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Seismic response and damage mechanism of tunnel lining in sensitive environment of soft rock stratum

Seismic response and damage mechanism of tunnel lining in sensitive environment of soft rock stratum 1IntroductionContinuously, tunnels and other underground structures have always been considered to perform good and not easily be damaged by earthquakes. However, seismic damage investigations show that some tunnels have experienced considerable damage [1,2,3,4,5] during recent strong earthquakes. And the tunnel lining at the tunnel portal approaching or adjacent to the fault fracture zones have been especially affected or destroyed seriously [6,7,8,9]. In the southwest of China and Sichuan–Tibet region, the bridge–tunnel overlapping section is a kind of special type of engineering combined by bridge, tunnel, slope, valley, and fragile surrounding rocks, which must be designed and constructed due to the limitations of terrain, landform, and geology reasons. Such kind of bridge–tunnel overlapping sections (the “bridge–tunnel overlapping section” shall hereinafter be collectively referred to as the “BTOS”) have always ensured smooth traffic in special sections of mountain areas. However, although the southwest mountain areas of China are located in the Himalayan seismic zone, there are a large number of bridge–tunnel overlapping projects that have been built or are being built in plan in these seismic sensitive areas. Therefore, the seismic fortification of tunnel portals in the bridge–tunnel overlapping section in strong dynamic sensitive environment have become key problems which need to be solved urgently enough in these kinds of engineering. And it has become one of the hot spots in the analyses or research works of those kind of complex engineering structures in recent years.In recent years, there are many scholars who have carried out a lot of research works on the dynamic responses of tunnel structures or tunnel portal sections through shaking table model test or numerical simulation methods at home and abroad. Wang et al. [10] compared and analyzed the influences and performances on the dynamic characteristics of the portal section of double tunnel in the presence or absence of the damping layers using shaking table test method. Tao et al. [11] conducted the shaking table tests on the portal section of mountain tunnel in weak surrounding rocks, and pointed out the amplification effects of the acceleration of surrounding rocks at the portal due to the existence of free surfaces of inverted slope, and got the conclusion that the seismic additional stress was mainly concentrated in tunnel spandrel and arch foot of the tunnel. Hou et al. [12] carried out the shaking table model tests on the portal section of mountain tunnel using the seismic excitations of Wenchuan waves in different loading directions, and analyzed the deformation modes and failure mechanism of tunnel structure caused by different excitation directions. By comparing the shaking table model tests and numerical calculation results of the portal section of the shallow buried biased tunnel, Li et al. [13] showed that those two kinds of results were in good agreements, and pointed out that the cross-sectional internal force of the non-biased tunnel showed an anti-symmetric distribution, while the biased tunnel showed a more unfavorable internal force value distribution and a large peak value. Shen et al. [14] found that the number of tunnel lining cracks with damping layers was significantly reduced with the different settings of damping layer (with or none damping layer) at the entrance section of mountain tunnels, while the maximum seismic response positions and failure modes of the tunnel were basically consistent with the failure condition of tunnel in Wenchuan earthquake of China on May 12, 2008 when without any damping layer.In addition, scholars and engineers have made some achievements in the research works of bridge and tunnel transition section over the past decade. Considering the interaction of surrounding rocks, tunnel linings, and abutments, Shi et al. [15] analyzed the influences of train speed, height span ratio, and the length of the abutment extending into the tunnel on the static and dynamic responses of tunnel structure using the three-dimensional static and dynamic finite element methods. Bi et al. [16] tested the influence of different vehicle lengths and vehicle speeds on the dynamic response of bridge tunnel transition section through field tests, and studied whether the dynamic characteristics of bridge–tunnel transition section are consistent when trains pass through the bridge–tunnel junction segment with different vehicle speeds and vehicle lengths. Chao et al. [17] established the dynamic coupling calculation model of vehicle and pavement according to the D’Alembert principle, and studied the impacts of vehicle on the pavement of bridge–tunnel transition section under the conditions of vehicle load mass, cargo position, driving speed, and differential settlements.To sum up, recent research results related to the impacts of strong dynamic sensitive environment on the bridge–tunnel connection sections mainly focus on the dynamic characteristics of the lining, surrounding rock, and slope of the tunnel portal section, as well as the dynamic response of the bridge–tunnel connecting structure under vehicle load. There are still very few reports or studies on the seismic dynamic characteristics of the tunnel lining in the bridge–tunnel overlapping section [18,19]. The bridge and tunnel overlapping structure is affected by the abutment and portal mountain, which makes its stress states and seismic responses very complex, and the existing seismic design codes do not fully consider the characteristics of bridge and tunnel overlapping structure [20,21,22]. Therefore, for those reasons mentioned above, we studied the dynamic characteristics and influencing factors of highway bridge–tunnel overlapping tunnel lining under different seismic loadings based on the method of shaking table test, so as to provide suggestions and references for earthquake-resistance design and construction of tunnel structures in the bridge–tunnel overlapping sections and projects in mountainous areas in southwest of China and Sichuan–Tibet region.2Shaking table model test scheme2.1Test equipmentThe shaking table tests were carried out in the National Engineering Laboratory for High-Speed Railway Construction. The shaking table is 4 m × 4 m six DOF movable table, the maximum displacement of which is 250 mm in X or Y direction, and the maximum acceleration is ±0.8 g under full loading, with the maximum displacement 160 mm in Z direction, the maximum acceleration ±1.6 g under full loading, and 0.1–50 Hz as the working frequency range. The shaking table and its control system are shown in Figure 1.Figure 1The shaking table system. (a) Aerial view of the shaking table; (b) surface of the shaking table; and (c) shaking table control system.2.2Similarity relationshipThe similarity relationship of this model test is deduced according to the equilibrium equation, the stress boundary conditions, and displacement boundary conditions of the prototype and model structures [10,11]. According to the second similarity theorem and dimensional analysis method, the length L, elastic modulus E, and density ρ are chosen as the three basic dimensions, other similar parameters are derived based on the above three parameters. The tunnel lining is an approximate elastic cylindrical shell structure, which bears both bending stress and axial force. The bending capacity and bending strains of the tunnel lining are the main control factors. So, the bending stiffness was chosen as the main similarity condition of the model in the tests. The geometric similarity ratio of the model test is 1/50, and the similarity constants in the shaking table model tests are shown in Table 1.Table 1Primary similitude coefficients of the modelPhysical quantitySimilarity relationSimilarity ratioPhysical quantitySimilarity relationSimilarity ratioLength llCl1/50Poisson’s ratio μCμ1Area AACA=Cl2{C}_{A}={C}_{l}^{2}1/502Time tCt=Cl0.5{C}_{t}={C}_{l}^{0.5}1/7.07Density ρ\rho Cρ{C}_{\rho }1Frequency fCf=Ct−1{C}_{f}={C}_{t}^{-1}7.07Elastic modulusEECE=CρCl{C}_{E}={C}_{\rho }{C}_{l}1/50Velocity vCv=Cl/Ct{C}_{v}={C}_{l}/{C}_{t}1/7.07Stress σ\sigma Cσ=ClCρ{C}_{\sigma }={C}_{l}{C}_{\rho }1/50Acceleration aCa=Cl/Ct2{C}_{a}={C}_{l}/{C}_{t}^{2}1Note: The site soil is mainly strong weathered shale, gravel bearing silty clay, and the site type is class II.For the tunnel model, with a geometric similarity ratio of 1 to 50, the model tunnel lining considers the comprehensive effect and reinforcement influence of the first support and secondary lining of the actual tunnel project.2.3Design of model test box and test boundaryThe model test box is an auxiliary device for the shaking table model test. A rigid model box has been used in this test, and the internal space dimensions of which are 3.5, 1.5, and 2.0 m in the length, width, and height (as shown in Figure 1). In order to increase the rigidity of the model box, the outside of the box wall is welded into a grid shape with channel steel and angle steel, and inclined supports are set at the height of 1.0 and 1.5 m. At the same time, to ensure good test results, the following treatments have also been carried out during the design and built periods of the model test box.(1)The bottom plate of the model test box shall be reserved with bolt holes for fixation according to the characteristics of the shaking table surface. Under circumstance that the structure of the model test box is firm, cut a window at an appropriate position, and place transparent tempered glass along the length of the model test box to facilitate photography and observation during the shaking model test process.(2)The natural frequency of the model test box shall be quite different to that of the “BTOS” model structure to prevent resonance between them. Through modal analysis, the first-order of natural frequencies of the model box is far away from that of the “BTOS” model rocks and soils, which shows that there will be no resonance between the model box and the internal rocks and soils during the seismic excitation processes.(3)In order to reduce the adverse effects of seismic waves at the bottom and the four side walls of the model box, the dynamic boundary of the test model (including the soil) is dealt with as follows: the bottom plate of the model is treated as a friction boundary, and the side walls of the model box are treated as flexible boundaries. A concrete plate of 8 cm thick is laid at the bottom of the model test box to make the bottom of the piles to be solid embedded. After that, a layer of 5 cm thick gravels is paved on the concrete plate to increase the friction between the surrounding rocks and the bottom of the model test box to reduce the relative displacements between the surrounding rocks and the bottom of the model test box during the test process. In order to absorb the reflected seismic waves, the confining effects of sidewalls on surrounding rock strata shall be weakened to a certain degree, then 5 cm thick polystyrene foam boards were pasted around the model test box internal walls. A layer of plastic film is attached to the surfaces of the foam boards, and on the surfaces of which oil shall be brushed to avoid the severe friction between the foam board and the rock layer, with the purpose not to affect the test results. Boundary treatments are shown in Figure 2.Figure 2Boundary treatments of model test box. (a) Treatments of model box internal walls and (b) model test box boundary treatments.2.4Model structure design and fabricationThe main design parameters of the bridge and tunnel prototypes in the shaking table model tests are as follows:(1)Prototype bridge: bridge superstructure: span 30 m × 30 m × 30 m high-speed public continuous box girder, 11.75 m wide, and 2.0 m high. The abutment is a 4-pile embedded abutment with a pile foundation diameter of 1.5 m.(2)Prototype tunnel: highway tunnel with inverted arch curved wall lining.(i)In the standard section, the net width inside the tunnel is 10.85 m. Tunnel lining parameters: 28 cm thick primary support, water proof layer, and 50 cm thick secondary lining.(ii)The enlarged section (i.e., bridge and tunnel overlapping section) has a net width of 12.0 m inside the tunnel. Tunnel lining parameters: 28 cm thick primary support, water proof layer, and 60 cm thick secondary lining.The tunnel lining is made of C30 steel reinforced micro concrete. After many mix proportion tests, the final determined material quality mix proportion of the tunnel lining is 496:631:159:5.95 (cement:sand:water:NOF-3 concrete water reducer), with internal reinforcement steel meshes of 0.5 mm diameter. The thickness of the tunnel lining standard section is 2 cm, and its length is 60 cm. The thickness of the tunnel lining enlarged section is 3 cm with a 5 cm thickness at the invert, and its length is 24.5 cm. The length of the piles model at the bottom of the tunnel lining enlarged section are all 76 cm, and its diameter is 3 cm with one φ6 ordinary R235 steel rebar along the longitudinal direction of each pile. The pile foundation at the bottom of the expanded section of the tunnel model and the lining were made up as a whole part in the structural model making process as shown in Figure 3. The bridge deck is made by C50 steel reinforced micro concrete, and the concrete material quality mix proportion of which is 477:572:167:2.39 (cement:sand:water:NOF-3 concrete water reducer). The structural models of the standard tunnel lining section, enlarged section, and bridge deck have been made, as shown in Figure 3.Figure 3Pictures of models. (a) Tunnel lining of standard section; (b) tunnel lining of enlarged section and piles at the bottom; and (c) bridge model.For weak surrounding rocks, according to the principle of similar Poisson’s ratio [15], the indoor material orthogonal tests have been carried out with unsaturated soil triaxial tester (GDS). Finally, the determined mix material plan is barite powder, quartz sand, and lithium-based lubricating oil, and its quality mix proportion is 10:5:1.2 (barite powder:quartz sand:lithium-based lubrication). In the tests, all models of bridge, tunnel, and surrounding rocks are made at the same time or in the same batch group during the modeling process. Soil in the test box was filled by layered compaction. The densities of each layer were measured for several times by cutting ring in the laying process, to ensure the consistency of soil compaction. The physical and mechanical parameters of the prepared materials are shown in Table 2.Table 2Rock material parametersSurrounding rock gradeMaterial typeModulus of elasticity/GPaPoisson’s ratioInternal friction angle/(°)Cohesion/MPaUnit weight/(kN/m³)Grade IVPrototype4.40.32341.7522Model0.0880.32340.03521.3Grade VPrototype1.80.38231.519Model0.0360.38230.0318.2The enlarged section of the tunnel portal in this test is a key component part of the whole portal structure. The mechanical model of such bridge–tunnel overlapping structure can be simplified as a model combined by the bridge, the tunnel, the road, and the surrounding rocks and soils considering the interactions between each part. Taking the influences caused by the car loadings as an example, the force transfer relationship can be assumed as: the car loading transfer first to the bridge by the road system, then to the abutments and foundations (with additional gravity of the bridge upper structures), and transfer to the tunnel structure and its surrounding rocks at last.2.5Sensor arrangementThe acceleration and dynamic strain response law of the standard section and enlarged section of the tunnel lining were mainly studied in the shaking table tests. The measuring instruments are unidirectional acceleration sensors and resistance strain gauges. The acceleration sensors used in the tests are 2210-002 type with measuring range of ±2 G and sensitivity of 2,000 mV/g. There are two types of strain gauges, one is BX120-100AA with resistance of 120 ± 0.1Ω, size of 100 mm × 3 mm, and sensitivity of 2.1 ± 2%. The other type of strain gauge is BX120-3AA, with resistance of 120 ± 1Ω, size of 3.0 mm × 2.2 mm, and sensitivity of 2.0 ± 1%. Model diagram and sensor arrangements in the test are shown in Figure 4.Figure 4Model diagram and sensor arrangements (unit: mm). (a) Diagram of model dimensions; (b) longitudinal section of measuring point arrangements of bridge–tunnel overlapping section; and (c) cross section of measuring point arrangements of bridge–tunnel overlapping section.The acceleration data of each measuring point during the test in the enlarged section and standard section of the tunnel are obtained through the following ways. Firstly, the actual acceleration data (generally 0–5 g, the letter “g” represents the acceleration of gravity) of each measure point was measured and recorded by high sensitivity acceleration sensors at each measuring point along all the three direction (direction along X, Y or Z). Then when multiple input directions are superimposed, these parameters should be accumulated by calculation results along every single direction.2.6Seismic waves and excitation schemeThe seismic wave in the shaking model test is EL Centro wave. The EL Centro seismic wave is one of the seismic waves that has been successfully recorded during such strong earthquakes on the whole process data in the world, which is of great significance to the research of earthquakes. EL Centro wave is the first seismic wave with intensity greater than 300 gal captured by human beings. The measurement of seismic wave data for large earthquakes has always been a complex problem. At that time, the instruments were relatively backward, and the measured data of these precise measurements were very rare. EL Centro wave is measured at the surface, which is suitable for Class II sites. And the dynamic responses of the “BTOS” model under different peak excitation accelerations have been analyzed. The X direction component of EL Centro wave has been chosen to load unidirectionally (X direction is horizontal and parallel to the longitudinal axis direction of the tunnel). The excitation direction is shown in Figure 4a, and the seismic excitation scheme in the test is shown in Table 3. According to the working frequency range of the test equipment, the seismic waves in the tests must be treated and simplified to the frequency range from 0.1 to 50 Hz. The acceleration–time history curve and Fourier spectrum of EL Centro wave are shown in Figure 5. From the Fourier spectrum, it can be seen that the excellent frequency of EL Centro wave is 8–17 Hz. The seismic wave acceleration excitation peak value is loaded step by step according to the order from of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 g.Table 3Seismic excitation scheme of shaking table testLoading orderSeismic wavePeak value/gDuration of time/sLoading orderSeismic wavePeak value/gDuration of time/sWN–X0.04—4EL Centro–X0.47.61EL Centro–X0.17.6WN–X0.04—WN–X0.04—5EL Centro–X0.57.62EL Centro–X0.27.6WN–X0.04—WN–X0.04—6EL Centro–X0.67.63EL Centro–X0.37.6WN–X0.04—WN–X0.04—Figure 5Acceleration–time history and Fourier spectrum of EL Centro X seismic wave. (a) Acceleration–time history curve and (b) Fourier spectrum.Before each test, a micro vibration test of white noise (Code WN–X) with a peak acceleration of about 0.04 g and a time length of about 30 s should be carried out, to observe the transformation of the dynamic characteristics of the model structure.3Test result and result analysisDue to limited time, content relevance, and the length of the article, although there are more initial measuring points and results in the test scheme, we have to choose the accelerations and strains of some key measuring points of the tunnel lining in this work for deep study. Other test results and analysis will be published in other articles.3.1Acceleration responses and damage mechanism of tunnel liningThe acceleration dynamic response characteristics of the model are analyzed by two indexes: the acceleration response peak value and the acceleration amplification coefficient. The acceleration amplification factor is defined as the ratio of the peak acceleration of the measuring point to the peak acceleration of the input seismic wave. Figure 6 shows the acceleration response time history curve of measuring point A1 near the portal end segment (at standard section I–I) of the tunnel lining when the peak excitation acceleration is 0.4 g.Figure 6Acceleration response time history curve of A1 measuring point under 0.4 g PGA of seismic wave. (a) Acceleration–time history curve and (b) Fourier spectrum.3.1.1Acceleration responses and damage mechanism at standard section I–I of tunnel liningFigure 7 shows the acceleration peak values and amplification coefficients of different measuring points at the standard section I–I of the tunnel lining under different excitation peak values.Figure 7Peak accelerations and acceleration amplification factors at the standard I–I section of the tunnel lining under different PGA of seismic waves. (a) Peak acceleration diagram and (b) acceleration amplification factor. 1 – A1, 2 – A2, 3 – A3, 4 – El-0.1 g, 5 – EL-0.2 g, 6 – EL-0.3 g, 7 – EL-0.4 g, 8 – EL-0.5 g, and 7 – EL-0.6 g.It can be seen from Figure 7a that under the seismic excitation of EL Centro X direction, the peak acceleration of inverted arch (measuring point A1), arch waist (measuring point A2), and vault (measuring point A3) in the standard section shows a nonlinear increasing trend with the increase in peak excitation acceleration, and its growth rate first increases then decreases with the increase in peak excitation acceleration. However, from 0.5 g to 0.6 g, the influence of the peak value of the earthquake excitation wave is small and basically at the maximum value. According to the preliminary judgments, the reason for this phenomenon may be that some surrounding rocks have entered the plastic state due to the increase in peak loading acceleration.In addition, it can be seen from Figure 7b that the acceleration values at each measuring point of the tunnel lining have a significant amplification effect compared with the initial excitation input seismic wave. Under the seismic excitation of EL Centro X direction with the peak value in the range of 0.1–0.6 g, the acceleration amplification factors of inverted arch (measuring point A1), arch waist (measuring point A2), and arch crown (measuring point A3) in the tunnel lining standard section are all greater than 1. And the value increases as the elevation increases. It shows that the acceleration effect of these parts is obviously amplified, and they are relatively easy to be damaged or cracked when encountering earthquakes. In addition, it is also found from the test results that the acceleration amplification coefficients at the peak values of 0.4 and 0.5 g seismic waves are significantly higher than those of the other four different peak values.3.1.2Acceleration responses and damage mechanism of tunnel lining along the tunnel axisFigure 8 shows the peak accelerations and acceleration amplification factors of the middle span (measuring point A6), the vault of the tunnel lining enlarged section (measuring point A5), the vault at the standard section I–I (measuring point A3) (near the portal end segment), and the vault at the standard section II–II (measuring point A4) (relatively far away from the portal end segment) of the tunnel lining standard section. The acceleration peak value of each measuring point increases with the increase in the seismic wave acceleration excitation peak value, and the acceleration peak value in the middle of the bridge span (measuring point A6) is the largest. This is mainly due to the bare part in the middle of the bridge span and a less constrain. The acceleration amplification coefficient of each measuring point decreases nonlinearly from the portal to the tunnel along the tunnel axis, which indicates that the acceleration amplification coefficient decreases due to the increased constraint of surrounding rocks on the tunnel lining from the portal along the tunnel axis to the tunnel depth. Because the front slope is closer to the vault of the tunnel lining enlarged section, the acceleration amplification effect of the tunnel vault (measuring point A5) of the enlarged section increases obviously due to the influence of the free surface of the front slope.Figure 8Peak accelerations and acceleration amplification factors along the axis of the tunnel under different excitation peak accelerations. (a) Peak acceleration diagram and (b) acceleration amplification factor. 1 – A3, 2 – A4, 3 – A5, 4 – A6, 5 – EL-0.1 g, 6 – EL-0.2 g, 7 – EL-0.3 g, 8 – EL-0.4 g, 9 – EL-0.5 g, and 10 – EL-0.6 g.3.2Dynamic strain responses and damage mechanism of tunnel lining3.2.1Longitudinal tensile strain responses and damage mechanismPeak values of the longitudinal tensile strains of the tunnel lining are shown in Figure 9.Figure 9Peak values of longitudinal tensile strains of the tunnel lining. (a) Peak value diagram of longitudinal tensile strain at standard section I–I of the tunnel lining and (b) peak value diagram of longitudinal tensile strain at enlarged section II–II of the tunnel lining. 1 – EL-0.1 g, 2 – EL-0.2 g, 3 – EL-0.3 g, 4 – EL-0.4 g, 5 – EL-0.5 g, and 6 – EL-0.6 g.It can be seen from Figure 9 that, in the direction of tunnel axial depth (longitudinal), the longitudinal tensile strain of the spandrel (measuring point BZ–4) at the standard section I–I of the tunnel lining standard section is the largest, reaching the maximum value of 86.68 με when the excitation peak value is 0.5 g. The longitudinal tensile strain peak of the vault (measuring point KD–8) at the enlarged section II–II of the tunnel lining enlarged section is the largest, reaching the maximum value of 82.40 με when the excitation peak is 0.5 g. It shows that the overall variation trends of longitudinal tensile strain at the standard section I–I of standard section and the enlarged section II–II of the tunnel lining enlarged section differ greatly. The variation trends of dynamic strain of the two sections are different, which may be mainly due to the different thickness and geometry of the two sections. Under the action of seismic waves parallel to the axial direction of the tunnel, the reason for the maximum tensile strain of the spandrel of the standard section and the vault of the tunnel lining enlarged section could be attributed to the friction resistance, which are greater between the surrounding rocks and the spandrel of the standard section or the vault of the enlarged section, thus resulting in more significant longitudinal deformation at both segments. The tensile strains of the two sections have little change trends under the excitation condition of 0.1–0.3 g, but the tensile strain change trend is obviously larger under the excitation condition of 0.4–0.6 g. The reason why the longitudinal tensile strain under 0.5 g condition is greater than that in 0.6 g condition should be due to the looseness between surrounding rocks and the tunnel lining in 0.5 g condition, thus resulting in the relative reduction in friction resistances between surrounding rocks and linings.3.2.2Circumferential tensile strain responses and damage mechanismPeak values of the circumferential tensile strains of the tunnel lining are shown in Figure 10.Figure 10Peak values of circumferential tensile strain of the tunnel lining. (a) Dynamic strain peak diagram at the standard section I–I of tunnel lining; (b) dynamic strain peak diagram at the standard section II–II of tunnel lining; (c) peak value diagram of circumferential dynamic strain at the enlarged section I–I of tunnel lining; and (d) peak value diagram of circumferential dynamic strain at the enlarged section II–II of tunnel lining. 1 – EL-0.1 g, 2 – EL-0.2 g, 3 – EL-0.3 g, 4 – EL-0.4 g, 5 – EL-0.5 g, and 6 – EL-0.6 g.According to Figure 10(a) and (b), the circumferential strain of the arch waist (measuring point BZ–3) at the standard section I–I of the tunnel lining standard section is the largest, reaching the maximum value of 79.35 με when the excitation peak value is 0.5 g. The circumferential strain of the inverted arch (measuring point BZ–6) at the standard section II–II of the tunnel lining standard section is the largest, reaching the maximum value of 122.08 με when the excitation peak value is 0.6 g. It can be seen from Figure 10(c) and (d) that the circumferential dynamic strain peak of the vault at both sections of the enlarged section is the largest, and the vault (measuring point KD–4) of the enlarged section I–I of the tunnel lining reaches the maximum value of 13.43 με, when the excitation peak is 0.5 g. The vault (measuring point KD–8) of the enlarged section II–II reaches the maximum value of 14.65 με, when the excitation peak value is 0.6 g.The possible reason for the maximum circumferential dynamic strain of the arch waist at the standard section I–I of the tunnel lining standard section is that the standard section I–I is closer to the connection segment between the standard section and the enlarged section. Due to the change in section size, the propagation direction of seismic waves changes, seismic waves are superimposed with each other, resulting in complex seismic wave field. Furthermore, the slope also reflects the input ground motion, then a large number of reflected waves in different directions and types are generated. Because of the dynamic coupling effect of the arch waist at the standard section I–I of the tunnel lining standard section, the circumferential deformation of the arch waist is the largest. Since the standard section II–II of the tunnel lining standard section is located in the middle of the standard section, the possible reason for the maximum circumferential strain of the inverted arch is that the dynamic response of the seismic inertia force to the middle of the standard section is the largest, and the deformation at the inverted arch of the tunnel lining is the most obvious.4ConclusionBased on the process and results of 1–50 scale ratio shaking table tests of the bridge–tunnel overlapping section in soft rock strata, we studied the acceleration and the dynamic strain results of tunnel lining under different earthquakes. Through the above research works, some conclusions can be drawn.(1)For the acceleration of tunnel lining, the peak acceleration of the standard section and the enlarged section increases significantly along with greater peak values. Most of the acceleration values at the measuring points have significant amplification effects compared to the input seismic waves. The amplification coefficients of the lining acceleration at the standard section and the enlarged section are greater than 1 and increase with the increase in elevation.(2)Longitudinal tensile strains appear both at the standard and the enlarged sections of the tunnel lining under EL Centro X direction seismic waves. But the evolutions of strains in different parts are different. The largest tensile strain appears at the tunnel spandrel of the standard section, while the enlarged section appears at the tunnel vault.(3)For the circumferential dynamic strain results of the tunnel lining, the largest tensile strains of the standard section appear at the arch waist of the standard section near the tunnel entrance and the inverted arch at the distal part. The circumferential tensile strain of the vault is the largest in both observation sections of the enlarged section. However, the strain values of the standard section and the enlarged section differ greatly, and the deformation results of the standard section are obviously larger than the enlarged section.Based on the above test results, it can be seen that in the anti-seismic design for the tunnel lining at the tunnel portal in the bridge–tunnel overlapping section of expressway in soft rock strata of sensitive environments, the longitudinal tensile design of tunnel lining needs to be strengthened. And the anti-seismic design standards and durability requirements of tunnel lining structure of the standard section adjacent to the enlarged section should be improved, so as to meet the stress deformation and overall stability requirements when affected by severe earthquakes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Rheology de Gruyter

Seismic response and damage mechanism of tunnel lining in sensitive environment of soft rock stratum

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Publisher
de Gruyter
Copyright
© 2023 the author(s), published by De Gruyter
eISSN
1617-8106
DOI
10.1515/arh-2022-0141
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Abstract

1IntroductionContinuously, tunnels and other underground structures have always been considered to perform good and not easily be damaged by earthquakes. However, seismic damage investigations show that some tunnels have experienced considerable damage [1,2,3,4,5] during recent strong earthquakes. And the tunnel lining at the tunnel portal approaching or adjacent to the fault fracture zones have been especially affected or destroyed seriously [6,7,8,9]. In the southwest of China and Sichuan–Tibet region, the bridge–tunnel overlapping section is a kind of special type of engineering combined by bridge, tunnel, slope, valley, and fragile surrounding rocks, which must be designed and constructed due to the limitations of terrain, landform, and geology reasons. Such kind of bridge–tunnel overlapping sections (the “bridge–tunnel overlapping section” shall hereinafter be collectively referred to as the “BTOS”) have always ensured smooth traffic in special sections of mountain areas. However, although the southwest mountain areas of China are located in the Himalayan seismic zone, there are a large number of bridge–tunnel overlapping projects that have been built or are being built in plan in these seismic sensitive areas. Therefore, the seismic fortification of tunnel portals in the bridge–tunnel overlapping section in strong dynamic sensitive environment have become key problems which need to be solved urgently enough in these kinds of engineering. And it has become one of the hot spots in the analyses or research works of those kind of complex engineering structures in recent years.In recent years, there are many scholars who have carried out a lot of research works on the dynamic responses of tunnel structures or tunnel portal sections through shaking table model test or numerical simulation methods at home and abroad. Wang et al. [10] compared and analyzed the influences and performances on the dynamic characteristics of the portal section of double tunnel in the presence or absence of the damping layers using shaking table test method. Tao et al. [11] conducted the shaking table tests on the portal section of mountain tunnel in weak surrounding rocks, and pointed out the amplification effects of the acceleration of surrounding rocks at the portal due to the existence of free surfaces of inverted slope, and got the conclusion that the seismic additional stress was mainly concentrated in tunnel spandrel and arch foot of the tunnel. Hou et al. [12] carried out the shaking table model tests on the portal section of mountain tunnel using the seismic excitations of Wenchuan waves in different loading directions, and analyzed the deformation modes and failure mechanism of tunnel structure caused by different excitation directions. By comparing the shaking table model tests and numerical calculation results of the portal section of the shallow buried biased tunnel, Li et al. [13] showed that those two kinds of results were in good agreements, and pointed out that the cross-sectional internal force of the non-biased tunnel showed an anti-symmetric distribution, while the biased tunnel showed a more unfavorable internal force value distribution and a large peak value. Shen et al. [14] found that the number of tunnel lining cracks with damping layers was significantly reduced with the different settings of damping layer (with or none damping layer) at the entrance section of mountain tunnels, while the maximum seismic response positions and failure modes of the tunnel were basically consistent with the failure condition of tunnel in Wenchuan earthquake of China on May 12, 2008 when without any damping layer.In addition, scholars and engineers have made some achievements in the research works of bridge and tunnel transition section over the past decade. Considering the interaction of surrounding rocks, tunnel linings, and abutments, Shi et al. [15] analyzed the influences of train speed, height span ratio, and the length of the abutment extending into the tunnel on the static and dynamic responses of tunnel structure using the three-dimensional static and dynamic finite element methods. Bi et al. [16] tested the influence of different vehicle lengths and vehicle speeds on the dynamic response of bridge tunnel transition section through field tests, and studied whether the dynamic characteristics of bridge–tunnel transition section are consistent when trains pass through the bridge–tunnel junction segment with different vehicle speeds and vehicle lengths. Chao et al. [17] established the dynamic coupling calculation model of vehicle and pavement according to the D’Alembert principle, and studied the impacts of vehicle on the pavement of bridge–tunnel transition section under the conditions of vehicle load mass, cargo position, driving speed, and differential settlements.To sum up, recent research results related to the impacts of strong dynamic sensitive environment on the bridge–tunnel connection sections mainly focus on the dynamic characteristics of the lining, surrounding rock, and slope of the tunnel portal section, as well as the dynamic response of the bridge–tunnel connecting structure under vehicle load. There are still very few reports or studies on the seismic dynamic characteristics of the tunnel lining in the bridge–tunnel overlapping section [18,19]. The bridge and tunnel overlapping structure is affected by the abutment and portal mountain, which makes its stress states and seismic responses very complex, and the existing seismic design codes do not fully consider the characteristics of bridge and tunnel overlapping structure [20,21,22]. Therefore, for those reasons mentioned above, we studied the dynamic characteristics and influencing factors of highway bridge–tunnel overlapping tunnel lining under different seismic loadings based on the method of shaking table test, so as to provide suggestions and references for earthquake-resistance design and construction of tunnel structures in the bridge–tunnel overlapping sections and projects in mountainous areas in southwest of China and Sichuan–Tibet region.2Shaking table model test scheme2.1Test equipmentThe shaking table tests were carried out in the National Engineering Laboratory for High-Speed Railway Construction. The shaking table is 4 m × 4 m six DOF movable table, the maximum displacement of which is 250 mm in X or Y direction, and the maximum acceleration is ±0.8 g under full loading, with the maximum displacement 160 mm in Z direction, the maximum acceleration ±1.6 g under full loading, and 0.1–50 Hz as the working frequency range. The shaking table and its control system are shown in Figure 1.Figure 1The shaking table system. (a) Aerial view of the shaking table; (b) surface of the shaking table; and (c) shaking table control system.2.2Similarity relationshipThe similarity relationship of this model test is deduced according to the equilibrium equation, the stress boundary conditions, and displacement boundary conditions of the prototype and model structures [10,11]. According to the second similarity theorem and dimensional analysis method, the length L, elastic modulus E, and density ρ are chosen as the three basic dimensions, other similar parameters are derived based on the above three parameters. The tunnel lining is an approximate elastic cylindrical shell structure, which bears both bending stress and axial force. The bending capacity and bending strains of the tunnel lining are the main control factors. So, the bending stiffness was chosen as the main similarity condition of the model in the tests. The geometric similarity ratio of the model test is 1/50, and the similarity constants in the shaking table model tests are shown in Table 1.Table 1Primary similitude coefficients of the modelPhysical quantitySimilarity relationSimilarity ratioPhysical quantitySimilarity relationSimilarity ratioLength llCl1/50Poisson’s ratio μCμ1Area AACA=Cl2{C}_{A}={C}_{l}^{2}1/502Time tCt=Cl0.5{C}_{t}={C}_{l}^{0.5}1/7.07Density ρ\rho Cρ{C}_{\rho }1Frequency fCf=Ct−1{C}_{f}={C}_{t}^{-1}7.07Elastic modulusEECE=CρCl{C}_{E}={C}_{\rho }{C}_{l}1/50Velocity vCv=Cl/Ct{C}_{v}={C}_{l}/{C}_{t}1/7.07Stress σ\sigma Cσ=ClCρ{C}_{\sigma }={C}_{l}{C}_{\rho }1/50Acceleration aCa=Cl/Ct2{C}_{a}={C}_{l}/{C}_{t}^{2}1Note: The site soil is mainly strong weathered shale, gravel bearing silty clay, and the site type is class II.For the tunnel model, with a geometric similarity ratio of 1 to 50, the model tunnel lining considers the comprehensive effect and reinforcement influence of the first support and secondary lining of the actual tunnel project.2.3Design of model test box and test boundaryThe model test box is an auxiliary device for the shaking table model test. A rigid model box has been used in this test, and the internal space dimensions of which are 3.5, 1.5, and 2.0 m in the length, width, and height (as shown in Figure 1). In order to increase the rigidity of the model box, the outside of the box wall is welded into a grid shape with channel steel and angle steel, and inclined supports are set at the height of 1.0 and 1.5 m. At the same time, to ensure good test results, the following treatments have also been carried out during the design and built periods of the model test box.(1)The bottom plate of the model test box shall be reserved with bolt holes for fixation according to the characteristics of the shaking table surface. Under circumstance that the structure of the model test box is firm, cut a window at an appropriate position, and place transparent tempered glass along the length of the model test box to facilitate photography and observation during the shaking model test process.(2)The natural frequency of the model test box shall be quite different to that of the “BTOS” model structure to prevent resonance between them. Through modal analysis, the first-order of natural frequencies of the model box is far away from that of the “BTOS” model rocks and soils, which shows that there will be no resonance between the model box and the internal rocks and soils during the seismic excitation processes.(3)In order to reduce the adverse effects of seismic waves at the bottom and the four side walls of the model box, the dynamic boundary of the test model (including the soil) is dealt with as follows: the bottom plate of the model is treated as a friction boundary, and the side walls of the model box are treated as flexible boundaries. A concrete plate of 8 cm thick is laid at the bottom of the model test box to make the bottom of the piles to be solid embedded. After that, a layer of 5 cm thick gravels is paved on the concrete plate to increase the friction between the surrounding rocks and the bottom of the model test box to reduce the relative displacements between the surrounding rocks and the bottom of the model test box during the test process. In order to absorb the reflected seismic waves, the confining effects of sidewalls on surrounding rock strata shall be weakened to a certain degree, then 5 cm thick polystyrene foam boards were pasted around the model test box internal walls. A layer of plastic film is attached to the surfaces of the foam boards, and on the surfaces of which oil shall be brushed to avoid the severe friction between the foam board and the rock layer, with the purpose not to affect the test results. Boundary treatments are shown in Figure 2.Figure 2Boundary treatments of model test box. (a) Treatments of model box internal walls and (b) model test box boundary treatments.2.4Model structure design and fabricationThe main design parameters of the bridge and tunnel prototypes in the shaking table model tests are as follows:(1)Prototype bridge: bridge superstructure: span 30 m × 30 m × 30 m high-speed public continuous box girder, 11.75 m wide, and 2.0 m high. The abutment is a 4-pile embedded abutment with a pile foundation diameter of 1.5 m.(2)Prototype tunnel: highway tunnel with inverted arch curved wall lining.(i)In the standard section, the net width inside the tunnel is 10.85 m. Tunnel lining parameters: 28 cm thick primary support, water proof layer, and 50 cm thick secondary lining.(ii)The enlarged section (i.e., bridge and tunnel overlapping section) has a net width of 12.0 m inside the tunnel. Tunnel lining parameters: 28 cm thick primary support, water proof layer, and 60 cm thick secondary lining.The tunnel lining is made of C30 steel reinforced micro concrete. After many mix proportion tests, the final determined material quality mix proportion of the tunnel lining is 496:631:159:5.95 (cement:sand:water:NOF-3 concrete water reducer), with internal reinforcement steel meshes of 0.5 mm diameter. The thickness of the tunnel lining standard section is 2 cm, and its length is 60 cm. The thickness of the tunnel lining enlarged section is 3 cm with a 5 cm thickness at the invert, and its length is 24.5 cm. The length of the piles model at the bottom of the tunnel lining enlarged section are all 76 cm, and its diameter is 3 cm with one φ6 ordinary R235 steel rebar along the longitudinal direction of each pile. The pile foundation at the bottom of the expanded section of the tunnel model and the lining were made up as a whole part in the structural model making process as shown in Figure 3. The bridge deck is made by C50 steel reinforced micro concrete, and the concrete material quality mix proportion of which is 477:572:167:2.39 (cement:sand:water:NOF-3 concrete water reducer). The structural models of the standard tunnel lining section, enlarged section, and bridge deck have been made, as shown in Figure 3.Figure 3Pictures of models. (a) Tunnel lining of standard section; (b) tunnel lining of enlarged section and piles at the bottom; and (c) bridge model.For weak surrounding rocks, according to the principle of similar Poisson’s ratio [15], the indoor material orthogonal tests have been carried out with unsaturated soil triaxial tester (GDS). Finally, the determined mix material plan is barite powder, quartz sand, and lithium-based lubricating oil, and its quality mix proportion is 10:5:1.2 (barite powder:quartz sand:lithium-based lubrication). In the tests, all models of bridge, tunnel, and surrounding rocks are made at the same time or in the same batch group during the modeling process. Soil in the test box was filled by layered compaction. The densities of each layer were measured for several times by cutting ring in the laying process, to ensure the consistency of soil compaction. The physical and mechanical parameters of the prepared materials are shown in Table 2.Table 2Rock material parametersSurrounding rock gradeMaterial typeModulus of elasticity/GPaPoisson’s ratioInternal friction angle/(°)Cohesion/MPaUnit weight/(kN/m³)Grade IVPrototype4.40.32341.7522Model0.0880.32340.03521.3Grade VPrototype1.80.38231.519Model0.0360.38230.0318.2The enlarged section of the tunnel portal in this test is a key component part of the whole portal structure. The mechanical model of such bridge–tunnel overlapping structure can be simplified as a model combined by the bridge, the tunnel, the road, and the surrounding rocks and soils considering the interactions between each part. Taking the influences caused by the car loadings as an example, the force transfer relationship can be assumed as: the car loading transfer first to the bridge by the road system, then to the abutments and foundations (with additional gravity of the bridge upper structures), and transfer to the tunnel structure and its surrounding rocks at last.2.5Sensor arrangementThe acceleration and dynamic strain response law of the standard section and enlarged section of the tunnel lining were mainly studied in the shaking table tests. The measuring instruments are unidirectional acceleration sensors and resistance strain gauges. The acceleration sensors used in the tests are 2210-002 type with measuring range of ±2 G and sensitivity of 2,000 mV/g. There are two types of strain gauges, one is BX120-100AA with resistance of 120 ± 0.1Ω, size of 100 mm × 3 mm, and sensitivity of 2.1 ± 2%. The other type of strain gauge is BX120-3AA, with resistance of 120 ± 1Ω, size of 3.0 mm × 2.2 mm, and sensitivity of 2.0 ± 1%. Model diagram and sensor arrangements in the test are shown in Figure 4.Figure 4Model diagram and sensor arrangements (unit: mm). (a) Diagram of model dimensions; (b) longitudinal section of measuring point arrangements of bridge–tunnel overlapping section; and (c) cross section of measuring point arrangements of bridge–tunnel overlapping section.The acceleration data of each measuring point during the test in the enlarged section and standard section of the tunnel are obtained through the following ways. Firstly, the actual acceleration data (generally 0–5 g, the letter “g” represents the acceleration of gravity) of each measure point was measured and recorded by high sensitivity acceleration sensors at each measuring point along all the three direction (direction along X, Y or Z). Then when multiple input directions are superimposed, these parameters should be accumulated by calculation results along every single direction.2.6Seismic waves and excitation schemeThe seismic wave in the shaking model test is EL Centro wave. The EL Centro seismic wave is one of the seismic waves that has been successfully recorded during such strong earthquakes on the whole process data in the world, which is of great significance to the research of earthquakes. EL Centro wave is the first seismic wave with intensity greater than 300 gal captured by human beings. The measurement of seismic wave data for large earthquakes has always been a complex problem. At that time, the instruments were relatively backward, and the measured data of these precise measurements were very rare. EL Centro wave is measured at the surface, which is suitable for Class II sites. And the dynamic responses of the “BTOS” model under different peak excitation accelerations have been analyzed. The X direction component of EL Centro wave has been chosen to load unidirectionally (X direction is horizontal and parallel to the longitudinal axis direction of the tunnel). The excitation direction is shown in Figure 4a, and the seismic excitation scheme in the test is shown in Table 3. According to the working frequency range of the test equipment, the seismic waves in the tests must be treated and simplified to the frequency range from 0.1 to 50 Hz. The acceleration–time history curve and Fourier spectrum of EL Centro wave are shown in Figure 5. From the Fourier spectrum, it can be seen that the excellent frequency of EL Centro wave is 8–17 Hz. The seismic wave acceleration excitation peak value is loaded step by step according to the order from of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 g.Table 3Seismic excitation scheme of shaking table testLoading orderSeismic wavePeak value/gDuration of time/sLoading orderSeismic wavePeak value/gDuration of time/sWN–X0.04—4EL Centro–X0.47.61EL Centro–X0.17.6WN–X0.04—WN–X0.04—5EL Centro–X0.57.62EL Centro–X0.27.6WN–X0.04—WN–X0.04—6EL Centro–X0.67.63EL Centro–X0.37.6WN–X0.04—WN–X0.04—Figure 5Acceleration–time history and Fourier spectrum of EL Centro X seismic wave. (a) Acceleration–time history curve and (b) Fourier spectrum.Before each test, a micro vibration test of white noise (Code WN–X) with a peak acceleration of about 0.04 g and a time length of about 30 s should be carried out, to observe the transformation of the dynamic characteristics of the model structure.3Test result and result analysisDue to limited time, content relevance, and the length of the article, although there are more initial measuring points and results in the test scheme, we have to choose the accelerations and strains of some key measuring points of the tunnel lining in this work for deep study. Other test results and analysis will be published in other articles.3.1Acceleration responses and damage mechanism of tunnel liningThe acceleration dynamic response characteristics of the model are analyzed by two indexes: the acceleration response peak value and the acceleration amplification coefficient. The acceleration amplification factor is defined as the ratio of the peak acceleration of the measuring point to the peak acceleration of the input seismic wave. Figure 6 shows the acceleration response time history curve of measuring point A1 near the portal end segment (at standard section I–I) of the tunnel lining when the peak excitation acceleration is 0.4 g.Figure 6Acceleration response time history curve of A1 measuring point under 0.4 g PGA of seismic wave. (a) Acceleration–time history curve and (b) Fourier spectrum.3.1.1Acceleration responses and damage mechanism at standard section I–I of tunnel liningFigure 7 shows the acceleration peak values and amplification coefficients of different measuring points at the standard section I–I of the tunnel lining under different excitation peak values.Figure 7Peak accelerations and acceleration amplification factors at the standard I–I section of the tunnel lining under different PGA of seismic waves. (a) Peak acceleration diagram and (b) acceleration amplification factor. 1 – A1, 2 – A2, 3 – A3, 4 – El-0.1 g, 5 – EL-0.2 g, 6 – EL-0.3 g, 7 – EL-0.4 g, 8 – EL-0.5 g, and 7 – EL-0.6 g.It can be seen from Figure 7a that under the seismic excitation of EL Centro X direction, the peak acceleration of inverted arch (measuring point A1), arch waist (measuring point A2), and vault (measuring point A3) in the standard section shows a nonlinear increasing trend with the increase in peak excitation acceleration, and its growth rate first increases then decreases with the increase in peak excitation acceleration. However, from 0.5 g to 0.6 g, the influence of the peak value of the earthquake excitation wave is small and basically at the maximum value. According to the preliminary judgments, the reason for this phenomenon may be that some surrounding rocks have entered the plastic state due to the increase in peak loading acceleration.In addition, it can be seen from Figure 7b that the acceleration values at each measuring point of the tunnel lining have a significant amplification effect compared with the initial excitation input seismic wave. Under the seismic excitation of EL Centro X direction with the peak value in the range of 0.1–0.6 g, the acceleration amplification factors of inverted arch (measuring point A1), arch waist (measuring point A2), and arch crown (measuring point A3) in the tunnel lining standard section are all greater than 1. And the value increases as the elevation increases. It shows that the acceleration effect of these parts is obviously amplified, and they are relatively easy to be damaged or cracked when encountering earthquakes. In addition, it is also found from the test results that the acceleration amplification coefficients at the peak values of 0.4 and 0.5 g seismic waves are significantly higher than those of the other four different peak values.3.1.2Acceleration responses and damage mechanism of tunnel lining along the tunnel axisFigure 8 shows the peak accelerations and acceleration amplification factors of the middle span (measuring point A6), the vault of the tunnel lining enlarged section (measuring point A5), the vault at the standard section I–I (measuring point A3) (near the portal end segment), and the vault at the standard section II–II (measuring point A4) (relatively far away from the portal end segment) of the tunnel lining standard section. The acceleration peak value of each measuring point increases with the increase in the seismic wave acceleration excitation peak value, and the acceleration peak value in the middle of the bridge span (measuring point A6) is the largest. This is mainly due to the bare part in the middle of the bridge span and a less constrain. The acceleration amplification coefficient of each measuring point decreases nonlinearly from the portal to the tunnel along the tunnel axis, which indicates that the acceleration amplification coefficient decreases due to the increased constraint of surrounding rocks on the tunnel lining from the portal along the tunnel axis to the tunnel depth. Because the front slope is closer to the vault of the tunnel lining enlarged section, the acceleration amplification effect of the tunnel vault (measuring point A5) of the enlarged section increases obviously due to the influence of the free surface of the front slope.Figure 8Peak accelerations and acceleration amplification factors along the axis of the tunnel under different excitation peak accelerations. (a) Peak acceleration diagram and (b) acceleration amplification factor. 1 – A3, 2 – A4, 3 – A5, 4 – A6, 5 – EL-0.1 g, 6 – EL-0.2 g, 7 – EL-0.3 g, 8 – EL-0.4 g, 9 – EL-0.5 g, and 10 – EL-0.6 g.3.2Dynamic strain responses and damage mechanism of tunnel lining3.2.1Longitudinal tensile strain responses and damage mechanismPeak values of the longitudinal tensile strains of the tunnel lining are shown in Figure 9.Figure 9Peak values of longitudinal tensile strains of the tunnel lining. (a) Peak value diagram of longitudinal tensile strain at standard section I–I of the tunnel lining and (b) peak value diagram of longitudinal tensile strain at enlarged section II–II of the tunnel lining. 1 – EL-0.1 g, 2 – EL-0.2 g, 3 – EL-0.3 g, 4 – EL-0.4 g, 5 – EL-0.5 g, and 6 – EL-0.6 g.It can be seen from Figure 9 that, in the direction of tunnel axial depth (longitudinal), the longitudinal tensile strain of the spandrel (measuring point BZ–4) at the standard section I–I of the tunnel lining standard section is the largest, reaching the maximum value of 86.68 με when the excitation peak value is 0.5 g. The longitudinal tensile strain peak of the vault (measuring point KD–8) at the enlarged section II–II of the tunnel lining enlarged section is the largest, reaching the maximum value of 82.40 με when the excitation peak is 0.5 g. It shows that the overall variation trends of longitudinal tensile strain at the standard section I–I of standard section and the enlarged section II–II of the tunnel lining enlarged section differ greatly. The variation trends of dynamic strain of the two sections are different, which may be mainly due to the different thickness and geometry of the two sections. Under the action of seismic waves parallel to the axial direction of the tunnel, the reason for the maximum tensile strain of the spandrel of the standard section and the vault of the tunnel lining enlarged section could be attributed to the friction resistance, which are greater between the surrounding rocks and the spandrel of the standard section or the vault of the enlarged section, thus resulting in more significant longitudinal deformation at both segments. The tensile strains of the two sections have little change trends under the excitation condition of 0.1–0.3 g, but the tensile strain change trend is obviously larger under the excitation condition of 0.4–0.6 g. The reason why the longitudinal tensile strain under 0.5 g condition is greater than that in 0.6 g condition should be due to the looseness between surrounding rocks and the tunnel lining in 0.5 g condition, thus resulting in the relative reduction in friction resistances between surrounding rocks and linings.3.2.2Circumferential tensile strain responses and damage mechanismPeak values of the circumferential tensile strains of the tunnel lining are shown in Figure 10.Figure 10Peak values of circumferential tensile strain of the tunnel lining. (a) Dynamic strain peak diagram at the standard section I–I of tunnel lining; (b) dynamic strain peak diagram at the standard section II–II of tunnel lining; (c) peak value diagram of circumferential dynamic strain at the enlarged section I–I of tunnel lining; and (d) peak value diagram of circumferential dynamic strain at the enlarged section II–II of tunnel lining. 1 – EL-0.1 g, 2 – EL-0.2 g, 3 – EL-0.3 g, 4 – EL-0.4 g, 5 – EL-0.5 g, and 6 – EL-0.6 g.According to Figure 10(a) and (b), the circumferential strain of the arch waist (measuring point BZ–3) at the standard section I–I of the tunnel lining standard section is the largest, reaching the maximum value of 79.35 με when the excitation peak value is 0.5 g. The circumferential strain of the inverted arch (measuring point BZ–6) at the standard section II–II of the tunnel lining standard section is the largest, reaching the maximum value of 122.08 με when the excitation peak value is 0.6 g. It can be seen from Figure 10(c) and (d) that the circumferential dynamic strain peak of the vault at both sections of the enlarged section is the largest, and the vault (measuring point KD–4) of the enlarged section I–I of the tunnel lining reaches the maximum value of 13.43 με, when the excitation peak is 0.5 g. The vault (measuring point KD–8) of the enlarged section II–II reaches the maximum value of 14.65 με, when the excitation peak value is 0.6 g.The possible reason for the maximum circumferential dynamic strain of the arch waist at the standard section I–I of the tunnel lining standard section is that the standard section I–I is closer to the connection segment between the standard section and the enlarged section. Due to the change in section size, the propagation direction of seismic waves changes, seismic waves are superimposed with each other, resulting in complex seismic wave field. Furthermore, the slope also reflects the input ground motion, then a large number of reflected waves in different directions and types are generated. Because of the dynamic coupling effect of the arch waist at the standard section I–I of the tunnel lining standard section, the circumferential deformation of the arch waist is the largest. Since the standard section II–II of the tunnel lining standard section is located in the middle of the standard section, the possible reason for the maximum circumferential strain of the inverted arch is that the dynamic response of the seismic inertia force to the middle of the standard section is the largest, and the deformation at the inverted arch of the tunnel lining is the most obvious.4ConclusionBased on the process and results of 1–50 scale ratio shaking table tests of the bridge–tunnel overlapping section in soft rock strata, we studied the acceleration and the dynamic strain results of tunnel lining under different earthquakes. Through the above research works, some conclusions can be drawn.(1)For the acceleration of tunnel lining, the peak acceleration of the standard section and the enlarged section increases significantly along with greater peak values. Most of the acceleration values at the measuring points have significant amplification effects compared to the input seismic waves. The amplification coefficients of the lining acceleration at the standard section and the enlarged section are greater than 1 and increase with the increase in elevation.(2)Longitudinal tensile strains appear both at the standard and the enlarged sections of the tunnel lining under EL Centro X direction seismic waves. But the evolutions of strains in different parts are different. The largest tensile strain appears at the tunnel spandrel of the standard section, while the enlarged section appears at the tunnel vault.(3)For the circumferential dynamic strain results of the tunnel lining, the largest tensile strains of the standard section appear at the arch waist of the standard section near the tunnel entrance and the inverted arch at the distal part. The circumferential tensile strain of the vault is the largest in both observation sections of the enlarged section. However, the strain values of the standard section and the enlarged section differ greatly, and the deformation results of the standard section are obviously larger than the enlarged section.Based on the above test results, it can be seen that in the anti-seismic design for the tunnel lining at the tunnel portal in the bridge–tunnel overlapping section of expressway in soft rock strata of sensitive environments, the longitudinal tensile design of tunnel lining needs to be strengthened. And the anti-seismic design standards and durability requirements of tunnel lining structure of the standard section adjacent to the enlarged section should be improved, so as to meet the stress deformation and overall stability requirements when affected by severe earthquakes.

Journal

Applied Rheologyde Gruyter

Published: Jan 1, 2023

Keywords: sensitive environment of soft rock stratum; bridge; tunnel overlapping; tunnel lining; seismic response; damage mechanism

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