Impact of surface-reflected seismic waves on the seismic isolation performance of circular tunnel isolation layers

Seismic isolation is an effective strategy to mitigate the risk of seismic damage in tunnels.However,the impact of surface-reflected seismic waves on the effectiveness of tunnel isolation layers remains under explored.In this study,we employ the wave function expansion method to provide analytical solutions for the dynamic responses of linings in an elastic half-space and an infinite elastic space.By comparing the results of the two models,we investigate the seismic isolation effect of tunnel isolation layers induced by reflected seismic waves.Our findings reveal significant differences in the dynamic responses of the lining in the elastic half-space and the infinitely elastic space.Specifically,the dynamic stress concentration factor(DSCF)of the lining in the elastic half-space exhibits periodic fluctuations,influenced by the incident wave frequency and tunnel depth,while the DSCF in the infinitely elastic space remain stable.Overall,the seismic isolation application of the tunnel isolation layer is found to be less affected by surface-reflected seismic waves.Our results provide valuable insights for the design and assessment of the seismic isolation effect of tunnel isolation layers.

Rockburst process and strength-weakening effect of the high-stress circular tunnel under internal unloading

To investigate the influence of unloading effect of a circular tunnel face on rockburst process,by innovatively combining rock drilling unloading devices and triaxial systems,the strain rockburst simulation under the entire stress path of“high initial stressþinternal unloadingþstress adjustment”(HUS test)was realized for the intact cubic red sandstone samples(100 mm×100 mm×100 mm).Comparative tests were conducted on cubic red sandstone samples with prefabricated circular holes(425 mm)under the stress path of“prefabricated circular hole+þhigh initial stress+stress adjustment”(PHS test),thereby highlighting the influence of internal unloading on rockburst failure.The test results revealed that with an increase in vertical stress,the sidewalls in both the HUS and PHS tests suffered strain rockburst failure.Compared with the PHS test,the initial failure stress in the HUS test is lower,and it is easier to induce sidewall rockbursts.This indicates that the internal unloading influences the sidewall failure,causing an obvious strength-weakening effect,which becomes more significant with an increase in buried depth.The strain rockburst failure was more severe in the HUS test owing to the influence of internal unloading.V-shaped rockburst pits were formed in the HUS tests,whereas in the PHS test,arcshaped rockburst pits were produced.It was also found that strain rockburst failure may occur only when the rock has a certain degree of rockburst proneness.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

Rock burst in a circular tunnel under high in-situ stress conditions was investigated with a numerical method coupled the rock failure process theory (RFPA) and discontinuous deformation theory (DDA). Some numerical tests were carraied out to investigate the failuer patterns of circular tunnel under unloading conditions. Compared the results under loading conditions,the shapes of failure zones are more regular under the unloading conditions. The failure pat-terns in the same type of rock mass are clearly different because of non-homogeneity of the rock material. The extension of cracks shows some predictability with an increasing of in-situ stress. When the homogeneity index of rocks (m) is ei-ther relatively high or low and lateral pressure coefficients (λ) is high,the number of regular shear slide cracks decreases and the probability of a rock burst also becomes lower. Our numerical simulation results show that the stability of sur-face rock and the natural bedding stratification of rock material greatly affect rock bursts. Installing bolts with due dili-gence and suitably can effectively prevent rock bursts. However,it is not effective to control rock bursts by releasing the strain energy with normal pre-boreholes.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

Research on the closure and creep mechanism of circular tunnels

A numerical code called Rock Failure Process Analysis (RFPA2D) was em- ployed to investigate the closure,damage and failure behavior of the horizontal tunnels.In this code the time-dependent deformation was described in terms of evolution of meso- scopic structure,leading to progressive degradation of elastic modulus and failure strength of material.In terms of material degradation,a series of numerical simulations were per- formed to study the convergence and subsequent failure in circular tunnels.The numerical results provide a complete illumination for the closure,damage and failure behavior with different loading conditions.It is shown that the depth and the ratio of far field stresses play an important role in the creep behavior of tunnels.Creep failure is expected to occur in the direction of the smallest far field stress component,which means that rheological failure of tunnels is influenced not only by the rock characteristic around the tunnels but also by the orientation and distribution of far field stress on a global scale.

Shaking table tests on the liquefaction-induced uplift displacement of circular tunnel structure

Underground structures are susceptible to float and move upward during earthquakes when located in a liquefiable soil deposit.There are examples of this phenomenon in past major earthquake events.In this study,the uplift of circular tunnels in a liquefiable sand layer was investigated with a series of shaking table tests.The research has focused on the buried depth of the tunnel,tunnel diameter,tunnel weight,liquefaction extent,uplift mechanism,and factor of safety against liquefaction-induced uplift.According to the test results,the shallow buried depth,larger diameter,and lower weight can intensify the tunnel uplift,so the displacement in post-liquefaction time continues at the same rate as during the shaking time.Due to the shear-induced dilation,pore water pressure generation around the tunnel was reduced compared with that of the free field.The excess pore water pressure dissipation in the soil overlying the uplifted tun-nel was significant,which leads to suction in the soil deposit.Furthermore,the acceleration response of overlying soil with the uplifted tunnel was similar to that of the free field.However,the soil acceleration response around the tunnel without uplift was similar to the base motion.

THE EFFECTS OF THREE-DIMENSIONAL PENNY-SHAPED CRACKS ON ZONAL DISINTEGRATION OF THE SURROUNDING ROCK MASSES AROUND A DEEP CIRCULAR TUNNEL

In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.

Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay

The safety assessment of tunnel stability is critical to tunnel construction and requires accurate analysis to obtain a reliable prediction.Strength anisotropy is an important aspect of clay behavior,but it is mostly neglected in practical stability analyses.In this study,the effects of undrained strength anisotropy and strength nonhomogeneity on the stability of unlined circular tunnels in clays are investi-gated.The static approach of lower-bound(LB)analysis using finite-element and second-order cone programming is employed to exam-ine the aforementioned effects.The anisotropic shear strength of clay is modeled by employing an elliptical yield function under plane strain conditions.A complete set of dimensionless parameters covering the cover depth ratios of tunnels,normalized overburden pressure ratios,normalized strength gradient ratios of clays,and anisotropic strength ratios,are systematically investigated.The new LB solutions indicate that the stability load factor of the problem has a nonlinear relationship with the cover depth ratio and the anisotropic strength ratio,and there exists a linear relationship with the normalized overburden pressure and the normalized strength gradient.Their influ-ence on the predicted failure mechanism is parametrically evaluated.A statistically approximate stability equation of unlined circular tunnels in anisotropic and non-homogeneous clay is proposed for the first time,which contains four new stability factors,namely,con-stant undrained strength,linearly increasing strength gradient,undrained strength anisotropy,and soil unit weight,and it can serve as a fast and accurate tool for predicting the undrained stability of this problem in practice.

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

非圆形隧洞衬砌支护下应力与位移的新解法

以往在利用平面弹性复变函数方法进行衬砌支护作用下非圆形隧洞的力学分析时,一般将洞室外域保角映射到象平面的单位圆外域,并认为可以利用同一个映射函数将衬砌截面映射到象平面的圆环域内。当衬砌厚度很薄时,这种方法是可行的,而当衬砌相对较厚时,利用同一映射函数所得到的衬砌截面形状发生严重失真。为解决此问题,本文引入两套映射函数,分别将洞室外域映射到象平面的单位圆的圆外域,衬砌截面映射到圆环域。这种方法可以适应于不同的衬砌厚度,利用这种方式获得的衬砌截面,在衬砌较厚时仍能保证衬砌厚度相对均匀。在求解解析函数过程中不再采用传统的幂级数解法,而是使用边界配点法,将两套映射函数结合,获得了该问题的应力解和位移解。本文以马蹄形隧洞为例,求解结果与ANSYS软件所得数值解吻合很好,分析了衬砌厚度对隧洞应力和位移的影响。根据本文解答可以方便、快捷地进行相近条件下隧道的初步设计。

Transient response of a concrete tunnel in an elastic rock with imperfect contact

The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.

Shear testing on rock tunnel models under constant normal stress conditions

Large shear deformation problems are frequently encountered in geotechnical engineering.To expose the shear failure mechanism of rock tunnels,compression-shear tests for rock models with circular tunnel were carried out,including single tunnel and adjacent double tunnels.The failure process is recorded by the external video and miniature cameras around the tunnel,accompanied by real-time acoustic emission monitoring.The experiments indicate that the shearing processes of rock tunnel can be divided into four steps:(i)cracks appeared around tunnels,(ii)shear cracks and spalling ejection developed,(iii)floor warping occurred,and(iv)shear cracks ran through the tunnel model.Besides,the roughness of the sheared fracture surface decreased with the increase in normal stress.Corresponding numerical simulation indicates that there are tensile stress concentrations and compressive stress concentrations around the tunnel during the shearing process,while the compressive stress concentration areas are under high risk of failure and the existence of adjacent tunnels will increase the degree of stress concentration.

基于参数化建模思想的四心圆公路隧道洞形优化

合理的四心圆公路隧道断面形式有助于改善衬砌结构的受力状态,减少复合式衬砌的开裂病害,提高隧道结构的耐久性。该文通过Ansys软件APDL参数化编程平台,基于“曲率连续”的设计思想,构建了拱脚区局部洞形几何尺寸参数化建模方程,建立了锚杆加固区等效力学参数计算方法及数值模拟模型,揭示了四心圆公路隧道拱脚区域局部洞形参数设计对衬砌结构内力的影响规律,结合实际工程研究显示:隧道拱脚弧与中墙弧的半径和长度对于隧道复合式衬砌结构内力的影响较明显,增大拱脚弧半径对于抑制衬砌结构内塑性区发展的效果最为明显;为了减小衬砌结构的开裂风险,提出采用衬砌拉应力为控制目标进行局部形状优化思想,通过中墙弧圆心角θ_(2)、拱脚弧圆心角θ_(3)及中墙弧半径R_(2)对衬砌结构内力极值的敏感性及影响规律分析为皮家岭隧道洞形优化提供了理论依据。

Investigating Effect of Tunnel Gate Shapes with Similar Cross Section on Inserted Forces on Its Coverage and Soil Surface Settlement

According to technology development and relative facilitation in digging and underground structures, ways, highways, all types of tunnels, underground train network, and other underground settle, storage are number of structure built and developed in advanced countries. In most situation, tunnel digging operations are done years after its construction or are not recorded in new structures regulations;therefore, this research investigates soil settlement and inserting force to tunnel coverage by limiting studies about effects of tunnel shapes on soil settlement using Plaxis, Seismo Signal, and Seismo Aspect. This study shows that rectangular tunnel has the most settlement in soil surface and circular tunnel has the least settlement but horseshoe tunnel has similar behavior to circular tunnel;however, earth subsidence level by digging this tunnel is more than circular tunnel. In addition, sectional shape has direct effect on inserting forces on tunnel coverage.

正方形布置四圆柱结构流致振动响应特性研究

通过风洞实验研究了正方形布置四圆柱的流致振动特性,实验雷诺数Re=3200~28900,圆柱间距比S/D=1.5~4.0(S为两圆柱圆心间距,D为圆柱直径),质量比m^(*)≈345.0.结果表明,当S/D≤2.0时,上游圆柱1和2呈现涡激振动和类弛振耦合响应,下游圆柱3和4呈现涡激共振和尾流弛振耦合响应;当S/D=2.5~3.0,上游圆柱1和2除了在约化速度超过一定值时存在弱振动外,基本接近单圆柱涡激振动响应,下游圆柱3和4表现为分离的涡激共振和尾流弛振响应;当S/D=4.0时,上游圆柱1和2振动响应几乎和单圆柱一样,而圆柱3和4仍呈现分离的涡激共振和尾流弛振响应.当圆柱呈现涡激振动(上游圆柱)或涡激共振(下游圆柱)时,涡脱频率f_(s)锁定于固有频率f_(n)的1倍谐频,而当圆柱呈现剧烈的类弛振响应(上游圆柱)或尾流弛振响应(下游圆柱)时,f_(s)则会出现明显的多倍谐频;圆柱模型振动频率f_(o)主频始终锁定于fn的1倍谐频.通过对比正方形四圆柱和双圆柱流致振动特性,发现双圆柱动力学响应规律在一定程度上仍适用于正方形布置四圆柱.

Limit analysis of supporting pressure in tunnels with regard to surface settlement

The proliferation of Hoek-Brown nonlinear failure criterion and upper bound theorem makes it possible to evaluate the stability of circular tunnels with an original curved collapsing mechanism. The arch effect of shallow circle tunnel is not taken into consideration so that the mechanical characteristics can be easily described. Based on the mechanism, the upper bound solution of supporting pressure of tunnels under the condition of surface settlements and overloads on the ground surface is derived. The objective function is formed from virtual work equations under the variational principle, and solutions are presented by the optimum theory. Comparisons with previous works are made. The numerical results of the present method show great agreement with those of existing ones. With regard to the surface settlement and overloads, the influence of different rock parameters on the collapsing shape is analyzed.

考虑围岩和衬砌保角映射差异的深埋非圆形隧道力学解析

非圆形隧道围岩和衬砌区域的保角映射函数不同,接触面边界上不同区域的同一点位在映射后的位置差异较大。因此,在求解非圆形隧道的力学解析表达式时,有必要考虑该映射差异。首先,引入基于边界积分的保角映射理论,编制了以多段圆弧为边界的有限双连通域和无限双连通域的保角映射程序;其次,考虑到围岩和衬砌保角映射差异,提出多点逼近的应力函数求解方法,并采用LSQR算法计算应力函数系数的最小二乘解,以满足隧道临空面边界和接触面边界上位移和应力条件;最后,通过多心圆隧道的算例,开展验证和分析。研究结果表明:所求围岩和衬砌保角映射函数具有良好的保角性和保圆性;随着应力函数项数增加,在边界上的应力误差和位移误差显著降低;当侧压力系数为0.50时,多心圆隧道洞周收敛变形的差异显著,拱顶和拱底变形远高于拱脚位置的变形,在衬砌拱脚位置所受围岩压力和切向力最大,并出现显著的应力集中现象;衬砌内外边界上应力和位移的解析解与数值解十分接近,验证了本文所提力学解析方法的正确性。

湍流特性对圆形高层建筑风荷载的影响研究

在四类不同湍流特性的风场和均匀风场中对圆形高层建筑模型进行同步测压试验,分析了模型表面风压系数、层风力系数及其功率谱、基底力矩系数及其功率谱的变化规律。结果表明:相比基准C类风场,湍流强度增大使得脉动风压系数明显增大,平均阻力系数减小,横风向脉动基底弯矩系数增大;随着湍流积分尺度的减小,背风面平均风压系数和脉动风压系数的绝对值均减小,CL2风场结果的减小值更为明显;层风力系数随湍流积分尺度减小而减小,湍流积分尺度的变化对层脉动升力系数和横风向脉动基底弯矩系数的影响可以忽略;湍流特性对基底力矩功率谱和顺风向层风力功率谱影响不大;随着湍流积分尺度的减小,横风向层风力功率谱谱峰对应的折减频率不断增大。