law of the Surrounding Rock of a Laminated Roadway Based on FLAC3D Secondary Development

To investigate and analyze the influence of different stress environments on the deformation and destabilization of the rocks surrounding laminated roadways under high stress, this study conducted numerical simulations of coal–rock combination under different circumferential pressures and of the surrounding rocks of highly stressed laminated roadways under different lateral pressure coefficients. In addition, a new custom constitutive structure model was constructed based on the Mohr–Coulomb criterion and realized in FLAC3D software by combining field working conditions. The model was then developed in FLAC3D software for a second time. The results show that the calculated results of the model in this study are in good agreement with the experimental results and the errors are small, while the calculated results of the Mohr–Coulomb model differ from the experimental values under two types of surrounding rock pressure. The deformation of the Mohr–Coulomb model is significantly smaller than that of the customized model, which verifies the reasonableness and superiority of the self-built model in combination with the field conditions. This provides theoretical and practical bases for the design and optimization of stratigraphic roadway support in underground coal mines.

The Dynamic Behavior of Silos with Grain-like Material during Earthquakes

Grain security is an important guarantee for sustainable development. However, the dynamic behavior of silos containing grain-like material is not well understood. The effective mass and dynamic effects are the key parameters for the assessment of the silo–bulk material system during earthquakes. Herein, on the basis of the Janssen continuum model, it is proposed that the seismic energy is entirely dissipated by the interactions between the materials and the silo and the materials themselves. The seismic inertia forces among storage materials were introduced, and dynamic equilibrium equations considering the vibrations of storage materials were established. Theoretical solutions for the horizontal forces exerted and the effective mass of the silo–bulk material system during earthquakes are proposed. It is worth noting that the additional stress on the side wall proposed in this work is related to the depth, silo radius, storage density, internal friction coefficient, lateral pressure coefficient, and seismic acceleration. In addition, the effective mass coefficient is negatively correlated with the external friction coefficient, the lateral pressure coefficient, and horizontal seismic acceleration under a storage vibration state. A narrower silo (i.e., with a larger height–diameter ratio) has a low effective mass coefficient. The results from our method are in good agreement with those attained using experimental data, which demonstrates the accuracy and universality of the proposed formulations.

Improved equations of ground pressure for shallow large-diameter shield tunnel considering multiple impact factors

Reasonable estimation of ground pressure is of vital importance for lining segments design in shield tunnelling. With the rapid development of the urban transportation, the diameter of the shield tunnel tends to become larger. The existing prediction of the ground pressure may overestimate the ground pressure of the shallow large-diameter shield tunnel and thus produce higher cost for the shield tunnel construction. To provide more reasonable solution for ground pressure surrounding the shallow large-diameter shield tunnel, a series of improved equations are proposed in this study. The two-stage method with non-uniform displacement pattern through numerical modelling is used to simulate the shield tunnelling at first. Secondly, the effect of multiple impact factors on horizontal and vertical ground pressure at tunnel vault, haunch and invert is analyzed and five key impact factors are determined. Thirdly, a series of improved equations are presented based on a large number of numerical modelling through nonlinear regression analysis. These improved equations can consider the effect of multiple impact factors and predict the ground pressure varying with position which is more realistic for the shallow large-diameter shield tunnel. Therefore, when compared with both the numerical modelling results and field measurements for 70 case histories, the improved equations show good performance. Also, the ground pressure of the above cases is calculated by traditional methods such as overburden pressure, Protodiaconov's formula and so on. By contrast to 7 traditional methods, the improved equations predict more reasonable result of ground pressure. At last, the influence of the tunnel axis depth, tunnel diameter, GAP parameter, ground classification and in-situ coefficient of lateral pressure at rest on the vertical ground pressure at tunnel vault is investigated through the improved equations. The results indicate that the tunnel size is of significant importance to the ground pressure as expected and thus special attention should be paid to shallow large-diameter shield tunnel. However, engineers may save the cost when tunnel diameter outweighs 15 m as ground pressure varies insignificantly. Furthermore, the initial stress as well as the GAP parameter which represents the shield tunnel construction details also play a vital role in ground pressure.

Semi–analytical solution for ultimate bearing capacity of straight–jointed segmental tunnel lining

The ultimate bearing capacity of a segmental tunnel lining significantly influences its service performance, particularly when the surrounding soil pressure changes. In this study, a semi–analytical force–method solution for a straight–jointed segmental tunnel lining was derived. The nonlinear joint stiffness was considered and expressed as a function of the bending moment, axial force, and rotational angle of the joint. An incremental iterative algorithm and the corresponding convergence criterion of the proposed model were established for the strong nonlinear system. The proposed model was then verified using the full–scale test results for the loading behavior of the joint and the segmental lining. The structural response of the tunnel under different external load distributions was analyzed using the proposed model, and the main conclusions are as follows. As the lateral pressure coefficient increases, the ultimate bearing capacity of the tunnel lining increases and the length of the first yield platform of the convergence deformation decreases. When P3/P1 increases from 0.71 to 0.83, the ultimate bearing capacity of the tunnel lining increases by 20%, but it has no significant effect on the ultimate convergence deformation. For the lining of the shield tunnel of the Shanghai Metro, the recommended convergent deformation limit is 110 mm.

Estimating Earth Pressure during Tunneling in Gravel-cobble Stratum by Considering Sensor-particle Size Effect

When tunneling in gravel-cobble stratum with earth balanced shield, the ratio between the diameters of the pressure sensor embodied in muck chamber and cut gravels is generally small. The small sensor-particle size ratio leads to considerable difference between the measured and actual earth pressure. This makes the configuration of earth pressure a difficult task and furtherly affects tunneling efficiency and safety. This work characterizes the variation of stress measurement error in a granular packing with consideration of the sensor-particle size ratio, the particle size distribution as well as the contact force distribution. The probability density function of stress measurement error is built according to a general probability distribution of inter-particle contact force. After then, a probability-based regressive procedure is proposed to estimate the applied stress with the measured stress. For stress samples with a same target stress but different biases, the stress estimated by the probability-based procedure has a minor variation and thus is more reliable than the arithmetic mean stress. Finally, the probability-based procedure is adopted to estimate the actual earth pressure of a well-tunneled section in Chengdu gravel-cobble stratum, according to which the lateral pressure coefficient of Chengdu gravel-cobble stratum is suggested as 0.20 – 0.28.

Influence of input motion and surface layer properties on seismic site response: A stochastic simulation method–based MLR model

AbstractSeismic site response analyses are simulations in which the effects of geological conditions on seismic waves are examined. The uncertainties that make these analyses crucial are defined as the source of motion, the travel path of seismic waves, and geological conditions. In this study, a series of non‐linear seismic response analyses were performed using data from site investigation studies. The results of non‐linear analyses performed under earthquakes with different characteristics based on real soil data were investigated in terms of acceleration time histories and response spectra. The relationship between site response with the surface layer properties and input motion properties used in the simulations was examined in a parametrical manner. Based on the results obtained, Monte Carlo simulation, which is a stochastic data simulation method, was performed. Additionally, multiple regression and variance analysis (ANOVA) was performed on the dataset created by both site response analysis and stochastic simulations. The MLR model displayed highly accurate results with a coefficient of determination, R2 of 0.9763, and a standard error of 0.109. The efficiency level of the independent variables used as input parameters in the simulations on the dependent variable, AF was examined. It was revealed that the coefficient of lateral earth pressure at rest (Ko), earthquake motion (i.e., PGA of input motion) and surface layer thickness (dsurface) from the soil properties had the highest effect on the amplification factor.

Mechanical model and numerical simulation of the formation of karst collapse columns in the Huainan coalfield of Northern China

Karst collapse columns (KCCs) are channels where groundwater and gas gather, and they pose a great threat to mining safety. In this study, a mechanical model and criterion for the roof collapse of KCCs were established, and simulations were performed to analyze the formation mechanism of KCCs in the Huainan coalfield of Northern China. The results showed that the roof collapse and upward development of KCCs were facilitated by increasing the cave radius of the KCC basement and decreasing the groundwater pressure, single-layer thickness of the roof strata, lateral pressure coefficient of the rock mass, and cohesion and internal friction angle between fractures. The KCC formation process in the Huainan coalfield could be divided into four stages: (I) early collapse, (II) middle-early rapid collapse, (III) middle-late slow collapse, and (IV) late filling compaction. The simulation results were generally consistent with actual KCCs observed in the Huainan coalfield, which verified the theoretical analysis. The results of this study provide an important reference for the formation mechanism and evolution of KCCs in Northern China.

Coupled rheological behavior of tunnel rock masses reinforced by rock bolts based on the non-hydrostatic stress field

The stress and deformation characteristics of the rock mass and the rock bolt reinforcement structure change over time, as a result, it is of significance to understand the coupled rheological behavior of these two systems. In this paper, we first develop viscoelastic solutions for the rock mass reinforced by rock bolts under non-hydrostatic stresses based on the distributed force model. Subsequently, the Maxwell-Maxwell (M−M) and the Maxwell-Burgers (M−B) constitutive models are applied to the rock bolts and the rock mass, respectively, and the corresponding viscoelastic analytical solutions are then obtained. Finally, the numerical software FLAC3D is used to verify the fidelity of the mechanistic model. Our results show that the lateral pressure coefficient is positively correlated with the radial stress and the radial displacement. The radial stress in the rock mass reaches a stable value with time. Furthermore, the lateral pressure coefficient has a positive correlation with the axial force in the rock bolts in elastic analysis. However, as the creep in the rock mass develops, the axial forces under different lateral pressure coefficients gradually reach a stable value. Moreover, the lateral pressure coefficient mainly affects the distribution of axial force and the slope of the axial force in the rock bolts.

The lateral pressure coefficient at rest of expansive soils in landfill at various vertical stresses and moisture contents

The lateral pressure coefficient at rest of expansive soils in landfill at various vertical stresses and moisture contents

Influence of geomechanics parameters on stress sensitivity in fractured reservoir

The complex fractures aggravate stress sensitivity and heterogeneity of the reservoir and seriously restrict effective development. Therefore, it is of great significance to study and quantitatively evaluate the stress sensitivity of the fractured reservoir. Taking the typical block of the Longmaxi shale reservoir in southern Sichuan as the engineering background, one uses the finite element method to develop a numerical model of a two-dimensional fracture closure variation subjected to the non-hydrostatic stress field. It explores the influence of different fracture occurrences and rock mechanical parameters on stress sensitivity. The theoretical model verifies the numerical simulation results to reveal the stress sensitivity mechanism of the fractured reservoir. The results show that the influence of the dip angle of fracture on the stress sensitivity depends on the anisotropy of applied in-situ stresses. The stronger stress sensitivity occurs in low-dip angles where the lateral pressure coefficient is less than 1. One defines the lateral pressure coefficient. On the contrary, the stronger stress sensitivity occurs in high-dip angles where the lateral pressure coefficient is more significant than 1. It is because the normal stress differences under different stress fields apply to the fracture. Under a given stress condition, the stress sensitivity of fracture negatively correlates with aspect ratio, elastic modulus, and Poisson’s ratio. Pressure maintenance may be more critical in a reservoir with a low aspect ratio and rich in soft minerals. The theoretical predicting model of fracture permeability under different conditions is established based on the linear elastic theory. The relative error between theoretically predicted results and numerical simulation ones is less than 10%, which verifies the accuracy of numerical simulation results. The fundamental reason for stress sensitivity in the fractured reservoir is the fracture geometry and mineral deformation change. The research results are of great significance for establishing the productivity equation considering the stress sensitivity, accurately evaluating the variation of reservoir seepage capacity, and formulating reasonable drainage and production system.

Effects of Geogrid Reinforcement on the Backfill of Integral Bridge Abutments

The construction of integral bridges is one of the most effective methods to reduce bridges’ construction and in-service costs. However, there are associated geotechnical problems with their abutments backfill due to the integrated abutments. The main goal of this study is to evaluate and quantify the benefits of geogrid reinforcement for reducing the backfill’s geotechnical problems. For this purpose, using small-scale physical modeling, the benefits of geogrid reinforcing of the backfill of an integral abutment bridge subjected to cyclic movements are evaluated. The results are then compared with a previous study performed on unreinforced backfill and two types of geocells. In this study, 120 loading cycles are applied to geogrid-reinforced soil to simulate the cyclic loadings on integral abutment backfill due to seasonal abutment displacement. The horizontal reaction load at the top of the wall, changes in pressure behind the wall, and deformation in backfill soil are measured during the test. Then the results are discussed in terms of equivalent peak lateral soil coefficient (Kpeak), lateral earth pressure coefficient (K*), and normalized settlement behind the wall (Sg/H). The derived lateral soil coefficients and settlement behind the abutment show that geogrid substantially reduces pressure and settlements after 120 cyclic loads. Based on the results, Kpeak and K* of the geogrid-reinforced backfill decrease by up to 36%, and Sg/H behind the wall decreases by 62%. In addition, the comparison of the results for geogrid with two geocell types shows that geogrid is more efficient in terms of lateral soil coefficients.

Numerical investigation of an improved deep-hole presplitting method based on notched blasting for deep-buried high sidewall structures

Under high stress conditions, the local stress concentration in the high sidewall structure of a deeply buried powerhouse is obvious, and sidewall presplitting formation is significantly affected. For deep hole presplitting blasting (DHPB) widely used in underground powerhouse, the non-uniform stress characteristics of DHPB were first revealed through three-dimension (3D) numerical simulation, and three crack formation modes were subsequently classified. Afterwards, an improved excavation method of notched blasting fusion to DHPB was proposed to reduce the difficulty and inhomogeneity of DHPB brought by complex stress environment. A single hole 3D model was used to confirm the stronger guiding effect of notched blasting on crack expansion when the maximum principal stress direction is different from its. And the feasibility of the improved presplitting method on high sidewalls is pointed out by 3D numerical simulation. The results show that, for DHPB, the stress concentration at sidewall foot induced by powerhouse excavation causes a gradual change in its stress environment, and the horizontal lateral pressure coefficient (Ratio of transverse to axial) decreases with hole depth basically, while there may be a principal stress direction dividing point with a coefficient of 1.0. The direction of crack formation near the top of presplitting holes tends to be lateral to the powerhouse, whereas that near the bottom of presplitting holes tends to be axial to the powerhouse. This effect is exacerbated further by continuous undercutting of the lower and middle parts, resulting in more uneven pre-cracking of DHPB. The improved excavation method based on notched blasting can ensure that the notched direction is the dominant crack expansion direction among both notch cutting and maximum principal stress direction, weaken the influence of uneven stress environment on the presplitting formation, and re-achieve the good crack formation between holes of DHPB.

A Study on the Deformation Mechanism of the Rock Surrounding a Weakly Cemented Cross-Layer Roadway, under Tectonic Stress

Maintaining the stability of the surrounding rock is an important prerequisite in ensuring the safe and efficient construction of underground mines—in particular, the surrounding rock of the cross-layer roadway, which is a combination of different media with different lithologies. Numerical models were established to investigate the effects of the different lateral pressure coefficients (λ), the angle (α) between the roadway and the maximum horizontal principal stress, and typical lithological combinations on the deformation of the surrounding rock of weakly cemented roadways. The main outcomes obtained from our research indicated the following: (1) under the action of tectonic stress, the focus should be on strengthening the roof of the roadway support of the slab, which is conducive to the stability of the surrounding rock; (2) roadway deformation and failure for the cases λ < 1.5 are approximately symmetrically distributed, whereas those for the cases λ > 1.5 are asymmetric; (3) roadway deformation and failure for the cases α < 45° are approximately symmetrically distributed, whereas those for the cases α > 45° are asymmetric; (4) tectonic stress has an important influence on stress redistribution, deformability, and damage in cross-layer roadways; and (5) when excavating cross-layer roadways under the action of tectonic stress, the concentrated stress around the end of the working face (especially the bottom corner) should be reduced. The research results provide insights for the roadway layout through coal seam and cross-layer excavation and deepen the understanding of the deformation mechanism of weakly cemented cross-layer roadway under tectonic stress.

DEM Investigation into the Effects of Liquefaction History–Induced Anisotropy on Sand Behaviors

Many studies have verified that liquefaction histories would change sand mesostructures. However, how much the liquefaction history–induced anisotropy affects sand mechanical properties under different loading conditions remains unknown. In this study, the triaxial behaviors and coefficients of lateral earth pressure (K0) of sand specimens with different liquefaction histories were simulated by a discrete element method (DEM). The triaxial tests included monotonic drained and undrained tests and cyclic undrained tests. The K0 tests included two cases: the K0VH test was conducted using one-dimensional compression in the vertical direction, while the K0HV test was conducted using one-dimensional compression in the horizontal direction. Simulation results showed that the anisotropy induced by the liquefaction history obviously affected the initial stiffness and contraction behavior of reconsolidated sand during monotonic drained and undrained tests. Once the anisotropy degree exceeded a threshold, all the reconsolidated sand was reliquefied after only one cycle, regardless of the void ratio and applied cyclic stress ratio. The K0 test of the reconsolidated sand had a good correlation with the anisotropy degree. Reconsolidated sand with a larger anisotropy degree exhibited a more remarkable discrepancy between K0VH and K0HV. These anisotropic behaviors were intrinsically the responses of the interparticle normal contact force chains to the boundary conditions of a certain test.

CIRCULAR TUNNEL STRUCTURAL ANALYSIS IN SOFT GROUND

Analytical bedded-beam spring model is most commonly adopted in the tunnel engineering practice due to its simplicity and promising outputs. Despite many well documented literatures exist concerning about the theories and fundamentals of various methods, there is a dearth of information on the modelling framework of a bedded-beam spring and many details are often overlooked in the modelling process. The main aim of this paper is to produce the modelling framework of the bedded-beam spring model in soft ground, for both direct and indirect approaches in considering the effects of segmental joints. Particular emphasis is devoted to the modelling techniques of each components of the structural model which in turn, is able to facilitate the modelling quality and process for the practicing engineers. Reviews on the technical papers of tunneling variables as well as parameters identification for the structural analysis have been first performed followed by the comparison of the consideration adopted in the modelling techniques. Analyses have been carried out to evaluate the structural forces on the tunnel lining and the obtained results are discussed in a comparison with the field measurements and design values of the actual tunneling projects. The results suggested that the direct approach always yields greater bending moments up to i) 26% for 6+1 ring configuration and ii) 21% for 5+1 ring configuration compared to that of the indirect approach. With the presence of more number of radial joints, the differences between the approaches have the tendency to be greater. With the validated models, parametric studies including tunnel lining flexibility ratio, compressibility ratio and the soil lateral earth pressure coefficient have been performed to provide better insight on the relative importance of each of the parameters. The results of the studies suggested that with the increase in flexibility ratio, the difference between the direct and indirect approach has shown to increase from 10% to 28%. However, insignificant influence has been observed on the axial forces regardless of the joint consideration approach a well as the compressibility ratio.

Study on the Safety Thickness of Rock Strata for Outburst Prevention in Deep Tunnel Based on Numerical Modeling and Backpropagation Neural Network

Water inrush and mud inrush pose a serious threat to safe construction in underground engineering, but it is very difficult to determine the safe distance of outburst prevention rock mass. Based on deep-buried tunnel engineering, this paper proposes a method to determine the safe distance from water inrush disaster between the tunnel and the fault fracture zone. This method combines numerical modeling and backpropagation (BP) neural network. By means of numerical simulation, the internal influence law of the water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel burial depth on the surrounding rock is analyzed. The evolution law of the minimum safe strata thickness under a single variable and the correlation degree between minimum safe strata thickness and various disaster factors are revealed. Based on the BP neural network analysis of the simulation results and the measured data of Wulaofeng Tunnel, the calculated values of safe strata thicknesses of fault fracture zone (F10) were determined. The results show that the thickness of the safe rock strata increases with increasing water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel burial depth. The minimum safe thickness of F10 of the tunnel ranges from 7.1 m to 7.4 m, and 10 m is reserved in the actual project. The calculated results are consistent with the reserved thickness value in the construction. This conclusion can provide a reference for similar projects.

Fracture initiation and propagation in the lined underground caverns for compressed air energy storage: Coupled thermo-mechanical phase-field modeling

In this study, to investigate the mechanism of fracture initiation and propagation in the CAES caverns, a coupled thermo-mechanical phase-field model (PFM) considering cavern excavation is proposed. The proposed PFM is coupled with the thermodynamic process of CAES and solved in COMSOL Multiphysics. To verify the capability and accuracy of the numerical model for predicating the tensile cracks of the CAES caverns, the numerical results obtained by using the proposed model are compared with the existing analytical and numerical results. The influence of the lateral pressure coefficient, critical energy release rate, elastic modulus of rock mass and buried depth on the fracture patterns and critical internal pressure is investigated. The results indicate that the fracture patterns are mainly related to the lateral pressure coefficient. As the lateral pressure coefficient of rock mass increases, the tensile fractures gradually deflect to the horizontal direction. With the increase in the lateral pressure coefficient, critical energy release rate, elastic modulus and buried depth, the critical internal pressure inducing the tensile fractures of the CAES caverns increases.