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Application of isolation technology in shallow super-large comprehensive pipe galleries in seismically vulnerable areas with weak soils

Application of isolation technology in shallow super-large comprehensive pipe galleries in... 1IntroductionThe rapid development of the infrastructure has led to a growing demand for large-section and comprehensive urban tunnels that integrate drainage pipelines, natural gas pipelines, energy, and transportation caves into a large cross-section structure [1]. Comprehensive urban tunnels are environmentally friendly and have high space utilization [2], but their large cross-section and multifunctionality can increase the risk of severe damage during earthquakes, resulting in economic and societal losses. Additionally, these comprehensive urban tunnels are often located in the downtown area, making seismic maintenance extremely difficult [3]. As a result, there is considerable interest in developing seismic response and seismic technology for super-large urban tunnels.It has long been believed that tunnels suffer less seismic excitation because they are surrounded by soils or rocks, but severe hazards have been observed in recent earthquake events, including rock falling, lining uplifting, soil liquefaction, structure cracking, as well as collapsing [4,5]. The seismic reviews have indicated that the urban tunnel, with weak geological conditions and shallow depth, may suffer much more serious catastrophes in the seismically vulnerable areas [6,7].In this regard, a large number of research works have been conducted on the seismic design for shallow urban tunnels, mainly containing the dynamic behaviors and seismic resistance. In terms of the dynamic response, Wang et al. and Sun et al. explored the dynamic response of shallow-bias tunnels with asymmetric loading [8,9]. Sun et al. and Wang et al. researched the seismic responses and damage mechanisms of the portal section of the shallow buried tunnel [10,11]. An et al. optimized the seismic ground motion parameters and analyzed their correlations with seismic behaviors for the shallow-buried rectangular tunnel [12]. Other parameters such as the rock joint [13], the cross-section [14], and geological conditions [4] have also been observed.The seismic resistance comprises the reinforcement method and shock absorption. In terms of the reinforcement method, the lining reinforcement (including the fiber-reinforced concretes, high-performance concrete, special seismic structure, etc.) and the rock strengthening (including the grouting, rock bolt, and so on) are two main fields [15]. Nevertheless, the reinforcement method cannot have an ideal effect in strong seismically vulnerable zones, especially in complex geological conditions [16]. Therefore, the Japanese scholars first proposed the isolation layer, that is, employing a layer of flexible special materials, aiming to absorb or isolate the seismic excitation on the tunnel structure [17,18]. Afterward, Wang and Cui proposed the isolation model of the tunnel, and factors such as layer stiffness, input motion, and damping were evaluated [19]. Ma et al. introduced foamed concrete as the isolation material and explored its shock absorption capacity through indoor tests and finite element method [20]. To date, various isolation layers have been put forward, such as the sponge rubber sheet, foam concrete, asphalt sand, and so on, and their thickness, construction position, and interaction with other aseismic measures are explored in detail. The above studies have provided a scientific guide for the urban tunnel in seismically active zones. However, due to the relatively slow development of the super-large and extremely shallow buried tunnels, the seismic response and shock absorption for the super-large pipe are rarely investigated, let alone for the tunnel in weak soils.Therefore, in this study, based on the largest section urban pipe gallery with a shallow buried depth in weak soils, the seismic response for the super-large urban pipe gallery is explored by the finite difference method, and the isolation scheme was explored. The seismic effect of the cushion scheme, the partial buffer layer, and the integral buffer layer were investigated by the full earthquake simulation. Various indexes such as the deformation, principal stresses, shear stress, and safety factors were analyzed in detail.2Research backgroundThe research object, located in the Xiong’an New Area of the Hebei Province, China, is a comprehensive urban pipe gallery consisting of four chambers in total, namely, a gas module, an integrated module, and two power modules, as illustrated in Figure 1. This pipe gallery, with the largest section and hoisting weight at present in China, was classified as the super-large section gallery referring to the China Code [21]. Besides, this pipe gallery employs the prefabrication and hoisting scheme for the construction. The segment is C45 waterproof concrete, and the 4 m and 8 m long pipes are approximately 201 t and 402 t, respectively [22]. Geologically, the tunnel is situated in weak soils, which mainly includes clay, silty clay, and silty fine sand. The seismic-fortification intensity of the tunnel site areas is eight degree, and it increases to nine degree for some significant facilities [23]. Therefore, the nine-degree seismic intensity is employed for the super-large pipe gallery in our research.Figure 1The super-large comprehensive urban pipe galley (unit: mm).3Full seismic model3.1Calculation conditionTo explore the isolation technology for the super-large pipe gallery, three seismic conditions with isolation schemes and one without approach were used in the numerical simulation, as listed in Table 1. The C25 concrete and the sponge rubber plate, with a thickness of 10 cm, were chosen as the cushion and the buffer layer, respectively. And the cushion and buffer layers are set between the initial support and linings. Figure 2 plots the detailed profiles of four calculation conditions, in which the red line represents the seismic measures.Table 1Calculation conditionsCalculation conditionRemarks1Original tunnel2Tunnel with cushion3Tunnel with partial buffer layer4Tunnel with integral buffer layerFigure 2Calculation conditions: (a) Condition 1; (b) Condition 2; (c) Condition 3; and (d) Condition 4.3.2Software situationFLAC3D, developed by Itasca International Inc., is a professional geotechnical analysis software. The software employs the Lagrange fast difference method, which can calculate the deformation, stress, and stability of the rock mass under various external loads, especially in the analysis of the large deformation problem and post-peak characteristics after soil failure [24]. At present, the software has been widely used in slopes, foundation pits, tunnels, underground caverns, mining, energy, and nuclear waste village. Besides, in terms of the nonlinear dynamic calculation, FLAC can conduct the three-dimensional complete dynamic analysis, and its fully nonlinear method can follow any nonlinear constitutive model that can be specified. It can not only simulate the interference of seismic waves with different frequencies and irreversible displacement but also reproduce the propagation of shear and compression waves.3.3Basic assumption(1)It is supposed that the rock, primary support, lining, cushion layer, and buffer layer are homogeneous and isotropic materials.(2)The failure of the rock mass follows the Mohr–Coulomb criterion, and the linear elastic model is adopted for primary lining, secondary lining, cushion, and buffer layers.(3)The lateral, longitudinal, and vertical directions of the seismic motion correspond to the x-, y-, and z-axis of the numerical model, respectively.3.4Numerical modelThe mesh is established by the professional CAE software (i.e., HyperMesh Software), and then imported into FLAC3D. Considering computer performances, working efficiency, grid control method (equation (1)), and a large number of trial calculations, the mesh for the buffer layer, cushion layer, and the mesh of the pipe gallery is 0.2–0.5 m, and the rock in blue is 0.5–1.0 m, while the mesh size of the rock in red and green is 1.0–3.0 m [25], as shown in Figure 3.(1)Δl≤(18−110)λ,\text{Δ}l\left\le \left(\frac{1}{8}\left-\frac{1}{10}\right)\lambda ,where Δl\text{Δ}lindicates the maximum size of the grid; and λ\lambda is the wavelength corresponding to the seismic waves with highest frequency.Figure 3Calculation model of the initial stress field.The bedrock layer is within 10 m from the bottom of the model to simulate the rigid foundation in the natural stratum. Moreover, it is indicated that there is complete contact between the surrounding rock and lining, lining and damping layer, that is, the normal and tangential displacement and stress between contact surfaces are equal.The isolation simulation comprises the initial stress calculation and the seismic dynamic calculation. First, the normal constraint and quiet boundary are employed at the four sides and bottom in the static model, as illustrated in Figure 3. Then, the excavation and support procedures of the tunnel are performed in the numerical simulation, to seek the actual stress field in the natural condition. A vital step in the static calculation is that the displacement field is eliminated, while the stress field is not modified.In the seismic dynamic calculation, the 2008 Wenchuan Earthquake acceleration waves, recorded by the Wolong Station, are chosen as the original dynamic loads [26]. The seismic boundary conditions are applied at the model boundary or internal nodes to simulate the external and internal dynamic loads borne by rock mass in the FLAC3D. In the present research, the seismic motions propagate upward from the bottom after filtering and baseline correction. Filtering can eliminate noise waves during the collection of seismic waves, while baseline correction can eliminate residual displacement at the end of dynamic calculations. Figure 4 plots the modified seismic waves employed in the simulation. Meanwhile, the free-field boundary is adopted to reduce or eliminate the reflection of seismic waves, as shown in Figure 5. Equations (2)–(4) give the calculation method of unbalanced force at the free-field boundary. Considering that the local damping is independent of frequency and could obtain a more accurate solution, the local damping with a coefficient of 0.157 is employed during the dynamic calculation [27].(2)Fx=−ρCp(υxm−υxff)A+Fxff,{F}_{x}=-\rho {C}_{\text{p}}({\upsilon }_{x}^{\text{m}}-{\upsilon }_{x}^{\text{ff}})A+{F}_{x}^{\text{ff}},(3)Fy=−ρCs(υym−υyff)A+Fyff,{F}_{y}=-\rho {C}_{\text{s}}({\upsilon }_{y}^{\text{m}}-{\upsilon }_{y}^{\text{ff}})A+{F}_{y}^{\text{ff}},(4)Fz=−ρCs(υzm−υzff)A+Fzff,{F}_{z}=-\rho {C}_{\text{s}}({\upsilon }_{z}^{\text{m}}-{\upsilon }_{z}^{\text{ff}})A+{F}_{z}^{\text{ff}},where Fx{F}_{x}, Fy{F}_{y}, and Fz{F}_{z}represent the force applied to the main mesh by the free-field boundary in the x-, y-, and z-directions, respectively; ρ\rho represents the density of the model along the vertical direction; Cp{C}_{\text{p}}and Cs{C}_{\text{s}}represent the propagation velocity of compression wave and shear wave of side boundaries, respectively; AArepresents the influence area of free field grid; υxm{\upsilon }_{x}^{\text{m}}, υym{\upsilon }_{y}^{\text{m}}, and υzm{\upsilon }_{z}^{\text{m}}represent the velocity in x-, y-, and z-directions of the main mesh of the side boundary, respectively; υxff{\upsilon }_{x}^{\text{ff}}, υyff{\upsilon }_{y}^{\text{ff}}, and υzff{\upsilon }_{z}^{\text{ff}}represent the velocity in x-, y-, and z-directions of the side free-field grid, respectively; Fxff{F}_{x}^{\text{ff}}, Fyff{F}_{y}^{\text{ff}}, and Fzff{F}_{z}^{\text{ff}}represent the nodal forces on free-field boundary meshes in x-, y-, and z-directions, respectively.Figure 4Seismic motions: (a) lateral load; (b) longitudinal load; and (c) vertical load.Figure 5Seismic model: (a) front view and (b) side view.3.5Mechanical parametersThe physical and mechanical parameters of surrounding rocks, tunnel lining, cushion, and buffer layer were obtained from the geological survey report and laboratory results, as listed in Table 2.Table 2Physical and material parametersMaterialDensity (kg/m3)Elastic modulus (GPa)Poisson’s ratioCohesion (MPa）Internal friction angle (°)Surrounding Ⅱ rock2,500200.21.550Surrounding Ⅴ rock2,0001.50.40.125C45 waterproof concrete2,50033.50.2——C25 Concrete2,200250.2——Buffer layer2,30080.25——Bedrock2,800200.21.5503.6Monitoring systemConsidering the super-large size of the segment, 23 measuring points (A1–A23) were arranged at the segment surface, in which A1, A3, A5, A7, A9, A15, A17, A19, A21, and A23 are at joints, A2, A4, A6, A8, A16, A18, A20, and A22 are on the plates, A10–A14 are on the partition walls, as illustrated in Figure 6.Figure 6Measuring points.4Result and analysis4.1Lining deformation analysisFigure 7 illustrates the deformation of the super-large pipe gallery under the nine-degree seismic motion. The deformation program presents the same characteristics in four conditions. The joint of the middle column (i.e., A19) suffers the largest deformation, while A10 at the left sidewall experiences relatively few seismically induced deformations. The utility tunnel is subject to various forces during earthquakes, including forced displacement, seismic inertial forces, and soil loads. The middle column’s deformation is the most significant due to the larger spans of the Integrated module and Power module 1. For Condition 1, the maximum and minimum deformations appear at A19 and A10, 12.15 and 10.05 mm, respectively. In Condition 2, the maximum and minimum deformation of the super-large gallery decreases to 10.56 and 9.64 mm after employing the cushion scheme. When the sponge rubber plate was partly adopted in the super-large gallery, the maximum deformation has a reduction percentage of 18.11% compared with Condition 1. Finally, the maximum and minimum deformation decreases to 7.68 and 6.38 mm when the integral buffer layer is performed. As a result, the cushion and buffer layers have decreased the seismic deformation for the super-large utility tunnel, in which the integral buffer layer presents the most dramatical seismic effect (36.79%), followed by the partial buffer layer (18.11%) and the cushion scheme (13.00%), as summarized in Table 3.Figure 7Deformation of the super-large gallery. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: m).Table 3Maximum segment deformationCalculation conditionsSeismic schemesMaximum deformation (mm)Reduction percentage1—12.15—2Cushion scheme10.5713.003Partial buffer layer9.9518.114Integral buffer layer7.6836.794.2Principal stress analysisFigure 8 plots the maximum principal stress (i.e., the maximum component of the principal stress) of the super-large pipe gallery under the action of the strong earthquakes. Generally, the stress concentration emerges at joints of the plates and column, especially at A15, A17, A19, A21, and A23. In Condition 1, the peak value of the maximum principal stress of the super-large gallery pipe is 1.18 MPa, and it decreases to 0.83 MPa, with a decreasing percentage of 29.66% in Condition 2. When the partial buffer layer is conducted in Condition 3, the maximum decreases to 0.78 MPa, with a 33.90% decreasing percentage. Finally, when the gallery pipe was wrapped integrally with the 10 cm thick sponge rubber plate, the maximum principal stress is 0.46 MPa, which presents a 61.02% reduction with respect to Condition 1.Figure 8Maximum principal stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Differing from the maximum principal stress, the concentration of the minimum principal stress (i.e., the minimum component of the principal stress) emerges at the roof plate (Figure 9), especially at A1, A2, A4, A6, and A8. The peak value of the minimum principal stress is 2.31 MPa in Condition 1, and it reduces to 2.19 MPa when the cushion is employed under the baseboard, with a 5.2% reduction. If the buffer layer is wrapped partially (i.e., Condition 3), the minimum principal stress decreases to 1.89 MPa, and an 18.18% decrease is observed compared with the original tunnel. In turn, the minimum principal stress decreases to 1.63 MPa, with a 29.44% reduction percentage accordingly, when employing the integral buffer layer for the super-large utility tunnel.Figure 9Minimum principal stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Table 3 lists the principal stress and reduction in the super-large pipe gallery compared with Condition 1. As will be readily seen, the application of four isolation schemes could reduce or absorb the seismic motion, thus weakening the seismic force on the tunnel, and finally relieving the stress concentration of the tunnel segments. In terms of the principal stress, the integral buffer layer presents the dramatical isolation effect for the super-large pipe gallery, followed by the partial buffer and the cushion scheme.4.3Shear stress analysisAs illustrated in Figure 10, the concentration of the maximum shear stress (i.e., the maximum component of the structural shear stress after the earthquake) appears on joints and columns, especially at A12, A13, A14, A15, and A23. From Table 4, the peak shear stress reaches 1.11 MPa for the super-large pipe gallery without seismic schemes. However, it reduces to 0.90 MPa when performing the C25 concrete cushion, with a reduction of 18.49%. In Condition 3, the maximum decreases to 0.76 MPa with a reduction of 31.86%, when the partial buffer layer was adopted for the super-large pipe gallery. Besides, the peak of the shear stress presents a dramatical reduction while the integral buffer layer conducts in the seismic design, with a peak value of 0.71 MPa and a corresponding reduction of 35.78%. Moreover, the stress concentration in the original tunnel and the tunnel with cushion scheme mainly occurs at the corners of the pipe gallery, whereas in calculation Conditions 3 and 4, it appears in the middle partition walls. This is due to the buffer layer not only reducing the seismic impact on the structure but also promoting more uniform force distribution, thus reducing the occurrence of stress concentration.Figure 10Maximum shear stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Table 4Maximum and minimum principal stressCalculation conditionsSeismic schemesMaximum principal stress (MPa)Reduction percentageMaximum principal stress (MPa)Reduction percentage1—1.18—2.31—2Cushion scheme0.8329.662.195.203Partial buffer layer0.7833.901.8918.184Integral buffer layer0.4661.021.6329.44To sum up, same as the deformation and principal stresses, the cushion, the partial buffer layer, and the integral buffer layer minimize the seismic motion on the segments, thus decreasing the shear stress. In the aspect of the shear stress, as listed in Table 5, the integral sponge rubber plate performs the most excellent seismic isolation behaviors, followed by the partial buffer layer and the cushion scheme.Table 5Maximum shear stressCalculation conditionsSeismic schemesMaximum shear stress (MPa)Reduction percentage1—1.11—2Cushion scheme0.9018.493Partial buffer layer0.7631.864Integral buffer layer0.7135.784.4Safety factor analysisThe safety factor, introduced in the China Code, was employed as the evaluation index of structural safety in seismically vulnerable areas in this study [28,29]. The safety factor is calculated by equations (5) and (6). From the history load of the safety of the A1 and A19 (Figures 11 and 12), the seismic response of different points and condition presents a huge difference. In theory, the tunnel presents a weaker seismic performance as the safety decreases. Thus, the minimum safety factors of the points for the super-large pipe gallery were summarized in Figure 13.(5)KN≤ϕδRabh,KN\le \phi \delta {R}_{a}bh,(6)KN≤ϕ1.75Rlbh6e0h−1,KN\le \phi \frac{1.75{R}_{l}bh}{\frac{6{e}_{0}}{h}-1},where K is the safety factor; ϕ\phi is the longitudinal bending coefficient; δ\delta is the influence coefficient of axial force eccentricity; Ra{R}_{a}is the ultimate compressive strength of concrete; b is the width of tunnel section; h is the thickness of section; Rl{R}_{l}is the ultimate tensile strength of concrete; and e0{e}_{0}is the eccentricity of the section.Figure 11Safety factors of A1. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer.Figure 12Safety factors of A19. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer.Figure 13Minimum safety factor.For the tunnel without the buffer layer, the minimum safety factor emerges at A15 and A23, 2.17 and 1.86, respectively. These two joints may suffer serious seismic injury under strong earthquakes, and isolation must be employed to increase the seismic behaviors. When the cushion scheme was adopted in the super-large pipe gallery, the minimum safety factor at A15 and A23 increases to 5.15 and 2.19, with a growth rate of 137.33 and 17.74%, respectively. Then, the minimum safety factor of A15 and A23 reaches 6.29 and 2.28, when the partial buffer layer was performed. Finally, while the gallery pipe was wrapped with the 10 cm thick sponge rubber plate, the minimum safety factor increases to 8.29 and 3.68, respectively. The application of four schemes increases the safety factor for the super-large pipe gallery.To clarify, the seismic isolation effect is defined in equation (7), that is, the growth rate of the minimum safety factor of the gallery in Conditions 2–4 with respect to Condition 1. In this study, the A23, as the most dangerous position, is chosen to calculate the seismic isolation effect of three schemes, as listed in Table 6. To sum up, the integral sponge rubber plate has the most excellent seismic isolation effect (97.85%), followed by the partial buffer layer (22.58%) and the cushion (15.07%).(7)ρs=SE−SOSO×100%,{\rho }_{\text{s}}=\frac{{S}_{\text{E}}-{S}_{\text{O}}}{{S}_{\text{O}}}\times 100 \% ,where ρs{\rho }_{\text{s}}represents the seismic isolation effect; SE{S}_{\text{E}}represents the minimum safety factor of the pipe gallery with seismic isolation measures (i.e., Conditions 2–4); and SO{S}_{\text{O}}represents the minimum safety factor of the original pipe gallery.Table 6Seismic isolation effectCalculation conditionsSeismic schemesMinimum safety factorSeismic isolation effect (%)1—1.86—2Cushion scheme2.1915.073Partial buffer layer2.2822.584Integral buffer layer3.6897.855ConclusionThis study explores the seismic isolation scheme for the largest section shallow pipe gallery located in the seismic vulnerability area in China. The aseismic effects of three seismic approaches, namely, the cushion scheme, partial buffer layer, and integral buffer layer, were investigated. The various indexes including the lining deformation, the principal stress, the shear stress, as well as the safety factor, under the strong seismic motions were researched. Although the types and excitation directions of seismic motion, anisotropy of materials, and theoretical derivation have not been explored in this article, some significant conclusions can still be drawn:(1)The cushion scheme was found to reduce the lining deformation by 13.00%, the maximum and minimum principal stress by 29.66 and 5.20%, respectively, the maximum shear stress by 18.49%, and the safety factor by 15.07% for the super-large comprehensive pipe gallery tunnel.(2)After the partial buffer layer was employed, the lining deformation, the maximum and minimum principal stresses, maximum shear stress, and safety factor of the super-large pipe gallery present a reduction of 18.11, 33.90, 18.18, 31.86, and 22.58%, respectively.(3)When the integral buffer layer is adopted in the super-large comprehensive pipe gallery, the lining deformation decreases by 36.79%, the maximum and minimum principal stress decreases by 61.02 and 29.44%, the maximum shear stress decreases by 35.78%, and the minimum safety increases by 97.85%.(4)The cushion scheme, the partial buffer layer, and the integral buffer layer can all absorb and minimize the seismic motion on the tunnel structure, thus reducing the deformation, stress concentration, and internal force, and ultimately enhancing the seismic safety of the super-large pipe gallery. The integral buffer layer presents the most dramatic seismic isolation effect, followed by the partial buffer layer and the cushion scheme.(5)Based on the deformation, principal stresses, shear stress, and structural safety factor, the integral buffer layer is recommended for employing the seismic design for the present super-large pipe gallery. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Rheology de Gruyter

Application of isolation technology in shallow super-large comprehensive pipe galleries in seismically vulnerable areas with weak soils

Ma, Jianfei; Cui, Guangyao; He, Shaohui; Liu, Xiabing
Applied Rheology , Volume 33 (1): 1 – Jan 1, 2023
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de Gruyter
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© 2023 the author(s), published by De Gruyter
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1617-8106
DOI
10.1515/arh-2022-0150
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Abstract

1IntroductionThe rapid development of the infrastructure has led to a growing demand for large-section and comprehensive urban tunnels that integrate drainage pipelines, natural gas pipelines, energy, and transportation caves into a large cross-section structure [1]. Comprehensive urban tunnels are environmentally friendly and have high space utilization [2], but their large cross-section and multifunctionality can increase the risk of severe damage during earthquakes, resulting in economic and societal losses. Additionally, these comprehensive urban tunnels are often located in the downtown area, making seismic maintenance extremely difficult [3]. As a result, there is considerable interest in developing seismic response and seismic technology for super-large urban tunnels.It has long been believed that tunnels suffer less seismic excitation because they are surrounded by soils or rocks, but severe hazards have been observed in recent earthquake events, including rock falling, lining uplifting, soil liquefaction, structure cracking, as well as collapsing [4,5]. The seismic reviews have indicated that the urban tunnel, with weak geological conditions and shallow depth, may suffer much more serious catastrophes in the seismically vulnerable areas [6,7].In this regard, a large number of research works have been conducted on the seismic design for shallow urban tunnels, mainly containing the dynamic behaviors and seismic resistance. In terms of the dynamic response, Wang et al. and Sun et al. explored the dynamic response of shallow-bias tunnels with asymmetric loading [8,9]. Sun et al. and Wang et al. researched the seismic responses and damage mechanisms of the portal section of the shallow buried tunnel [10,11]. An et al. optimized the seismic ground motion parameters and analyzed their correlations with seismic behaviors for the shallow-buried rectangular tunnel [12]. Other parameters such as the rock joint [13], the cross-section [14], and geological conditions [4] have also been observed.The seismic resistance comprises the reinforcement method and shock absorption. In terms of the reinforcement method, the lining reinforcement (including the fiber-reinforced concretes, high-performance concrete, special seismic structure, etc.) and the rock strengthening (including the grouting, rock bolt, and so on) are two main fields [15]. Nevertheless, the reinforcement method cannot have an ideal effect in strong seismically vulnerable zones, especially in complex geological conditions [16]. Therefore, the Japanese scholars first proposed the isolation layer, that is, employing a layer of flexible special materials, aiming to absorb or isolate the seismic excitation on the tunnel structure [17,18]. Afterward, Wang and Cui proposed the isolation model of the tunnel, and factors such as layer stiffness, input motion, and damping were evaluated [19]. Ma et al. introduced foamed concrete as the isolation material and explored its shock absorption capacity through indoor tests and finite element method [20]. To date, various isolation layers have been put forward, such as the sponge rubber sheet, foam concrete, asphalt sand, and so on, and their thickness, construction position, and interaction with other aseismic measures are explored in detail. The above studies have provided a scientific guide for the urban tunnel in seismically active zones. However, due to the relatively slow development of the super-large and extremely shallow buried tunnels, the seismic response and shock absorption for the super-large pipe are rarely investigated, let alone for the tunnel in weak soils.Therefore, in this study, based on the largest section urban pipe gallery with a shallow buried depth in weak soils, the seismic response for the super-large urban pipe gallery is explored by the finite difference method, and the isolation scheme was explored. The seismic effect of the cushion scheme, the partial buffer layer, and the integral buffer layer were investigated by the full earthquake simulation. Various indexes such as the deformation, principal stresses, shear stress, and safety factors were analyzed in detail.2Research backgroundThe research object, located in the Xiong’an New Area of the Hebei Province, China, is a comprehensive urban pipe gallery consisting of four chambers in total, namely, a gas module, an integrated module, and two power modules, as illustrated in Figure 1. This pipe gallery, with the largest section and hoisting weight at present in China, was classified as the super-large section gallery referring to the China Code [21]. Besides, this pipe gallery employs the prefabrication and hoisting scheme for the construction. The segment is C45 waterproof concrete, and the 4 m and 8 m long pipes are approximately 201 t and 402 t, respectively [22]. Geologically, the tunnel is situated in weak soils, which mainly includes clay, silty clay, and silty fine sand. The seismic-fortification intensity of the tunnel site areas is eight degree, and it increases to nine degree for some significant facilities [23]. Therefore, the nine-degree seismic intensity is employed for the super-large pipe gallery in our research.Figure 1The super-large comprehensive urban pipe galley (unit: mm).3Full seismic model3.1Calculation conditionTo explore the isolation technology for the super-large pipe gallery, three seismic conditions with isolation schemes and one without approach were used in the numerical simulation, as listed in Table 1. The C25 concrete and the sponge rubber plate, with a thickness of 10 cm, were chosen as the cushion and the buffer layer, respectively. And the cushion and buffer layers are set between the initial support and linings. Figure 2 plots the detailed profiles of four calculation conditions, in which the red line represents the seismic measures.Table 1Calculation conditionsCalculation conditionRemarks1Original tunnel2Tunnel with cushion3Tunnel with partial buffer layer4Tunnel with integral buffer layerFigure 2Calculation conditions: (a) Condition 1; (b) Condition 2; (c) Condition 3; and (d) Condition 4.3.2Software situationFLAC3D, developed by Itasca International Inc., is a professional geotechnical analysis software. The software employs the Lagrange fast difference method, which can calculate the deformation, stress, and stability of the rock mass under various external loads, especially in the analysis of the large deformation problem and post-peak characteristics after soil failure [24]. At present, the software has been widely used in slopes, foundation pits, tunnels, underground caverns, mining, energy, and nuclear waste village. Besides, in terms of the nonlinear dynamic calculation, FLAC can conduct the three-dimensional complete dynamic analysis, and its fully nonlinear method can follow any nonlinear constitutive model that can be specified. It can not only simulate the interference of seismic waves with different frequencies and irreversible displacement but also reproduce the propagation of shear and compression waves.3.3Basic assumption(1)It is supposed that the rock, primary support, lining, cushion layer, and buffer layer are homogeneous and isotropic materials.(2)The failure of the rock mass follows the Mohr–Coulomb criterion, and the linear elastic model is adopted for primary lining, secondary lining, cushion, and buffer layers.(3)The lateral, longitudinal, and vertical directions of the seismic motion correspond to the x-, y-, and z-axis of the numerical model, respectively.3.4Numerical modelThe mesh is established by the professional CAE software (i.e., HyperMesh Software), and then imported into FLAC3D. Considering computer performances, working efficiency, grid control method (equation (1)), and a large number of trial calculations, the mesh for the buffer layer, cushion layer, and the mesh of the pipe gallery is 0.2–0.5 m, and the rock in blue is 0.5–1.0 m, while the mesh size of the rock in red and green is 1.0–3.0 m [25], as shown in Figure 3.(1)Δl≤(18−110)λ,\text{Δ}l\left\le \left(\frac{1}{8}\left-\frac{1}{10}\right)\lambda ,where Δl\text{Δ}lindicates the maximum size of the grid; and λ\lambda is the wavelength corresponding to the seismic waves with highest frequency.Figure 3Calculation model of the initial stress field.The bedrock layer is within 10 m from the bottom of the model to simulate the rigid foundation in the natural stratum. Moreover, it is indicated that there is complete contact between the surrounding rock and lining, lining and damping layer, that is, the normal and tangential displacement and stress between contact surfaces are equal.The isolation simulation comprises the initial stress calculation and the seismic dynamic calculation. First, the normal constraint and quiet boundary are employed at the four sides and bottom in the static model, as illustrated in Figure 3. Then, the excavation and support procedures of the tunnel are performed in the numerical simulation, to seek the actual stress field in the natural condition. A vital step in the static calculation is that the displacement field is eliminated, while the stress field is not modified.In the seismic dynamic calculation, the 2008 Wenchuan Earthquake acceleration waves, recorded by the Wolong Station, are chosen as the original dynamic loads [26]. The seismic boundary conditions are applied at the model boundary or internal nodes to simulate the external and internal dynamic loads borne by rock mass in the FLAC3D. In the present research, the seismic motions propagate upward from the bottom after filtering and baseline correction. Filtering can eliminate noise waves during the collection of seismic waves, while baseline correction can eliminate residual displacement at the end of dynamic calculations. Figure 4 plots the modified seismic waves employed in the simulation. Meanwhile, the free-field boundary is adopted to reduce or eliminate the reflection of seismic waves, as shown in Figure 5. Equations (2)–(4) give the calculation method of unbalanced force at the free-field boundary. Considering that the local damping is independent of frequency and could obtain a more accurate solution, the local damping with a coefficient of 0.157 is employed during the dynamic calculation [27].(2)Fx=−ρCp(υxm−υxff)A+Fxff,{F}_{x}=-\rho {C}_{\text{p}}({\upsilon }_{x}^{\text{m}}-{\upsilon }_{x}^{\text{ff}})A+{F}_{x}^{\text{ff}},(3)Fy=−ρCs(υym−υyff)A+Fyff,{F}_{y}=-\rho {C}_{\text{s}}({\upsilon }_{y}^{\text{m}}-{\upsilon }_{y}^{\text{ff}})A+{F}_{y}^{\text{ff}},(4)Fz=−ρCs(υzm−υzff)A+Fzff,{F}_{z}=-\rho {C}_{\text{s}}({\upsilon }_{z}^{\text{m}}-{\upsilon }_{z}^{\text{ff}})A+{F}_{z}^{\text{ff}},where Fx{F}_{x}, Fy{F}_{y}, and Fz{F}_{z}represent the force applied to the main mesh by the free-field boundary in the x-, y-, and z-directions, respectively; ρ\rho represents the density of the model along the vertical direction; Cp{C}_{\text{p}}and Cs{C}_{\text{s}}represent the propagation velocity of compression wave and shear wave of side boundaries, respectively; AArepresents the influence area of free field grid; υxm{\upsilon }_{x}^{\text{m}}, υym{\upsilon }_{y}^{\text{m}}, and υzm{\upsilon }_{z}^{\text{m}}represent the velocity in x-, y-, and z-directions of the main mesh of the side boundary, respectively; υxff{\upsilon }_{x}^{\text{ff}}, υyff{\upsilon }_{y}^{\text{ff}}, and υzff{\upsilon }_{z}^{\text{ff}}represent the velocity in x-, y-, and z-directions of the side free-field grid, respectively; Fxff{F}_{x}^{\text{ff}}, Fyff{F}_{y}^{\text{ff}}, and Fzff{F}_{z}^{\text{ff}}represent the nodal forces on free-field boundary meshes in x-, y-, and z-directions, respectively.Figure 4Seismic motions: (a) lateral load; (b) longitudinal load; and (c) vertical load.Figure 5Seismic model: (a) front view and (b) side view.3.5Mechanical parametersThe physical and mechanical parameters of surrounding rocks, tunnel lining, cushion, and buffer layer were obtained from the geological survey report and laboratory results, as listed in Table 2.Table 2Physical and material parametersMaterialDensity (kg/m3)Elastic modulus (GPa)Poisson’s ratioCohesion (MPa）Internal friction angle (°)Surrounding Ⅱ rock2,500200.21.550Surrounding Ⅴ rock2,0001.50.40.125C45 waterproof concrete2,50033.50.2——C25 Concrete2,200250.2——Buffer layer2,30080.25——Bedrock2,800200.21.5503.6Monitoring systemConsidering the super-large size of the segment, 23 measuring points (A1–A23) were arranged at the segment surface, in which A1, A3, A5, A7, A9, A15, A17, A19, A21, and A23 are at joints, A2, A4, A6, A8, A16, A18, A20, and A22 are on the plates, A10–A14 are on the partition walls, as illustrated in Figure 6.Figure 6Measuring points.4Result and analysis4.1Lining deformation analysisFigure 7 illustrates the deformation of the super-large pipe gallery under the nine-degree seismic motion. The deformation program presents the same characteristics in four conditions. The joint of the middle column (i.e., A19) suffers the largest deformation, while A10 at the left sidewall experiences relatively few seismically induced deformations. The utility tunnel is subject to various forces during earthquakes, including forced displacement, seismic inertial forces, and soil loads. The middle column’s deformation is the most significant due to the larger spans of the Integrated module and Power module 1. For Condition 1, the maximum and minimum deformations appear at A19 and A10, 12.15 and 10.05 mm, respectively. In Condition 2, the maximum and minimum deformation of the super-large gallery decreases to 10.56 and 9.64 mm after employing the cushion scheme. When the sponge rubber plate was partly adopted in the super-large gallery, the maximum deformation has a reduction percentage of 18.11% compared with Condition 1. Finally, the maximum and minimum deformation decreases to 7.68 and 6.38 mm when the integral buffer layer is performed. As a result, the cushion and buffer layers have decreased the seismic deformation for the super-large utility tunnel, in which the integral buffer layer presents the most dramatical seismic effect (36.79%), followed by the partial buffer layer (18.11%) and the cushion scheme (13.00%), as summarized in Table 3.Figure 7Deformation of the super-large gallery. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: m).Table 3Maximum segment deformationCalculation conditionsSeismic schemesMaximum deformation (mm)Reduction percentage1—12.15—2Cushion scheme10.5713.003Partial buffer layer9.9518.114Integral buffer layer7.6836.794.2Principal stress analysisFigure 8 plots the maximum principal stress (i.e., the maximum component of the principal stress) of the super-large pipe gallery under the action of the strong earthquakes. Generally, the stress concentration emerges at joints of the plates and column, especially at A15, A17, A19, A21, and A23. In Condition 1, the peak value of the maximum principal stress of the super-large gallery pipe is 1.18 MPa, and it decreases to 0.83 MPa, with a decreasing percentage of 29.66% in Condition 2. When the partial buffer layer is conducted in Condition 3, the maximum decreases to 0.78 MPa, with a 33.90% decreasing percentage. Finally, when the gallery pipe was wrapped integrally with the 10 cm thick sponge rubber plate, the maximum principal stress is 0.46 MPa, which presents a 61.02% reduction with respect to Condition 1.Figure 8Maximum principal stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Differing from the maximum principal stress, the concentration of the minimum principal stress (i.e., the minimum component of the principal stress) emerges at the roof plate (Figure 9), especially at A1, A2, A4, A6, and A8. The peak value of the minimum principal stress is 2.31 MPa in Condition 1, and it reduces to 2.19 MPa when the cushion is employed under the baseboard, with a 5.2% reduction. If the buffer layer is wrapped partially (i.e., Condition 3), the minimum principal stress decreases to 1.89 MPa, and an 18.18% decrease is observed compared with the original tunnel. In turn, the minimum principal stress decreases to 1.63 MPa, with a 29.44% reduction percentage accordingly, when employing the integral buffer layer for the super-large utility tunnel.Figure 9Minimum principal stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Table 3 lists the principal stress and reduction in the super-large pipe gallery compared with Condition 1. As will be readily seen, the application of four isolation schemes could reduce or absorb the seismic motion, thus weakening the seismic force on the tunnel, and finally relieving the stress concentration of the tunnel segments. In terms of the principal stress, the integral buffer layer presents the dramatical isolation effect for the super-large pipe gallery, followed by the partial buffer and the cushion scheme.4.3Shear stress analysisAs illustrated in Figure 10, the concentration of the maximum shear stress (i.e., the maximum component of the structural shear stress after the earthquake) appears on joints and columns, especially at A12, A13, A14, A15, and A23. From Table 4, the peak shear stress reaches 1.11 MPa for the super-large pipe gallery without seismic schemes. However, it reduces to 0.90 MPa when performing the C25 concrete cushion, with a reduction of 18.49%. In Condition 3, the maximum decreases to 0.76 MPa with a reduction of 31.86%, when the partial buffer layer was adopted for the super-large pipe gallery. Besides, the peak of the shear stress presents a dramatical reduction while the integral buffer layer conducts in the seismic design, with a peak value of 0.71 MPa and a corresponding reduction of 35.78%. Moreover, the stress concentration in the original tunnel and the tunnel with cushion scheme mainly occurs at the corners of the pipe gallery, whereas in calculation Conditions 3 and 4, it appears in the middle partition walls. This is due to the buffer layer not only reducing the seismic impact on the structure but also promoting more uniform force distribution, thus reducing the occurrence of stress concentration.Figure 10Maximum shear stress. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer. (Unit: Pa).Table 4Maximum and minimum principal stressCalculation conditionsSeismic schemesMaximum principal stress (MPa)Reduction percentageMaximum principal stress (MPa)Reduction percentage1—1.18—2.31—2Cushion scheme0.8329.662.195.203Partial buffer layer0.7833.901.8918.184Integral buffer layer0.4661.021.6329.44To sum up, same as the deformation and principal stresses, the cushion, the partial buffer layer, and the integral buffer layer minimize the seismic motion on the segments, thus decreasing the shear stress. In the aspect of the shear stress, as listed in Table 5, the integral sponge rubber plate performs the most excellent seismic isolation behaviors, followed by the partial buffer layer and the cushion scheme.Table 5Maximum shear stressCalculation conditionsSeismic schemesMaximum shear stress (MPa)Reduction percentage1—1.11—2Cushion scheme0.9018.493Partial buffer layer0.7631.864Integral buffer layer0.7135.784.4Safety factor analysisThe safety factor, introduced in the China Code, was employed as the evaluation index of structural safety in seismically vulnerable areas in this study [28,29]. The safety factor is calculated by equations (5) and (6). From the history load of the safety of the A1 and A19 (Figures 11 and 12), the seismic response of different points and condition presents a huge difference. In theory, the tunnel presents a weaker seismic performance as the safety decreases. Thus, the minimum safety factors of the points for the super-large pipe gallery were summarized in Figure 13.(5)KN≤ϕδRabh,KN\le \phi \delta {R}_{a}bh,(6)KN≤ϕ1.75Rlbh6e0h−1,KN\le \phi \frac{1.75{R}_{l}bh}{\frac{6{e}_{0}}{h}-1},where K is the safety factor; ϕ\phi is the longitudinal bending coefficient; δ\delta is the influence coefficient of axial force eccentricity; Ra{R}_{a}is the ultimate compressive strength of concrete; b is the width of tunnel section; h is the thickness of section; Rl{R}_{l}is the ultimate tensile strength of concrete; and e0{e}_{0}is the eccentricity of the section.Figure 11Safety factors of A1. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer.Figure 12Safety factors of A19. (a) Original tunnel; (b) tunnel with the cushion; (c) tunnel with the partial buffer layer; and (d) tunnel with the integral buffer layer.Figure 13Minimum safety factor.For the tunnel without the buffer layer, the minimum safety factor emerges at A15 and A23, 2.17 and 1.86, respectively. These two joints may suffer serious seismic injury under strong earthquakes, and isolation must be employed to increase the seismic behaviors. When the cushion scheme was adopted in the super-large pipe gallery, the minimum safety factor at A15 and A23 increases to 5.15 and 2.19, with a growth rate of 137.33 and 17.74%, respectively. Then, the minimum safety factor of A15 and A23 reaches 6.29 and 2.28, when the partial buffer layer was performed. Finally, while the gallery pipe was wrapped with the 10 cm thick sponge rubber plate, the minimum safety factor increases to 8.29 and 3.68, respectively. The application of four schemes increases the safety factor for the super-large pipe gallery.To clarify, the seismic isolation effect is defined in equation (7), that is, the growth rate of the minimum safety factor of the gallery in Conditions 2–4 with respect to Condition 1. In this study, the A23, as the most dangerous position, is chosen to calculate the seismic isolation effect of three schemes, as listed in Table 6. To sum up, the integral sponge rubber plate has the most excellent seismic isolation effect (97.85%), followed by the partial buffer layer (22.58%) and the cushion (15.07%).(7)ρs=SE−SOSO×100%,{\rho }_{\text{s}}=\frac{{S}_{\text{E}}-{S}_{\text{O}}}{{S}_{\text{O}}}\times 100 \% ,where ρs{\rho }_{\text{s}}represents the seismic isolation effect; SE{S}_{\text{E}}represents the minimum safety factor of the pipe gallery with seismic isolation measures (i.e., Conditions 2–4); and SO{S}_{\text{O}}represents the minimum safety factor of the original pipe gallery.Table 6Seismic isolation effectCalculation conditionsSeismic schemesMinimum safety factorSeismic isolation effect (%)1—1.86—2Cushion scheme2.1915.073Partial buffer layer2.2822.584Integral buffer layer3.6897.855ConclusionThis study explores the seismic isolation scheme for the largest section shallow pipe gallery located in the seismic vulnerability area in China. The aseismic effects of three seismic approaches, namely, the cushion scheme, partial buffer layer, and integral buffer layer, were investigated. The various indexes including the lining deformation, the principal stress, the shear stress, as well as the safety factor, under the strong seismic motions were researched. Although the types and excitation directions of seismic motion, anisotropy of materials, and theoretical derivation have not been explored in this article, some significant conclusions can still be drawn:(1)The cushion scheme was found to reduce the lining deformation by 13.00%, the maximum and minimum principal stress by 29.66 and 5.20%, respectively, the maximum shear stress by 18.49%, and the safety factor by 15.07% for the super-large comprehensive pipe gallery tunnel.(2)After the partial buffer layer was employed, the lining deformation, the maximum and minimum principal stresses, maximum shear stress, and safety factor of the super-large pipe gallery present a reduction of 18.11, 33.90, 18.18, 31.86, and 22.58%, respectively.(3)When the integral buffer layer is adopted in the super-large comprehensive pipe gallery, the lining deformation decreases by 36.79%, the maximum and minimum principal stress decreases by 61.02 and 29.44%, the maximum shear stress decreases by 35.78%, and the minimum safety increases by 97.85%.(4)The cushion scheme, the partial buffer layer, and the integral buffer layer can all absorb and minimize the seismic motion on the tunnel structure, thus reducing the deformation, stress concentration, and internal force, and ultimately enhancing the seismic safety of the super-large pipe gallery. The integral buffer layer presents the most dramatic seismic isolation effect, followed by the partial buffer layer and the cushion scheme.(5)Based on the deformation, principal stresses, shear stress, and structural safety factor, the integral buffer layer is recommended for employing the seismic design for the present super-large pipe gallery.

Journal

Applied Rheology – de Gruyter

Published: Jan 1, 2023

Keywords: shallow pipe gallery; isolation scheme; buffer layer; cushion scheme; seismic response

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