Influence of confined water on the limit support pressure of tunnel face in weakly water-rich strata

In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.

Estimation of earth pressure against retaining walls with different limited displacement modes based on elastic theory

The earth pressure acting on retaining walls due to creep and consolidation is under limited equilibrium conditions(limited displacement). Linear elastic constitutive theory can be applied to determine earth pressure distribution along retaining walls under limited displacement condition. In addition,tangent modulus in Duncan-Chang nonlinear elastic model was introduced to reflect the variations of soil modulus with confining pressure, and boundary strains were derived from Rankine active earth pressure, Rankine passive earth pressure, static earth pressure and principal stress direction deflection.According to the above four boundary strains, earth pressure on retaining walls was divided into five state zones. By comparing the calculation results obtained from the equations proposed in this paper with those of experimental tests, the following conclusions can be drawn: earth pressure distribution was always nonlinear along retaining walls for translation displacement(T mode), rotation displacement around wall base(RB mode), and translation + rotation displacement around wall base(RBT mode). Also,calculated earth pressure distributions along with the depth of wall were found to be consistent with measured values under three displacement modes.Additionally, a parametric study was carried out to evaluate the effects of internal friction angle and backfill soil cohesion on earth pressure. It could be seen from the above series of studies that the earth pressure equations derived in this work could be well applied in practical engineering in designing retaining walls.

Mechanical formula for the plastic limit pressure of stent during expansion

The mechanics of cardiovascular stents during the process of expansion are very important for stent function and safety. In general, finite element method （FEM） or experi- ments are major methods used to ascertain mechanical prop- erties of the stent. In this paper, we develop a theoretical model of the tubular stent, derive formulas for the axial forces and moments on the stent end, and propose formu- las for the plastic limit pressure vs. the stent＇s radius during expansion. Examples covering different geometrical param- eters and material parameters are provided, and the plastic limit pressures calculated by FEM and the present method are compared, proving that the present formulas are acceptable and meaningful for the design and innovation of the stent.

Limit analysis method for active earth pressure on laggings between stabilizing piles

Stabilizing pile is a kind of earth shoring structure frequently used in slope engineering. When the piles have cantilever segments above the ground,laggings are usually installed to avoid collapse of soil between piles. Evaluating the earth pressure acting on laggings is of great importance in design process.Since laggings are usually less stiff than piles,the lateral pressure on lagging is much closer to active earth pressure. In order to estimate the lateral earth pressure on lagging more accurately,first,a model test of cantilever stabilizing pile and lagging systems was carried out. Then,basing the experimental results a three-dimensional sliding wedge model was established. Last,the calculation process of the total active force on lagging is presented based on the kinematic approach of limit analysis. A comparison is made between the total active force on lagging calculated by the formula presented in this study and the force on a same-size rigid retaining wall obtained from Rankine's theory. It is found that the proposed method fits well with the experimental results.Parametric studies show that the total active force on lagging increases with the growth of the lagging height and the lagging clear span; while decreases asthe soil internal friction angle and soil cohesion increase.

Spatio-temporal variation in transpiration responses of maize plants to vapor pressure deficit under an arid climatic condition

The transpiration rate of plant is physically controlled by the magnitude of the vapor pressure deficit（VPD） and stomatal conductance. A limited-transpiration trait has been reported for many crop species in different environments, including Maize（Zea mays L.）. This trait results in restricted transpiration rate under high VPD, and can potentially conserve soil water and thus decrease soil water deficit. However, such a restriction on transpiration rate has never been explored in maize under arid climatic conditions in northwestern China. The objective of this study was to examine the transpiration rate of field-grown maize under well-watered conditions in an arid area at both leaf and whole plant levels, and therefore to investigate how transpiration rate responding to the ambient VPD at different spatial and temporal scales. The transpiration rates of maize at leaf and plant scales were measured independently using a gas exchange system and sapflow instrument, respectively. Results showed significant variations in transpiration responses of maize to VPD among different spatio-temporal scales. A two-phase transpiration response was observed at leaf level with a threshold of 3.5 k Pa while at the whole plant level, the daytime transpiration rate was positively associated with VPD across all measurement data, as was nighttime transpiration response to VPD at both leaf and whole plant level, which showed no definable threshold vapor pressure deficit, above which transpiration rate was restricted. With regard to temporal scale, transpiration was most responsive to VPD at a daily scale, moderately responsive at a half-hourly scale, and least responsive at an instantaneous scale. A similar breakpoint（about 3.0 k Pa） in response of the instantaneous leaf stomatal conductance and hourly canopy bulk conductance to VPD were also observed. At a daily scale, the maximum canopy bulk conductance occurred at a VPD about 1.7 k Pa. Generally, the responsiveness of stomatal conductance to VPD at the canopy scale was lower than that at leaf scale. These results indicate a temporal and spatial heterogeneity in how maize transpiration responses to VPD under arid climatic conditions. This could allow a better assessment of the possible benefits of using the maximum transpiration trait to improve maize drought tolerance in arid environment, and allow a better prediction of plant transpiration which underpin empirical models for stomatal conductance at different spatio-temporal scales in the arid climatic conditions.

Deformation mechanism and limit support pressure of cutting steel plate during connection between pipes in large spacing using pipe curtain structure method

The pipe curtain structure method(PSM)is a novel construction method to control ground deformation strictly.Compared with the traditional pipe-roofing and pipe jacking method,the connection between pipes in large spacings using PSM is widely acknowledged as a unique construction procedure.Further study on this connection procedure is needed to resolve similar cases in that the pipes are inevitably constructed on both sides of existing piles.Cutting the steel plate during the connection procedure is the first step,which is crucial to control the safety and stability of the surrounding environment and existing structures.The deformation mechanism and limit support pressure of the cutting steel plate during the connection between pipes in large spacings are studied in this paper,relying on the undercrossing Yifeng gate tower project of Jianning West Road River Crossing Channel in Nanjing,China.A modified 3D wedge-prism failure model is proposed using the 3D discrete element method.Combined with Terzaghi loose earth pressure theory and the limit equilibrium theory,the analytical solutions for the limit support pressure of the excavation face of the cutting steel plate are derived.The modified 3D wedge-prism failure model and corresponding analytical solutions are categorised into two cases:(a)unilateral cutting scheme,and(b)bilateral cutting scheme.The analytical solutions for the two cases are verified from the numerical simulation and in-situ data and compared with the previous solutions.The comparative analysis between the unilateral and bilateral cutting schemes indicates that the bilateral cutting scheme can be adopted as a priority.The bilateral cutting scheme saves more time and induces less ground deformation than the unilateral one due to the resistance generated from the superimposed wedge.In addition,the parametric sensitivity analysis is carried out using an orthogonal experimental design.The main influencing factors arranged from high to low are the pipe spacing,the cutting size,and the pipe burial depth.The ground deformation increases with the increased cutting size and pipe spacing.The pipe burial depth slightly affects the ground deformation if the other two factors are minor.Cutting steel plates in small sizes,excavating soil under low disturbance,and supporting pipes for high frequency can effectively reduce the ground surface subsidence.

The geomechanics of Shenhua carbon dioxide capture and storage(CCS) demonstration project in Ordos Basin,China

Carbon dioxide(CO2) capture and storage(CCS) is considered widely as one of promising options for CO2emissions reduction,especially for those countries with coal-dominant energy mix like China.Injecting and storing a huge volume of CO2in deep formations are likely to cause a series of geomechanical issues,including ground surface uplift,damage of caprock integrity,and fault reactivation.The Shenhua CCS demonstration project in Ordos Basin,China,is the first and the largest full-chain saline aquifer storage project of CO2in Asia.The injection started in 2010 and ended in 2015.during which totally 0.3 million tonnes(Mt) CO2was injected.The project is unique in which CO2was injected into 18 sandstone formations simultaneously and the overlying coal seams will be mined after the injection stopped in 2015.Hence,intense geomechanical studies and monitoring works have been conducted in recent years,including possible damage resulting from the temperature difference between injected CO2and formations,injection induced stress and deformation change,potential failure mode and safety factor,interaction between coal mining and CO2geological storage,determination of injection pressure limit,and surface monitoring by the interferometric synthetic aperture radar(InSAR) technology.In this paper,we first described the background and its geological conditions of the Shenhua CCS demonstration project.Then,we gave an introduction to the coupled thermo-hydro-mechano-chemical(THMC) processes in CO2geological storage,and mapped the key geomechanical issues into the THMC processes accordingly.Next,we proposed a generalized geomechanical research flowchart for CO2geological storage projects.After that,we addressed and discussed some typical geomechanical issues,including design of injection pressure limit.CO2injection induced near-field damage,and interaction between CO2geological storage and coal mining,in the Shenhua CCS demonstration project.Finally,we concluded some insights to this CCS project.

Pile end bearing capacity in rock mass using cavity expansion theory

Much empiricism is involved in design of rock-socketed piles in rock masses.In light of this,an analytical solution based on the cavity expansion theory is proposed for calculating the ultimate bearing capacity at the tip of a pile embedded in rock masses obeying the Hoek-Brown failure criterion.The ultimate end bearing capacity is evaluated by assuming that the pressure exerted at the boundaries of a pressure bulb immediately beneath the pile tip is equal to the limit pressure required to expand a spherical cavity.In addition,a relationship is derived to predict the pile load-settlement response.To demonstrate the applicability of the presented solution,the results of this study were compared to those of 91 field tests from technical literature.Despite the limitations,it is found that the end bearing resistance computed by the present work is in good agreement with the field test results.

Analytical solutions of limit support pressure and vertical earth pressure on cutting face for tunnels

This paper focuses on theoretical analytical models to calculate the limit support pressure and vertical earth pressure on the cutting face for tunnels.The failure zone is divided into two parts:a sliding failure zone and an upper loosen zone,and the limit support pressure calculation equation is derived.To verify the rationality of the theoretical model,it was compared with the existing theory,numerical simulation,and centrifugal test,and then the parameter analysis was carried out.The results show that the results of this paper agree well with the existing theory,numerical simulation,and centrifugal test.The inclination angle of the proposed mechanism is determined based on the results of the existing centrifuge test,and the recommended inclination angle is between 52°+φ/2 and 54°+φ/2.The method is proven to be safe and accurate.It can provide a theoretical basis for similar projects.

STUDY ON COPYING QUALITY IN CONTOUR GRINDING

A criterion is proposed to the feasibility on radial copying grinding, i.e.the pressure angleapplying to a point on the workpiece contour to be profiled should be smaller than its angle limit.Therefore, the expressions of the angle applying to copying grinding and the angle limit to copyingmechanism are derived, with the measures taken for the quality improvement of copying movementin contour grinding discussed.

Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations

The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.

Limit Analysis of Defect-Free Pipe Elbow Under Internal Pressure With Mean Yield Criterion

With mean yield（MY）criterion,an analytical solution of the collapse load for a defect-free pipe elbow under internal pressure is first obtained.It is a function of ratio of thickness to radius t0/r0,strain hardening exponent n,curvature influence factor mand ultimate tensile strength.The collapse load increases with the increase of m,and it is the same as the burst pressure of straight pipe if m=1is assumed.The MY-based solution is compared with those based on Tresca,Mises and twin shear stress（TSS）yield criteria,and the comparison indicates that Tresca and twin shear stress yield criteria predict a lower bound and an upper bound to the collapse load respectively.However,the MY-based solution lies just between the TSS and Tresca solutions,and almost has the same precision with the Mises solution.

Face stability analysis of large shield-driven tunnel in rock-soil interface composite formations

A new 3D log-spiral model(LS-M model)is proposed to determine the minimal support pressure on the tunnel face of a large shielddriven tunnel in rock-soil interface(RSI)composite formations.In the proposed LS-M model,we define the RSI angle ω and use a new approach to calculate the equivalent tunnel face area,which provides a collapse zone with more realistic geometry than the traditional wedge model.And it has acceptable accuracy with simpler implementation than limit equilibrium analysis.Comparing with previous studies and 3D numerical analysis,it indicates that:(i)the LS-M results agree well with others in full-soil formations on the variation patterns of minimum support pressure and stability coefficients N_(c) and N_(γ);(ii)the critical RSI angle ω_(cr),which is predominantly influenced by soil cohesion,increases with the soil property values;(iii)the limit support pressure starts to increase with ω only when ω>ω_(cr);(iv)the peak support pressure occurs at lower C/D with a lower ω;(v)ω can only affect stability coefficients N_(c) and N_(γ) when ω and the friction angle are relatively small,while N_(s) is substantially influenced by RSI angle ω.