Predicting Response of Constructed Tunnel to Adjacent Excavation with Dewatering
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Hindawi Geofluids Volume 2021, Article ID 5548817, 17 pages https://doi.org/10.1155/2021/5548817 Research Article Predicting Response of Constructed Tunnel to Adjacent Excavation with Dewatering Panpan Guo ,1 Feifei Liu,2 Gang Lei ,1,3 Xian Li ,2 Cheng-wei Zhu ,4 Yixian Wang ,2,5 Mengmeng Lu,6 Kang Cheng ,1,7 and Xiaonan Gong1 1 Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China 2 School of Civil Engineering, Hefei University of Technology, Hefei 230009, China 3 Beijing Urban Construction Design & Development Group Company Limited, Beijing 100037, China 4 Institut für Geotechnik, Universität für Bodenkultur Wien, Feistmantelstrasse 4, 1180 Vienna, Austria 5 State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China 6 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China 7 China Railway 11th Bureau Group Co., Ltd., Wuhan 430061, China Correspondence should be addressed to Gang Lei; 11812105@zju.edu.cn and Xian Li; 2012800022@hfut.edu.cn Received 27 January 2021; Revised 25 February 2021; Accepted 2 March 2021; Published 18 March 2021 Academic Editor: Yu Wang Copyright © 2021 Panpan Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper proposes a new method for predicting the displacement and internal force of constructed tunnels induced by adjacent excavation with dewatering. In this method, the total excavation-induced additional stress on the constructed tunnel is derived by superposing the additional stresses induced by excavation unloading and dewatering effects. The additional stress induced by unloading effect is calculated using Mindlin’s solution. The additional stress induced by dewatering effect is calculated using the principle of effective stress and the Dupuit precipitation funnel curve. With the beam on elastic foundation method, the total additional stress is then used for calculating the tunnel displacement and internal force caused by adjacent excavation with dewatering. Based on three well-documented case histories, the performance of the proposed method is verified. Moreover, a parametric analysis is also performed to capture the effects of excavation depth, tunnel-to-excavation distance, initial water level, excavation plan view size, and specific yield on the responses of the constructed tunnels. The results indicate that the effect of excavation depth on the tunnel maximum vertical displacement, maximum bending moment, and maximum shear force is more significant at an excavation depth greater than the cover depth of the constructed tunnel. The tunnel maximum vertical displacement, maximum bending moment, and maximum shear force decrease nonlinearly with an increase in the tunnel-to- excavation distance and the initial water level. Among the investigated parameters, the excavation dimension in the tunnel longitudinal direction affects most the tunnel responses. The effect of specific yield on the tunnel displacement and internal force induced by adjacent excavation with dewatering becomes more obvious as increasing the initial water level and excavation depth. 1. Introduction cent excavation has an adverse effect on the constructed structures or facilities, and many studies have focused on this The rapid development of urban rail traffic provides conve- issue in recent decades [6–8]. It has been found that the nience of getting around for people. The development advan- excavation-induced redistribution of ground stress can lead tage along an urban rail traffic line has been stimulating the to the generation of additional stress and deformation in construction of high-rise buildings adjacent to the urban rail the tunnel structure. If the induced tunnel deformation is traffic line. Therefore, it is not rare to find an excavation that excessive, the safe operation of the subway or other facilities is adjacent to preexisting subway tunnels, piles, pipelines, or will be affected [9–12]. As a result, an investigation into the other shallowly buried facilities [1–5]. Inevitably, the adja- excavation-induced internal force and deformation
2 Geofluids characteristics of a constructed subway tunnel has great sig- takes account of the excavation dewatering effect but is not nificance to the safe operation of the subway tunnel [13–15]. applicable to the condition where the excavation is adjacent Many analysis methods for excavation-induced internal laterally to the constructed tunnel. In addition, based on force and deformation in a subway tunnel have been pro- Darcy’s law and the Dupuit approximation, Anderson [42] posed, which can be classified into the numerical analysis derived a formula describing the steady flow of groundwater method [16–19], field monitoring method [20–23], and the- and determined the precipitation funnel curve using the oretical analysis method [24–26]. The numerical analysis groundwater surfaces on the external and internal method can simulate the complex process of excavation boundaries. and is therefore a favored choice for engineers and In this paper, the excavation unloading effect and the researchers. However, this method suffers from several dis- excavation dewatering effect are modelled separately. Mind- advantages such as cumbersome modelling, time- lin’s solution is used to calculate the additional stress in the consuming computation, large discrepancy between the constructed tunnel induced by the excavation unloading computed results using different numerical analysis software, effect. Based on the Dupuit precipitation funnel curve, the and low reliability of the computed results. The field moni- effective stress in the constructed tunnel induced by the exca- toring method can directly obtain the excavation-induced vation dewatering effect is obtained. The additional stress deformation behavior of the constructed tunnel during the and the effective stress obtained above are then superimposed whole excavation phase. However, this method is susceptible to derive the total additional stress in the constructed tunnel. to the workers’ operating skill and the quality of monitoring After this, the additional load method is adopted to predict equipment. Moreover, the field monitoring method corre- the internal force and displacement characteristics for the sponds to only a specific engineering project and does not constructed tunnel adjacent to an excavation with dewater- involve a discussion of the deformational mechanism and ing. The innovation of this study lies in that the calculation therefore has a limited guiding significance for the excava- of the excavation-induced additional stress takes account of tions in other areas. not only the excavation unloading and dewatering effects The theoretical analysis method for excavation-induced but also the entire region subjected to the influence of dewa- internal force and deformation characteristics in a subway tering by introducing the Dupuit precipitation funnel curve. tunnel has been extensively investigated by many scholars. At the present time, the most common-adopted theoretical 2. Total Additional Stress Induced by analysis method is the two-stage method [27, 28]. This Excavation with Dewatering method divides the considered problem into two separate stages: the excavation unloading stage and the tunnel In calculating the additional stress in the constructed tunnel responding stage. Depending on the concept of predicting induced by excavation with dewatering, the time effect the excavation-induced response of the constructed tunnel, involved in the excavation and dewatering process is not the method for calculating the excavation-induced internal taken into account, and only the initial state and the final force in the constructed tunnel can be categorized into the state of the excavation with dewatering have been considered. additional load method and the additional displacement In general, the additional stress in the constructed tunnel method [29–31]. The additional load method is performed induced by excavation with dewatering is composed of two in two steps. First, apply the excavation-induced additional parts: one is the effective stress effect induced by dewatering, stress in the tunnel position calculated by Mindlin’s solution and the other is the unloading effect induced by excavation. to the constructed subway tunnel. Second, calculate the inter- nal force and deformation in the constructed tunnel under 2.1. Additional Stress Induced by Dewatering. It is assumed the effect of the applied excavation-induced additional stress, that the phreatic line induced by dewatering conforms to by adopting the beam on elastic foundation theory [32, 33]. the Dupuit approximation [42]. In detail, the assumptions The additional displacement method is also performed in are as follows: (1) the aquifer is homogeneous, isotropic, iso- two steps. First, calculate the excavation-induced ground dis- pachous, and horizontal; (2) the flow of the groundwater is placement in the tunnel position by using Peck’s formula laminar and stable and conforms to Darcy’s law; (3) the static [34]. Second, impose the calculated displacement in the first water level is horizontal; and (4) the contour of recharge of step on the constructed tunnel to predict the internal force the pumping well is of fixed water level and is cylindrical in and deformation in the constructed tunnel [35, 36]. shape. A schematic of the dewatering during an excavation The change of the initial stress field in the ground is presented in Figure 1. induced by an excavation is a rather complex phenomenon. The adopted water level lowing curve has the form This phenomenon is associated with not only the excavation ln x − ln r unloading effect but also the excavation dewatering effect. 2 2 y2 = h ′ + H 2 − h ′ , ð1Þ Previous research has indicated that excavation dewatering ln R − ln r affects significantly the internal force and deformation char- acteristics of the constructed facilities adjacent to the excava- where y = elevation of the phreatic line after dewatering (m), tion [37–40]. Based on the effective stress principle, Ou et al. h ′ = distance between the water level of the dewatering well [41] proposed an analytical method for predicting the influ- and the impermeable layer (m), H = elevation of the initial ence of excavation with dewatering on the response of the water level (m), r = radius of the dewatering well (m), R = constructed tunnel underlying the excavation. This method radius of influence of dewatering (m), x = horizontal
Geofluids 3 y Table 1: Empirical values of the specific yield for various types of soils. Ground surface Soil type Specific yield ho Excavation Initial groundwater level Clay 0.02–0.035 h Loam 0.03–0.045 Excavation Groundwater level due Sandy loam 0.035–0.06 bottom to dewatering H Loess-like loam 0.02–0.05 Dewatering Loess-like sandy loam 0.03–0.06 well H′ h′ Tunnel Silty sand 0.06–0.08 Impermeable layer Silty fine sand 0.07–0.01 X R Fine sand 0.08–0.11 Medium-fine sand 0.085–0.12 Figure 1: Schematic of dewatering during excavation. Medium sand 0.09–0.13 Medium-coarse sand 0.10–0.15 distance to the axis of the dewatering well (m), and H ′ = Coarse sand 0.11–0.15 distance between tunnel axis and impermeable layer. Clay cemented sandstone 0.02–0.03 The radius of influence of dewatering can be calculated Fractured limestone 0.008–0.10 using an empirical equation pffiffiffiffiffiffiffiffi R = 2s HK , ð2Þ lin’s solution [43]. A schematic of the calculation model for the additional stress induced by unloading is presented in where s = dewatering depth of the dewatering well (m) and Figure 2. The assumptions involved in Mindlin’s solution K = permeability coefficient of the ground (m/d). are as follows: (1) the ground is a homogeneous, elastic The change of the water level above the constructed tunnel half-space, (2) the time and space effects involved in the exca- can thus be estimated using Equations (1) and (2). The vertical vation are overlooked, and (3) the influence of the con- additional stress applied on the constructed tunnel is calcu- structed tunnel on the excavation unloading stress is not lated using the effective stress principle. Before dewatering, taken into account. the constructed tunnel is subjected to earth pressure and pore According to Mindlin’s solution, under the effect of unit water pressure, and the effective stress is calculated by force σdξdη applied at the point ðξ, ηÞ at the excavation bot- tom, the vertical and horizontal additional stresses at the σ = h0 γ0 + ðH − yÞðγsat − γw Þ, ð3Þ point (x, y, z) on the tunnel axis are calculated by γd ð1 − 2νÞðz − d Þ ð1 − 2νÞðz − d Þ where h0 = distance between ground surface and initial water σvd = − − level (m), γ0 = dry unit weight of soil (kN/m3), γsat = 8πð1 − νÞ R31 R32 saturated unit weight (kN/m3), and γw = unit weight of water 3ðz − d Þ3 3ð3 − 4νÞz ðz + d Þ2 − 3d ðz + dÞð5z − d Þ (kN/m3). + + R51 R52 After dewatering, the effective stress applied to the con- # structed tunnel is given by 30zd ðz + d Þ3 + , R72 σ ′ = h0 γ0 + ðH − yÞðγsat − ð1 − μÞγw Þ, ð4Þ ð6Þ where μ = specific yield. The magnitude of μ is associated 2 with soil properties including the mineral composition, par- γd ð1 − 2νÞðz − dÞ 3ðx − ξÞ ðz − dÞ σhd = − − + ticle size, grain grading, degree of sorting, and void ratio. 8πð1 − vÞ R13 R51 The mineral composition affects the specific yield by the ð1 − 2νÞ½3ðz − dÞ − 4vðz + dÞ adsorption force on the hydrone. A summary of the empiri- − R32 cal values of the specific yield for various types of soils is pre- n o sented in Table 1. 3ð3 − 4νÞðx − ξÞ2 ðz − dÞ − 6dðz + dÞ½ð1 − 2νÞz − 2νd + The dewatering-induced change of the vertical effective R52 stress applied on the constructed tunnel is calculated by " # 2 4ð1 − νÞð1 − 2νÞ ðx − ξÞ ðx − ξÞ + 1− − R2 ðR2 + z + dÞ R2 ðR2 + z + dÞ R22 σvw = σ ′ − σ = μðH − yÞγw = μhγw : ð5Þ # 30ðx − ξÞ2 zdðz + dÞ 2.2. Additional Stress Induced by Unloading. The calculation + , R72 of the additional stress in the constructed tunnel induced by excavation unloading effect is generally based on Mind- ð7Þ
4 Geofluids z By integrating Equations (6) and (7) over the excavation Ground bottom and integrating Equations (9) and (10) over the ver- surface tical side of the excavation, the excavation unloading- x y induced additional stress corresponding to the excavation bottom and to the vertical side of the excavation can be derived, respectively. In this case, the total vertical and hori- Excavation zontal additional stresses in the constructed tunnel induced by excavation with dewatering, σv and σh , have the forms d L Unloading direction σv = σvw + σvd + σvc , ð12aÞ B σh = σhd + σhc : ð12bÞ D Tunnel 3. Response of Constructed Tunnel Figure 2: Schematic of the calculation model for additional stress The internal force and displacement characteristics for the induced by excavation unloading. constructed tunnel under the effect of the additional stress induced by the adjacent excavation with dewatering are pre- qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dicted in this section based on the beam on elastic foundation R1 = ðx − ξÞ2 + ðy − ηÞ2 + ðz − d Þ2 , ð8aÞ theory. To achieve this, it is assumed that (1) the constructed qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tunnel is equivalent to a long beam on an elastic foundation, ð8bÞ (2) the contact between the constructed tunnel and the R2 = ðx − ξÞ2 + ðy − ηÞ2 + ðz + dÞ2 : ground is perfect, and (3) compatibility of deformation is sat- Similarly, under the effect of a unit force K 0 γτdηdτ isfied. A schematic of the calculation model for the response applied at the point ðη, τÞ on the vertical side of the excava- of the constructed tunnel under the additional stress is pre- tion, the vertical and horizontal additional stresses at the sented in Figure 3. point (x, y, z) on the tunnel axis are calculated by According to the Winkler foundation beam model, the equation of deflection curve for the constructed tunnel under the effect of the additional stress has the form K 0 γτS −ð1 − 2νÞ 3ðz − τÞ2 ð1 − 2νÞ σvc = − + + 8πð1 − νÞ R33 R53 R34 d 4 w ðx Þ EI eq + DkwðxÞ = pðxÞ, ð13Þ 3ð3 − 4νÞðz + τÞ 2 dx4 + ð9Þ R54 !# where EI eq = equivalent longitudinal stiffness of the con- −6τ 5z ðz + τÞ2 structed tunnel (kN·m2), wðxÞ = displacement of the con- + 5 τ + ð1 − 2νÞðz + τÞ + , R4 R24 structed tunnel (m), D = external diameter of the constructed tunnel (m), k = coefficient of subgrade reaction (kN·m3), and pðxÞ = additional stress applied on the constructed tunnel Κ0 γτS ð1 − 2νÞ 3S2 ð1 − 2νÞð5 − 4vÞ σhc = − + 5 + (kPa). 8πð1 − νÞ R33 R3 R34 In Equation (13), pðxÞ and EI eq are given by 3ð3 − 4νÞS2 4ð1 − νÞð1 − 2νÞ S2 ð3R4 + z + τÞ + + 3 − R54 R4 ðR4 + z + τÞ2 R24 ðR4 + z + τÞ pðxÞ = σD, ð14aÞ 6τ 5xS2 − 5 3τ − ð3 − 2νÞðz + τÞ + 2 , EI eq = ηEI, ð14bÞ R4 R4 ð10Þ where η = reduction coefficient and EI = actual longitudinal qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi stiffness of the constructed tunnel (kN·m2). R3 = ðx − ξÞ2 + ðy − ηÞ2 + ðz − τÞ2 , ð11aÞ The magnitude of the reduction coefficient η varies, depending on many factors such as the form of tunnel cir- qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cumferential seam, bolt quantity, and tunnel lining thickness R4 = ðx − ξÞ2 + ðy − ηÞ2 + ðz + τÞ2 , ð11bÞ [44–46]. By performing a series of experiments, Xu [47] investigated the magnitude of the reduction coefficient η at where γ = unit weight of soil (kN/m3), d = excavation depth various forms of tunnel circumferential seam. It was found (m), ν = Poisson’ s ratio, K 0 = coefficient of lateral earth that the magnitudes of the reduction coefficient η are, respec- pressure at rest (K 0 = 1 − sin φ, where φ is the angle of tively, 0.145, 0.13, and 0.114 at homogeneous, staggered, and internal friction of soil), S = distance between the vertical side continuous forms of the tunnel circumferential seam. of the excavation and the axis of the constructed tunnel (m), A previous experimental study has indicated that the and τ = depth of the calculation point on the vertical side of coefficient of subgrade reaction k is related to not only the the excavation (m). soil strength but also the stiffness of the foundation beam
Geofluids 5 ð∞ P (X) 2DkC e−λx ðcos ðλxÞ + sin ðλxÞÞdx = P0 : ð20Þ 0 Tunnel Manipulation of Equation (20) leads to D k P0 λ C= : ð21Þ Figure 3: Schematic of calculation model for tunnel response under 2Dk the additional stress. Substituting Equation (21) into Equation (19), the form [48, 49]. Therefore, the empirical equation proposed by Vesic of the general solution becomes [50] and Attewell et al. [51] was adopted to estimate the coef- ficient of subgrade reaction k: P0 λ −λx w ðx Þ = e ðcos ðλxÞ + sin ðλxÞÞ: ð22Þ sffiffiffiffiffiffiffiffiffiffi 2Dk 1:3Es 12 Es D4 k = 2kVesic = , ð15Þ Dð 1 − ν 2 Þ EI eq For a tunnel subjected to an additional distributed load qðxÞ, the point load at the point ξ on the tunnel is qðξÞdξ. where Es = elastic modulus of the ground (MPa). Under this point load, the induced displacement at the point As Equation (13) is an inhomogeneous differential equa- x on the tunnel, dwðxÞ, is calculated, according to Equation tion of fourth order with a constant coefficient, it is extremely (22), as difficult to derive directly its analytical solution. Therefore, the form of the analytical solution was assumed to be PðξÞλ −λjx−ξj composed of two parts: the general solution part and the dwðxÞ = e ðcos ðλjx − ξjÞ + sin ðλjx − ξjÞÞdξ: 2Dk particular solution part. Let pðxÞ = 0, one can obtain the cor- ð23Þ responding homogeneous differential equation d 4 w ðx Þ Integrating Equation (23) over the range of the distribu- EI eq + DkwðxÞ = 0: ð16Þ tion of the additional distributed load, the solution for dx4 Equation (13) is derived: Therefore, the general solution has the form ð +∞ λ wðx Þ = PðξÞe−λjx−ξj ðcos ðλjx − ξjÞ + sin ðλjx − ξjÞÞdξ: wðxÞ = eλx ðC 1 cos ðλxÞ + C2 sin ðλxÞÞ 2Dk −∞ ð17aÞ + e−λx ðC 3 cos ðλxÞ + C4 sin ðλxÞÞ, ð24Þ sffiffiffiffiffiffiffiffiffiffiffi DK Consequently, the bending moment and shear force at λ= 4 , ð17bÞ the point x on the tunnel axis are calculated, respectively, 4EI eq by where C 1 , C2 , C 3 , and C 4 = undetermined coefficients and λ = elastic characteristic coefficient. d 2 w ðx Þ M = −EI eq , ð25Þ Considering the symmetry of the beam on an elastic dx2 foundation, we have wðxÞjx→∞ = 0, ð18aÞ dM d 3 w ðx Þ Q= = −EI eq : ð26Þ dx dx3 dwðxÞ = 0: ð18bÞ The proposed method for predicting the response of a dx x→∞ constructed tunnel to an adjacent excavation with dewater- By manipulation of Equations (17) and (18), one obtains ing treats the constructed tunnel as a long beam on an elas- C 1 = C 2 = 0 and C 3 = C 4 . Let C3 = C4 = C, the form of the tic foundation and calculates the internal force and general solution for Equation (16) can be transformed to deformation for the constructed tunnel by using the Wink- ler foundation model. The required parameters for the pro- wðxÞ = Ce−λx ðcos ðλxÞ + sin ðλxÞÞ: ð19Þ posed method include the equivalent longitudinal stiffness of the constructed tunnel EI eq , external diameter of the Assume that a point load P0 is applied at the central sec- constructed tunnel D, and coefficient of subgrade reaction tion of the beam on an elastic foundation. Considering the k. The advantages of the proposed method over other equilibrium between the subgrade reaction and the external models are lesser parameters and convenient calculation load, we have process.
6 Geofluids 4. Verification 24 m y The performance of the proposed theoretical method for pre- dicting the deformation and internal force characteristics of a 18.1 m constructed tunnel induced by an adjacent excavation with Excavation x dewatering is challenged against three well-documented case histories. The predicted tunnel displacement characteristics are verified by the comparisons with the monitoring data 28 m obtained in the field and the three-dimensional finite element Up-line tunnel analysis results obtained in this study. The ability of the pro- Down-line tunnel posed method in well predicting the tunnel internal force Figure 4: Site plan view for the SDRI Project. characteristics is demonstrated by comparing it with the three-dimensional finite element analysis results. Table 2: Soil parameters for the SDRI Project [52]. 4.1. Shanghai Dongfang Road Interchange Project. The first Soil layer h (m) γ (kN/m3) c (kPa) μ ES (MPa) case history used for verifying the proposed method is the Artificial fill 1.82 18.5 16 NA NA Shanghai Dongfang Road Interchange (SDRI) Project Silty clay ②1 1.13 18.4 10 0.4 6.43 reported in Xu and Huang [52]. In this case history, the plan Silty clay ②2 0.82 17.7 13 0.3 3.71 view showing the relative position of the excavation and the tunnels is presented in Figure 4. The soil parameters for this Silty clay ③1 1.08 17.7 14 0.3 4.43 case history are listed in Table 2. The geometry of the excava- Sandy silt ③2 2.28 18.3 3 0.35 9.72 tion resembles a parallelogram of 26 m in length and 18 m in Silty clay ③3 2.46 17.2 13 0.35 3.63 width. The short side of the excavation is oriented at 66° rel- Sandy silt 8.7 16.6 14 0.35 2.27 ative to the x-axis of the coordinate system. The excavation Clay ⑤1 2.41 17.9 19 0.4 4.07 depth is approximately 6.5 m. The angle between the axis of Silty clay ⑤2 3.89 18.1 18 0.4 4.55 the constructed tunnels and the y-axis of the coordinate sys- Silty clay 4.25 19.4 43 0.35 6.09 tem is 45°. The upline of the constructed tunnels is directly below the excavation. The minimum distance between the Note. h = soil thickness; γ = unit weight; c = cohesion; μ = Poisson’ s ratio; ES = modulus of compressibility; NA = not available. tunnel crown and the excavation bottom is 2.76 m, with the tunnel cover depth being approximately 9.26 m. The external 24 diameter and the equivalent stiffness of the constructed tun- nels are, respectively, 6.2 m and 3:93 × 107 kN·m2. In theoret- 20 ical calculation, it was assumed that the upline of the constructed tunnels was parallel with the excavation, consid- Vertical displacement (mm) 16 ering the relatively small angle between the upline and the excavation. 12 In theoretical calculation for this case history, the hori- zontal additional stress in the upline of the constructed tun- 8 nels induced by excavation can be neglected because of the relative position of the upline and the excavation. In other 4 words, the predicted tunnel deformation using the proposed method takes account of only the vertical additional stress induced by excavation. 0 Figure 5 presents the excavation-induced vertical dis- placements of the upline tunnel for the SDRI Project –4 –75 –60 –45 –30 –15 0 15 30 45 60 75 obtained by finite element analysis, field measurement, and theoretical calculation. The finite element analysis results y (m) presented in Figure 5 were obtained by Xu and Huang [52] using the MARC software. From Figure 5, it can be indicated Numerical calculation by Xu and Huang (2008) that the distribution of the tunnel vertical displacement along Field measurement by Xu and Huang (2008) the tunnel axis is similar for different methods. The distribu- Theoretical calculation by the proposed method tion conforms approximately to a Gaussian distribution. The Figure 5: Excavation-induced tunnel vertical displacements for the tunnel vertical displacements reach maxima in the middle of SDRI Project. the upline tunnel axis intersecting with the vertical projection of the excavation. The maximum tunnel vertical displace- ments are, respectively, 11.5, 16, and 16.96 mm correspond- able to the field measurement when compared with the finite ing to the finite element analysis, field measurement, and element analysis result. Moreover, the predicted tunnel verti- theoretical calculation. The maximum tunnel vertical dis- cal displacements by the proposed theoretical method are placement calculated by the proposed method is more agree- generally greater than that by finite element analysis and field
Geofluids 7 N Hengfeng bank office building Up-line tunnel 6 5 4 3 2 1 18 17 16 15 14 13 12 11 10 9 8 7 30 29 28 27 26 25 24 23 22 21 20 19 Down-line tunnel Monitoring points (a) 2.0 m 9.0–10.7 m 9.0–10.7 m Supporting 5.1 m Pile 3.8 m Supporting Lattice column m 10.3–10.9 m Bottom plate 6.2 Down-line tunnel Up-line tunnel 13 m Upright pile Diaphragm wall (b) Figure 6: Schematic of the relative position of the excavation and the tunnel for the HBOB Project: (a) plan view and (b) cross-section view. Table 3: Soil parameters for the HBOB Project [53]. 10 γ c ES φ Soil layer h (m) (kN/m3) (kPa) (MPa) (degree) Horizontal displacement (mm) Plain fill ① 2.0–4.5 18.9 15 NA 10 Powder sticky 5 2.5–4.8 19.6 32.35 6.01 13.74 clay ② Silt ③ 1.2–4.3 18.8 9.84 10.76 27.83 Silty clay ④1 2.1–5.6 18.9 17.46 6.54 13.91 Silty clay ④2 1.8–3.8 18.7 10.86 7.6 20.29 0 Silty clay ④3 5.8–7.0 18.9 20.58 5.18 12.26 Clay ⑤ 3.1–4.1 20.1 60.78 7.67 13.81 Silty clay ⑥ 6.0–7.2 19.1 34.59 7.53 16.65 Silty clay ⑦ 2.0–3.5 18.8 20.4 6.47 13.19 –5 Silty clay ⑧ 8.8–9.9 18.7 15.36 6.97 20.24 32 28 24 20 16 12 8 4 0 Silty clay ⑨ 5.0–6.9 19.5 27.34 6.85 12.53 Monitoring points 11.5– Silty clay ⑩ 19.4 23.22 7.31 14.07 12.1 Theoretical calculation by the proposed method Note. h = soil thickness; γ = unit weight; c = cohesion; ES = modulus of Field measurement by sun (2017) compressibility; φ = internal friction angle; NA = not available. Poisson’s ratio was taken as 0.35 in the calculation for all the soil layers. Figure 7: Excavation-induced tunnel horizontal displacements for the HBOB Project.
8 Geofluids Table 4: Soil parameters for the HMLYRS Project. Soil layer h (m) γ (KN/m3) c (kPa) μ ES (MPa) φ (degree) k (m/d) Miscellaneous soil 5.1 17.5 8 0.35 NA 10 0.001 Clay1 4.7 19.8 10 0.3 40 13 0.0006 Clay2 6.4 20.2 15 0.29 30 13 0.0004 Clay3 6.5 20.5 25 0.26 30 14 0.0004 SWS 1.1 21 30 0.26 70 20 NA Weathered sandstone NA 22 40 0.24 90 25 NA Note. h = soil thickness; γ = unit weight; c = cohesion; μ = Poisson’ s ratio; ES = modulus of compressibility; φ = internal friction angle; k = permeability coefficient; NA = not available; SWS = strongly weatherly sandstone. measurement. For this, the primary reason is that the pro- 120 Excavation m posed theoretical method has not taken account of the influ- 20 m ence of excavation supporting on the excavation unloading- induced additional stress. m 40 40 m 4.2. Hengfeng Bank Office Building Project. The second case history used for verifying the proposed method is the Heng- feng Bank Office Building (HBOB) Project reported by Sun [53]. In this case history, an excavation adjacent to the m Suzhou Metro Line 1 was made for the construction of an 140 Tunnel office building for Hengfeng Bank. The excavation geometry is approximately a rectangle with its length and width being, respectively, 85 m and 45 m. The average excavation depth is Figure 8: Meshing of numerical model for the HMLYRS Project. 10.6 m. To ensure stability and safety, diaphragm walls and concrete structs were used to support the excavation. The rel- 4.3. Hefei Metro Line 1 Yungu Road Station Project. The third ative position of the excavation and the tunnel is depicted in case history used for verifying the proposed method is the Figure 6. Table 3 summarizes the soil parameters for the Hefei Metro Line 1 Yungu Road Station (HMLYRS) Project. HBOB Project. An imaginary excavation is made adjacent to the HMLYRS From Figure 6, it can be seen that the tunnel axis is Project. By performing three-dimensional finite element approximately parallel with the south side of the excavation. analysis, the excavation-induced tunnel internal force and The distance between the excavation side and the tunnel deformation characteristics are compared between the theo- periphery ranges from 10.3 m to 10.9 m. The cover depth of retical calculation and numerical analysis results. the tunnel ranges from 9.0 m to 10.7 m. The minimum dis- According to the drilling data in terms of age of deposi- tance between the upline and downline tunnels is 6.8 m. tion and genetic type as well as the laboratory testing results, The external and internal diameters and the equivalent stiff- the ground stratums for the HMLYRS Project are composed ness are, respectively, 6.2 m, 5.5 m, and 3:45 × 107 kN·m2. of six layers: miscellaneous fill, clayey soil I, clayey soil II, Monitoring was performed at 30 cross-sections of the upline clayey soil III, highly weathered sandstone, and moderately and downline tunnels with the interval being 5 ring-lengths. weathered sandstone. The parameters for these soil layers For convenience, in theoretical calculation, it was assumed are summarized in Table 4. The miscellaneous fill consists that the tunnels are parallel with the excavation and that of construction waste, natural fibers [54–58], and other mate- the excavation is rectangular in shape. rials. The groundwater level is about 2.5 m below the ground A comparison of the excavation-induced horizontal dis- surface. The specific yield was taken as 0.1 in the theoretical placements of the upline tunnel for the HBOB Project calculation. between the theoretical calculation and field measurement In the three-dimensional finite element analysis, the plan is made in Figure 7. It can be noted that a slight discrepancy view size of the excavation was assumed to be 40 m × 20 m exists between the theoretical calculation and field measure- × 10 m. The water level within the excavation after dewater- ment. The maximum tunnel horizontal displacement occurs ing was assumed to be 0.5 m below the excavation bottom. at a position corresponding to the middle of the excavation, The cover depth of the axis of the constructed tunnels for both for the theoretical calculation and field measurement. the HMLYRS Project is 20 m. The distance between the exca- The maximum tunnel horizontal displacements predicted vation boundary and the tunnel axis is 10 m. The external by the proposed method and monitored by instrumentations and internal diameters of the constructed tunnels are, respec- are, respectively, 6 mm and 5.2 mm. The overestimate of the tively, 6.2 m and 5.4 m. Taking no account of the influence of maximum tunnel horizontal displacement by the proposed the segment joint strength, the equivalent stiffness of the con- method is attributed to the overlook of the influence of exca- structed tunnels was taken as 3:45 × 107 kN·m2. In order to vation supporting and stratigraphic distribution. ensure that the numerical analysis results are consistent with
Geofluids 9 10 Displacement TZ (m) +6.45268e–003 14.0% +5.85304e–003 Vertical displacement (mm) 4.0% +5.25339e–003 6.0% 5 +4.65374e–003 6.0% +4.05409e–003 4.0% +3.45445e–003 4.0% +2.85480e–003 4.0% +2.25515e–003 0 4.0% +1.65550e–003 8.0% +1.05586e–003 8.0% +4.56209e–004 12.0% –1.43439e–004 26.0% –7.43086e–004 –5 –60 –40 –20 0 20 40 60 Vertical displacement contour by numerical analysis Tunnel axis (m) Numerical analysis using midas GTS NX Theoretical calculation by the proposed method Figure 9: Excavation-induced tunnel vertical displacements by numerical and theoretical calculation. the theoretical calculation results and to mitigate the influ- and incidence of the excavation-induced tunnel vertical dis- ence of tunnel dimension on the excavation unloading, the placement obtained by numerical analysis are greater than one-dimensional beam element was used to represent the that obtained by theoretical calculation. constructed tunnel in numerical modelling. Figure 8 shows Figure 10 compares the distribution of excavation- the meshing of the numerical model for the HMLYRS Pro- induced tunnel vertical bending moment along the tunnel ject. It is shown that the dimensions of the numerical model axis between numerical and theoretical calculation results. are 120 m × 40 m × 140 m. The Modified Mohr-Coulomb Note that the numerical analysis results in Figure 10 repre- (MMC) model was used to simulate the stress-strain behav- sent the incremental change of the tunnel vertical bending ior of the soils. In the MMC model adopted by the present moment before and after the excavation. Clearly, a similar numerical analysis, the secant modulus by standard drained distribution of the excavation-induced tunnel vertical bend- triaxial tests was estimated by Equation (27) for the miscella- ing moment is found between the numerical analysis and neous fill and clay (i.e., Eref 50 ) and by Equation (28) for the theoretical calculation results. This distribution is almost w- ~ ref shaped and symmetrical with respect to the middle of the sandstone (i.e., E50 ); the unloading/reloading stiffness was tunnel axis. The maximum tunnel vertical bending moments estimated by Equation (29) for the miscellaneous fill and clay are achieved at the middle of the tunnel axis with the magni- (i.e., Eref ~ ref ur ) and by Equation (30) for the sandstone (i.e., Eur ): tudes being, respectively, 608 kN·m and 560.31 kN·m for the theoretical calculation and numerical analysis results. With Eref ref 50 = 2Eoed , ð27Þ an increase in the distance between a point on the tunnel axis and the middle of the tunnel axis, the tunnel vertical bending ~ ref ~ ref ð28Þ moments decrease gradually both for the theoretical calcula- E 50 = Eoed , tion and numerical analysis results. When this distance reaches about 20 m, the tunnel vertical bending moments Eref ref ur = 5E50 , ð29Þ reverse their direction. The negative tunnel vertical bending moment peaks, respectively, at the distance of about 30 m ~ ref E ~ ref ur = 3E50 , ð30Þ with a magnitude of -272 kN·m and at the distance of about 27 m with a magnitude of -302.83 kN·m for the theoretical where Eref oed = tangential stiffness in uniaxial compression tests calculation and numerical analysis results. The tunnel verti- on miscellaneous fill or clay and E ~ ref oed = tangential stiffness in cal bending moments become zero at the ends of the tunnel uniaxial compression tests on sandstone. axis due to the limitation of the excavation depth and length. A comparison of the distribution of excavation-induced Figure 11 presents a comparison of the distribution of tunnel vertical displacement along the tunnel axis is made excavation-induced tunnel vertical shear force along the tun- in Figure 9 between the numerical and theoretical calculation nel axis between numerical analysis and theoretical calcula- results. It is clear that the two distributions are similar in tion results. Note that the numerical analysis results in form. The maximum tunnel vertical displacements are, Figure 11 represent the incremental change of the tunnel ver- respectively, 6.45 mm and 5.70 mm for the numerical and tical shear force before and after the excavation. It can be theoretical calculation results. Moreover, both the magnitude indicated that the distributions obtained by theoretical
10 Geofluids Beam force Beam force 1000 Bending MMNT Z (kN⁎m) Bending MMNT Z (kN⁎m) +2.57143e+002 +3.06894e+002 3.2% 13.3% +2.18170e+002 +2.23987e+002 Vertical bending moment (kN.m) 750 5.1% 21.0% +1.79197e+002 +1.41080e+002 5.1% 16.2% +1.40225e+002 +5.81733e+001 500 7.0% 13.3% +1.01252e+002 –2.47337e+001 6.3% 9.5% +6.22795e+001 –1.07641e+002 6.3% 2.9% +2.33069e+001 –1.90548e+002 250 7.0% 3.8% –1.56657e+001 –2.73455e+002 13.9% 3.8% –5.46383e+001 –3.56362e+002 0 15.2% 1.9% –9.36109e+001 –4.39269e+002 16.5% 3.8% –1.32583e+002 –5.22176e+002 10.8% 3.8% –250 –1.71556e+002 –6.05083e+002 3.8% 6.7% –2.10529e+002 –6.87990e+002 Before excavation After excavation –5000 –60 –40 –20 0 20 40 60 Vertical bending moment contours by numerical analysis Tunnel axis (m) Numerical analysis using midas GTS NX Theoretical calculation by the proposed method Figure 10: Excavation-induced tunnel vertical bending moments by numerical and theoretical calculation. 100 Beam force Beam force Shear force Y (kN) Shear force Y (kN) +1.35510e+002 +1.78419e+002 3.6% 1.8% +1.13107e+002 +1.48928e+002 8.5% 3.7% 50 +9.07042e+001 Vertical shear force (kN) 9.1% +1.19437e+002 +6.83013e+001 9.2% 9.1% +8.99465e+001 +4.58983e+001 10.5% 9.1% +6.04557e+001 +2.34954e+001 11.4% 9.1% +3.09649e+001 0 +1.09244e+000 11.4% 9.1% +1.47407e+000 –2.13105e+001 11.4% 9.1% –2.80168e+001 –4.37134e+001 11.4% 9.1% –5.75076e+001 –6.61164e+001 11.2% –50 9.1% –8.69984e+001 –8.85193e+001 9.8% 9.1% –1.16489e+002 –1.10922e+002 6.2% 6.0% –1.45980e+002 –1.33325e+002 1.8% –1.75471e+002 –100 Before excavation After excavation –60 –40 –20 0 20 40 60 Vertical shear force contours by numerical analysis Tunnel axis (m) Numerical analysis using midas GTS NX Theoretical calculation by the proposed method Figure 11: Excavation-induced tunnel vertical shear forces by numerical and theoretical calculation. calculation and numerical analysis are similar in form. The tion characteristics for a constructed tunnel is validated. distributions are nearly antisymmetric about the middle of Therefore, the proposed theoretical method may serve as a the tunnel axis. The excavation-induced tunnel vertical shear tool to provide a preliminary prediction of the response of force is zero in the middle of the tunnel axis and reaches the a constructed tunnel to an adjacent excavation with maximum at a distance of 14 m from the middle of the tunnel dewatering. axis for the theoretical calculation result and at a distance of 18 m for the numerical analysis result. The maxima are, 5. Parametric Analysis respectively, 48.12 kN and 50.55 kN for the theoretical calcu- lation and numerical analysis results. The shear force stabi- By performing parametric analysis, this section investigates lizes at a distance of approximately 50 m from the middle the influence of excavation and tunnel parameters on the ver- of the tunnel axis. tical displacement and internal force characteristics of a con- Based on the three case histories presented above, the structed tunnel induced by an adjacent excavation with performance of the proposed theoretical method in well pre- dewatering. To this end, an imaginary case is considered dicting the excavation-induced internal force and deforma- where the longer side of a rectangular excavation is parallel
Geofluids 11 20 2000 Maximum vertical displacement (mm) Maximum bending moment (kN.m) 15 1500 10 1000 5 500 0 0 0 5 10 15 20 0 5 10 15 20 Distance between excavation and tunnel (m) Distance between excavation and tunnel (m) Specific yield Specific yield = 0.05 = 0.25 = 0.05 = 0.25 = 0.15 = 0.35 = 0.15 = 0.35 (a) (b) 150 120 Maximum shear force (kN) 90 60 30 0 0 5 10 15 20 Distance between excavation and tunnel (m) Specific yield = 0.05 = 0.25 = 0.15 = 0.35 (c) Figure 12: Effects of the distance between excavation and tunnel on (a) tunnel maximum vertical displacement; (b) tunnel maximum bending moment; (c) tunnel maximum shear force. with the axis of the constructed tunnel. For this imaginary excavation and the periphery of the constructed tunnel: 3.0, case, the soil and tunnel parameters are the same as in the 6.0, 9.0, 12.0, 15.0, and 18.0 m. Figure 12 presents the effects HMLYRS Project described in the former section. In this of the distance between excavation and tunnel on tunnel parametric analysis, the investigated parameters are the dis- maximum vertical displacement, tunnel maximum bending tance between excavation and tunnel, initial water level, exca- moment, and tunnel maximum shear force. It can be indi- vation depth, excavation plan view size, and specific yield. cated from Figure 12 that the tunnel maximum vertical dis- placement, maximum bending moment, and maximum 5.1. Effect of Distance between Excavation and Tunnel. Six shear force decrease nonlinearly with an increase in the dis- different distances are considered between the side of the tance between excavation and tunnel. This decreasing trend
12 Geofluids 20 1500 Maximum vertical displacement (mm) Maximum bending moment (kN.m) 15 1200 900 10 600 5 300 0 0 20 25 30 35 40 45 20 25 30 35 40 45 Initial water level (m) Initial water level (m) Specific yield Specific yield = 0.05 = 0.25 = 0.05 = 0.25 = 0.15 = 0.35 = 0.15 = 0.35 (a) (b) 100 80 Maximum shear force (kN) 60 40 20 0 20 25 30 35 40 45 Initial water level (m) Specific yield = 0.05 = 0.25 = 0.15 = 0.35 (c) Figure 13: Effects of the initial water level on (a) tunnel maximum vertical displacement; (b) tunnel maximum bending moment; (c) tunnel maximum shear force. is of a lower rate at a greater distance between excavation and displacement, maximum bending moment, and maximum tunnel. At the 18.0 m distance between excavation and tun- shear force decrease with increasing the specific yield, irre- nel, the tunnel maximum vertical displacement, maximum spective of the distance between excavation and tunnel. At bending moment, and maximum shear force are, respec- the 3.0 m distance between excavation and tunnel, an tively, 2.2 mm, 220.0 kN·m, and 17.5 kN. When the distance increase in the specific yield from 0.05 to 0.35 leads to an between excavation and tunnel exceeds 18.0 m, the influence approximately 30% reduction in the tunnel maximum ver- of excavation with dewatering on the responses of the con- tical displacement, maximum bending moment, and maxi- structed tunnel can be neglected. Moreover, it can also be mum shear force. This reduction increases to indicated from Figure 12 that the tunnel maximum vertical approximately 65% when the distance between excavation
Geofluids 13 20 2000 Maximum vertical displacement (mm) Maximum bending moment (kN.m) 15 1500 10 1000 500 5 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Excavation depth (m) Excavation depth (m) Specific yield Specific yield = 0.05 = 0.25 = 0.05 = 0.25 = 0.15 = 0.35 = 0.15 = 0.35 (a) (b) 150 120 Maximum shear force (kN) 90 60 30 0 0 5 10 15 20 25 30 Excavation depth (m) Specific yield = 0.05 = 0.25 = 0.15 = 0.35 (c) Figure 14: Effects of the excavation depth on (a) tunnel maximum vertical displacement; (b) tunnel maximum bending moment; (c) tunnel maximum shear force. and tunnel reaches 18.0 m. This indicates that the specific level on the tunnel maximum vertical displacement, maxi- yield has a significant effect on the tunnel maximum verti- mum bending moment, and maximum shear force are pre- cal displacement, maximum bending moment, and maxi- sented in Figure 13. It can be indicated that the tunnel mum shear force. maximum vertical displacement, maximum bending moment, and maximum shear force decrease with an 5.2. Effect of Initial Water Level. Six different initial water increase in the initial water level. This is attributed to the levels are considered in the parametric analysis: 25.0, 28.0, reduced vertical additional stress on the constructed tunnel 31.0, 34.0, 37.0, and 40.0 m. The effects of the initial water at a higher dewatering depth. Moreover, at an initial water
14 Geofluids 40 4000 Maximum vertical displacement (mm) Maximum bending moment (kN.m) 30 3000 20 2000 10 1000 0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 L/B L/B Specific yield Specific yield = 0.05 = 0.25 = 0.05 = 0.25 = 0.15 = 0.35 = 0.15 = 0.35 (a) (b) 300 250 Maximum shear force (kN) 200 150 100 50 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 L/B Specific yield = 0.05 = 0.25 = 0.15 = 0.35 (c) Figure 15: Effects of the excavation plan view size on (a) tunnel maximum vertical displacement; (b) tunnel maximum bending moment; (c) tunnel maximum shear force. level, the tunnel maximum vertical displacement, maximum the influence of the specific yield on the tunnel displacement bending moment, and maximum shear force decrease with and internal force characteristics is more significant at a an increase in the specific yield. The rate of this decrease is higher initial water level. higher at a greater initial water level. At the 25.0 m initial water level, an increase in the specific yield from 0.05 to 5.3. Effect of Excavation Depth. Seven different excavation 0.35 leads to, respectively, 9.6%, 24.1%, and 22.2% reductions depths are considered in the parametric analysis: 6.0, 9.0, in the tunnel maximum vertical displacement, maximum 12.0, 15.0, 18.0, 21.0, and 24.0 m. Figure 14 depicts the effects bending moment, and maximum shear force. The reductions of excavation depth on the tunnel maximum vertical dis- are, respectively, 70.0%, 60.1%, and 74.0% at the 40.0 m ini- placement, maximum bending moment, and maximum tial water level. This indicates that at an excavation depth, shear force. It is shown that the rate of increase in the tunnel
Geofluids 15 maximum vertical displacement, maximum bending method which can account for both the excavation unloading moment, and maximum shear force as increasing the excava- and excavation dewatering effects. The conclusions drawn tion depth decreases until reaching the 15.0 m excavation from this study can be summarized as follows. depth and then increases after reaching this excavation depth. At an excavation depth greater than 15.0 m, a striking (i) The proposed theoretical method taking account increase in the tunnel maximum vertical displacement, max- of the excavation unloading and dewatering effects imum bending moment, and maximum shear force can be is capable of predicting excavation-induced addi- observed with an increase in the excavation depth. This indi- tional stress on the constructed tunnel that agrees cates that the effect of excavation depth on tunnel maximum well with the actual engineering. By adopting the vertical displacement, maximum bending moment, and max- beam on elastic foundation theory, the tunnel imum shear force is more significant at an excavation depth displacement and internal force under the action greater than the cover depth of the constructed tunnel. In of the excavation-induced additional stress are addition, the tunnel maximum vertical displacement, maxi- derived. This derivation is simple in calculation. mum bending moment, and maximum shear force decrease The derived results are reliable with increasing the specific yield. At the 6.0 m excavation (ii) Based on three well-documented case histories, the depth, an increase in the specific yield from 0.05 to 0.35 causes, respectively, 28.0%, 40.8%, and 48.0% reductions in predicted excavation-induced tunnel displacement the tunnel maximum vertical displacement, maximum bend- and internal force characteristics using the proposed ing moment, and maximum shear force. The reductions are, method are compared with the field monitoring and respectively, 27.4%, 38.0%, and 55.0% at the 24.0 excavation numerical analysis results. The comparison verifies depth. This indicates that the specific yield has a significant the performance of the proposed method. The pro- effect on the tunnel maximum vertical displacement, maxi- posed method lay the theoretical foundations for mum bending moment, and maximum shear force. the safety assessment and disaster prevention in sim- ilar engineering 5.4. Effect of Excavation Plan View Size. The excavation plan view size is described with the ratio of excavation length to (iii) A parametric analysis is performed for the effects of excavation width (i.e., L/B). In the parametric analysis, seven excavation depth, distance between excavation and different excavation plan view sizes are considered: 0.67, 0.8, tunnel, excavation plan view size, initial water level, 1.0, 1.25, 1.5, 1.75, and 2.0. The excavation length is fixed at and specific yield on the tunnel displacement and 40.0 m when L/B < 1:0; otherwise, the excavation width is internal force characteristics. It is found that the fixed at 40.0 m. Figure 15 presents the effects of the excava- effect of excavation depth becomes significant when tion plan view size on the tunnel maximum vertical displace- the excavation depth exceeds the cover depth of the ment, maximum bending moment, and maximum shear constructed tunnel. The influence of adjacent exca- force. It can be indicated that at L/B < 1:0 or L/B > 1:0, the vation on the constructed tunnel can be overlooked tunnel maximum vertical displacement, maximum bending if the distance between excavation and tunnel is moment, and maximum shear force increase approximately greater than the tunnel cover depth. The effect of linearly with an increase in L/B. Moreover, the rate of the excavation plan view size on the side parallel increase is greater at L/B > 1:0 than at L/B < 1:0, indicating with the tunnel axis is more significant than that that the effect of changing the excavation width paralleling on the side perpendicular to the tunnel axis. A with the tunnel axis on the tunnel displacement and internal higher initial water level corresponds to a smaller force characteristics is more significant than that for the exca- excavation-induced additional stress on the con- vation length perpendicular to the tunnel axis. In addition, structed tunnel. An increase in the specific yield with an increase in the specific yield, the tunnel maximum from 0.05 to 0.35 leads to an approximately 70% vertical displacement, maximum bending moment, and max- reduction in the tunnel displacement and internal imum shear force decrease. At an excavation depth and ini- force tial water level, the effect of specific yield on the tunnel displacement and internal force characteristics is not signifi- Data Availability cant for all the considered excavation plan view sizes. The data used to support the findings of this study are avail- 6. Conclusions able from the corresponding authors upon request. The safety operation of a constructed tunnel is affected by an Conflicts of Interest adjacent excavation with dewatering. It is significant for practicing engineers to predict the displacement and internal The authors declare that they have no conflicts of interest. force characteristics of a constructed tunnel induced by an adjacent excavation with dewatering. However, most of the Acknowledgments previous theoretical studies relating to this topic focus on the excavation unloading effect and have neglected the effect This paper gets its funding from projects (51774107, of dewatering. In view of this, this paper proposes a new 51774322, 51774131, and 51874112) supported by the
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