S S symmetry
Article Influence of Cairo Metro Tunnel Excavation on Pile Deep Foundation of the Adjacent Underground Structures: Numerical Study
Mo’men Ayasrah 1,*, Hongsheng Qiu 2 and Xiedong Zhang 2
1 Communication and Transportation Engineering, School of Transportation, Wuhan University of Technology, Wuhan 430063, China 2 Road and Railway Engineering, School of Transportation, Wuhan University of Technology, Wuhan 430063, China; [email protected] (H.Q.); [email protected] (X.Z.) * Correspondence: [email protected]; Tel.: +86-15623766037
Abstract: Day by day the call to solve traffic congestion problems is increasing. Subway tunnels and high-speed railway are commonly used for transportation. Therefore, tunnel construction induces soil movement, which in turn affects the stability and integrity of adjacent existing buildings. A series of numerical simulations have been established to investigate the effects of tunnel construction of the Greater Cairo Metro–Line 3-Phase-1 on adjacent pile cap foundations of Garage El-Attaba building. Many parameters have been investigated such as tunnel diameter and the distance between pile and tunnel at different tunnel axis and deep and shallow tunnel. After thorough analysis of the results’ simulation, it was found that the tunneling induces additional axial forces and bending moment as well as increasing axial settlement and lateral deflection. Moreover, the results obtained from the parametric study for the shallow and deep tunnel show that the tunnel depth has a much significant effect on piles responses. Finally, the tunnel diameter has an impact on pile responses as well as the Citation: Ayasrah, M.; Qiu, H.; pile cap foundation influenced by the tunnel when the tunnel is in very close vicinity of the pile, and Zhang, X. Influence of Cairo Metro its effect is modest to negligible if located far away from the buildings. Tunnel Excavation on Pile Deep Foundation of the Adjacent Keywords: tunnel construction; soil movement; numerical simulations; bending moment; lateral Underground Structures: Numerical Study. Symmetry 2021, 13, 426. deflection; shallow tunnel; deep tunnel https://doi.org/10.3390/sym13030426
Academic Editor: Igor V. Andrianov 1. Introduction Received: 6 February 2021 In the light of the fast-urban developments in major cities, the demand for under- Accepted: 3 March 2021 ground public facilities is vastly increasing. In recent years, the construction of tunnels Published: 6 March 2021 has been relied on solving traffic congestion problems in many cities of the world. Pile foundation is commonly used in high-rise buildings to transmit the upper load to the Publisher’s Note: MDPI stays neutral subsurface. During the tunnel construction, many considerations must be taken especially with regard to jurisdictional claims in tunneling effects on neighboring buildings with deep foundations [1–7]. published maps and institutional affil- It is well-acknowledged that the ground deformation occurring during the tunnel iations. construction process relative to existing piles plays a significant role. Ground deformation affects the performance and the stability of piles, which in turn changes piles behavior. These changes induce additional axial settlements and lateral deflections as well as addi- tional axial forces and bending moments. Consequently, it may lead to structural distress Copyright: © 2021 by the authors. or failure of foundations and subsequently damage of the super-structure [2,8–17]. Based Licensee MDPI, Basel, Switzerland. on the relative length of the pile compared to the depth of the tunnel, two main categories This article is an open access article can be made: the deep tunnel “short pile” where the tunnel axis is located below the tip of distributed under the terms and the existing piles, (Lp/H < 1), while the second one is the shallow tunnel “long pile” where conditions of the Creative Commons the tunnel axis is located above the tip of the existing pile, (Lp/H > 1) [18–20]. Attribution (CC BY) license (https:// In the past decades, there has been a growing interest to understand the simple and creativecommons.org/licenses/by/ reliable predictions of the tunneling effect on adjacent structures and soil movements 4.0/).
Symmetry 2021, 13, 426. https://doi.org/10.3390/sym13030426 https://www.mdpi.com/journal/symmetry Symmetry 2021, 13, 426 2 of 22
around the tunnel. However, several authors [21–24] have proposed an empirical relation- ship between tunneling effects and associated structural damage based on the analysis of previous case studies. In addition, simple physical tests were built in laboratories, such as centrifuge model tests, and based on the results from analysis, design guidance for practical engineering constructions can be provided [8,25–27]. On the other hand, several studies based on numerical modeling, especially the finite element method, have been presented to simulate tunnel excavation. In addition, numerical simulation of any geotechnical problem depends mainly on the accuracy of the constitutive model used to simulate the stress-strain relationship of the soil. There are many constitutive soil models that have been developed based on the different purposes and concepts [28,29]. According to the full 3D FEM, modeling analysis conducted by [30] carried out a 3D finite element model to study the effects of tunneling on the adjacent piled structures using modified Mohr–Coulomb. The results showed that some critical responses reach maximum worth during tunneling, and it is not necessary to take place at the end of tunneling. In addition, the soil settlement was reduced; however, the increasing pile axial loads raise the risk on the piled structure. Moreover, the decrement in soil settlement indicated that the piles which extended deeper than the tunnel actually supported the soil above the tunnel. Meanwhile, Lee and Jacobsz [31] conducted 3D elastic–plastic numerical for tunnel- pile interactions. It was found that when a pile is located within 0–0.6 and 1.2–2.4 times the tunnel diameter, the surface settlement may not follow the normal settlement distributions. Therefore, they suggested, for safety, the position of piles should be at least one time the tunnel diameter measured laterally from the tunnel’s crown to preserve the serviceability of the piled foundations. In addition, [32] executed out three-dimensional finite element analyses to investigate the shear stress transfer mechanism of single piles during tunneling in weathered residual soil. The results showed that the shear stress of the upper part of the pile is large, while the bottom is small in the tunneling process. It was also determined, relating to the pile position, that the majority of the axial force on the pile was evolving within ±2 times the diameter of the tunnel behind and ahead of the piles. Jongpradist et al. [18] numerically conducted a three-dimensional simulation to inves- tigate the effects of tunneling on adjacent pile foundations. It was found that when the pile tip was located within +3 to −1 times, the tunnel diameter from the tunnel horizontal axis, a considerable settlement occurred at the pile head. Moreover, the impact of the region had the 60◦ inclination with respect to the horizontal direction. Hence, it can be concluded that most of the studies were ultimately related to study the effect of the tunnel construction on piles and pile groups. However, the main purpose of the present study is to investigate the influence of tunneling progress (remove of soil elements and install of the lining) adjacent to existing pile cap foundations. In view of that, a three-dimensional model using a Modified Mohr–Coulomb constitutive model for the soil layers was established for this objective. In this paper, the Greater Cairo Metro–Line 3-Phase-1 adjacent to Garage El-Attaba building pile cap foundations is taken as a case study. Furthermore, different factors have been studied with two different tunnel axes; deep and shallow tunnel on the response of pile cap foundation, among which tunnel diameter and the distance between pile and tunnel, to provide a better understanding of the behavior of pile responses influenced by tunneling. The remainder of this paper is structured as follows. In Section2, the details of the case study and soil conditions are presented. The Finite Element Modeling including numerical modeling, constitutive models and material parameters, and tunnel construction stage are discussed in Section3. In Section4, verification of the numerical model is investigated. Numerical results and discussion including the various factors are discussed in Section5. Finally, conclusions are drawn in Section6. Symmetry 2021, 13, x FOR PEER REVIEW 3 of 23
construction stage are discussed in Section 3. In Section 4, verification of the numerical model is investigated. Numerical results and discussion including the various factors are discussed in Section 5. Finally, conclusions are drawn in Section 6.
2. Case Study Symmetry 2021, 13, 426 3 of 22 2.1. Greater Cairo Metro-Line 3 Phase-1 The Greater Cairo Underground Metro project is one of the Egyptian mega projects created to solve many2. Casetraffic Study problems that have been recently elevated. Cairo Metro network connects the 2.1.capital Greater provinces Cairo Metro-Line with 3 th Phase-1e center of the city through three lines, line 1, line 2, and line 3. The GreaterThe Greater Cairo Cairo UndergroundMetro-Line Metro 3 was project constructed is one of the by Egyptian a slurry mega shield projects created to solve many traffic problems that have been recently elevated. Cairo Metro Tunnel Boring Machinenetwork (TBM), connects with the capitala 9.55 provinces m diameter. with the center The of tunnel the city throughhas external three lines, and line 1, internal diameters of 9.15line 2, and and line8.35 3. m, The respec Greatertively. Cairo Metro-Line The precast 3 was constructedsegmental by lining a slurry thickness shield Tunnel is 0.4 m. This line is 47.87Boring km Machine in length, (TBM), withstarting a 9.55 from m diameter. Imbaba The to tunnel Cairo has airport; external and also, internal as diameters of 9.15 and 8.35 m, respectively. The precast segmental lining thickness is 0.4 m. planned, it is going toThis be line constructed is 47.87 km in in length, four starting phases. from In Imbaba this tostudy, Cairo airport; The Greater also, as planned, Cairo it Metro, Line 3, Phase-1is moves going to underground be constructed in from four phases. El-Attaba In this to study, El-Abbasia The Greater stations Cairo Metro, and Linewas 3, considered to show thePhase-1 tunneling moves underground effect on fromGarage El-Attaba El-Attaba to El-Abbasia building stations foundation. and was considered This to show the tunneling effect on Garage El-Attaba building foundation. This Phase is 4.3 km Phase is 4.3 km in lengthin length and consists and consists of of5 5underground underground stations stations and 4and annexed 4 annexed structures, structures, as shown in as shown in Figure 1. Figure1.
(a) (b)
Figure Figure1. (a) 1.The(a) TheGreater Greater Cairo Cairo Metro-LineMetro-Line 3, after 3, afte Nationalr National Authority Authority for Tunneling; for (b )Tunneling; zone of the study (b) [zone33]. of the study [33]. Garage El-Attaba building is 77.04 m in length and 45.55 m in width. It is founded nearby the Greater Cairo Metro-Line 3-phase-1, built with eight stories as shown in Figure2 . Garage El-AttabaThis building building is about77.04 6.45 m min from length the center and of45.55 the tunnel m in and width. making It an is angle founded of about ◦ nearby the Greater Cairo42 fromMetro-Line the tunnel 3-phase-1, as shown in built Figure with3. This eight building stories was as supported shown in by Figure 245 non- displacement concrete piles arranged in the pile caps group. The pile dimensions are 0.6 m 2. This building is aboutin diameter6.45 m andfrom 20 mthe in center length and of passesthe tunnel through and layered making soil. The an design angle allowable of about load 42° from the tunnel ascapacity shown for the in pile Figure is 1200 kN3. [This34]. Fundamental building towas note thatsupported only the four by piles 245 caps non- (PC1, displacement concretePC2, piles PC3, arranged and PC4) thatin the are thepile nearest caps to group. the tunnel The are pile assigned dimensions in this study. are Figure 0.64 shows the pile caps details and the pile cap and pile tip location to tunnel axis. m in diameter and 20 m in length and passes through layered soil. The design allowable load capacity for the pile is 1200 kN [34]. Fundamental to note that only the four piles caps (PC1, PC2, PC3, and PC4) that are the nearest to the tunnel are assigned in this study. Figure 4 shows the pile caps details and the pile cap and pile tip location to tunnel axis.
Symmetry 2021, 13, x FORSymmetry PEER2021 REVIEW, 13, 426 44 of 22of 23 Symmetry 2021, 13, x FOR PEER REVIEW 4 of 23
Figure 2. Location of Garage El-Attaba according to Greater Cairo Metro and instruments system FigureFigure 2. 2.Location Location of Garage of Garage El-Attaba El-Attaba according according to Greater Cairoto Greater Metro andCairo instruments Metro and system instruments layout [33,35 system]. layout [33,35]. layout [33,35].
Figure 3. The pile caps position relative to the tunnel route. Units in (m). Figure 3. The pileFigure caps 3. positionThe pile caps relative position to relativethe tunnel to the route. tunnel Units route. Unitsin (m). in (m).
Symmetry 2021, 13, 426 5 of 22 SymmetrySymmetry 2021 2021, 13,, x13 FOR, x FOR PEER PEER REVIEW REVIEW 5 of5 23of 23
(a) (a) (b) (b) FigureFigure 4. (( aa4.)) The( Thea) The pile pile pile caps caps caps details details details and and and ( (b)) (pile pileb) pile cap cap and and pile pile tip locationtip location to tunnel to tunnel axis. axis. Units Units Units i inn (m) in (m) [34] [34 ].[34]. .
2.2.2.2.2.2. Soil Soil Soil Conditions Conditions Conditions GeotechnicalGeotechnicalGeotechnical investigation investigation investigation of of theof the the Greater Greater Greater Cairo Cairo Cairo Metro, Metro, Metro, Line Line Line 3, Phase Phase-13, Phase-1 included -1 included the the drillingdrillingdrilling of of thirteen thirteenof thirteen boreholes boreholes boreholes and and and stand standard standardard penetration penetration penetration tests tests tests [35] [35 [35]].. As As. Asshown shown shown in in FigureinFigure Figure 22,, 2, boreholeboreholeborehole No. No. No. 2A 2A 2Ais isnearest is nearest nearest to to theto the the Gar Garage Garageage El- El-AttabaAttabaEl-Attaba building. building. Therefore, Therefore, Therefore, the the soil the soil soilcross cross cross--sec--sec- tionsectiontion at thisat at thisthis borehole borehole borehole was was was taken taken taken as representativeas as representative representative of theof of the soil the soil soilprofile profile profile in thisin in this thisstudy. study. study. The The Thede- de- scriptiondescriptionscription of theof the thesoil soil soillayers layers layers is presented is is presented presented from fromfrom the the study the study study by by[36] by[36] which [36 which] which used used field used field and field and labor- and labor- atorylaboratoryatory tests tests for tests fordetermining for determining determining the the soil the soil properties soil properties properties as shownas as shown shown in Figurein in Figure Figure 5. The 5.5. The Thegroundwater groundwater groundwater ex- ex- istedexistedisted at an atat anaveragean averageaverage depth depthdepth of of1.65of 1.651.65 m mbelowm belowbelow the thethe ground groundground surface. surface.surface.
Figure 5. Soil profile at the location of BHD. 2A [35]. FigureFigure 5. Soil 5. Soil profile profile at theat the location location of BHD.of BHD. 2A 2A [35 ].[35].
SymmetrySymmetry2021 2021, 13, 13, 426, x FOR PEER REVIEW 6 ofof 2223
3.3. FiniteFinite ElementElement ModellingModelling 3.1.3.1. NumericalNumerical ModelModel AccordingAccording toto thethe overviewoverview ofof thethe GreaterGreater CairoCairo MetroMetro Line Line 3-phase-1 3-phase-1 project, project, there there isis thethe GarageGarage El-AttabaEl-Attaba building near the construction construction line. line. A A three three-dimensional-dimensional model model is isestablished established to tostudy study the the effect effect of excavation of excavation and andtunnel tunnel construction construction of Cairo of CairoMetro Metro on the onfoundations the foundations of adjacent of adjacent GarageGarage El-Attaba El-Attaba building building using Midas using GTS Midas-NX GTS-NX finite element finite elementpackage. package. Considering Considering the influence the influence of boundary of boundary effects on effects the accuracy on the of accuracy the numerical of the numericalresults, the results, area with the area the with most the risk most of construction risk of construction was chosen was chosen to establish to establish a 3D afinite 3D finiteelement element model model to investigate to investigate the the influence influence of of tunnel tunnel construction construction on on 17 adjacent adjacent pile pile groups.groups. InIn thisthis study,study, a a perspective perspective view view of of the the numerical numerical model model is is shown shown in in Figure Figure6 .6. The The meshmesh appliedapplied in in this this model model consisted consisted of of 51,838 51,838 nodes nodes and and 300,647 300,647 elements. elements. The The mesh mesh size size isis extendedextended inin 108108 mm (length),(length), 108108 mm (width),(width), andand 5555 mm (depth)(depth) inin X,X, Y,Y, andand ZZ directions,directions, respectively,respectively, as as shown shown in in Figure Figure6 .6. These These dimensions dimensions were were sufficiently sufficiently large large to to minimize minimize boundaryboundary effectseffects inin thethe numericalnumerical modelingmodeling becausebecause thethe largerlarger increaseincrease inin mesh mesh size size did did notnot leadlead toto anyany changechange inin thethe analysisanalysis results.results. TheThe groundground soil, soil, piles, piles, pile pile caps, caps, and and tunnel tunnel lininglining were were simulated simulated using using tetrahedron tetrahedron elements. elements. The The shield shield was was simulated simulated as a plateas a plate and theand interface the interface element element is not is prescribed not prescribed between between the pile the and pile the and soil. the soil.
FigureFigure 6. 6.3D 3D finitefinite element element model. model.
InIn thisthis model, ground ground soil, soil, tunnel tunnel lining, lining, piles, piles, and and pile pile caps caps were were simulated simulated as con- as continuumtinuum solids, solids, while while the shield the shield machine machine was considered was considered as a continuum as a continuum shell. The shell. bound- The boundaryary conditions conditions were wereassumed assumed to be topinned be pinned at the at end the endof the of lower the lower soil soilto prevent to prevent any anymovement movement in any in any direction direction,, and and a roller a roller was was applied applied in inthe the side side of of the the model model to to allow allow a amovement movement in in the the vertical vertical direction. direction. A A relatively relatively fine fine mesh was usedused nearnear thethe tunneltunnel andand pilespiles locationlocation duedue toto thethe intensificationintensification ofof widewide shearshear strains;strains; whilewhile furtherfurther awayaway fromfrom outsideoutside thesethese zones,zones, thethe coarsercoarser mesh mesh was was used. used.
3.2.3.2. ConstitutiveConstitutive ModelsModels andand MaterialMaterial ParametersParameters ManyMany factorsfactors impact the the performance performance and and the the results results accuracy accuracy of the of thenumerical numerical sim- simulationulation such such as the as theconstitutive constitutive model model and calculation and calculation parameters. parameters. The Modified The Modified Mohr– Mohr–CoulombCoulomb successfully successfully employed employed in simulation in simulation the behavior the behavior of various of various types types of soils, of soils, both bothsoft and soft stiff and soils stiff soils[37–39] [37.– In39 ].addition, In addition, The Modified The Modified Mohr Mohr–Coulomb–Coulomb formulation formulation incor- incorporatesporates two hardening two hardening mechanisms, mechanisms, shear shearand density and density hardening. hardening. In the case In the of the case tun- of the tunneling construction progress, the loading and unloading behavior of soil must be
Symmetry 2021, 13, 426 7 of 22
simulated [40–45]. Therefore, in this study, the constitutive behavior of soil layers was modeled as a Modified Mohr–Coulomb model. Furthermore, the Modified Mohr–Coulomb constitutive model is described more accurately because it takes into account three different soil stiffness parameters, which cor- respond to three loading conditions, namely, triaxial loading stiffness, oedometer loading stiffness, and unloading-reloading modulus. For every stress increment, if the soil exposes undergoing primary loading, there is a corresponding incremental elastic and plastic strain. Otherwise, if the soil is exposed to unloading–reloading, there is an elastic strain only [46]. Based on the geotechnical investigations’ report [35], the physical characteristics of the soil strata (Figure5) are summarized in Table1. For the clay layer, undrained shear strength 2 (qu) of 222 kN/m was determined using the unconfined compression test. Therefore, the 2 undrained cohesion (Cu) is taken as 111 kN/m in this analysis. Moreover, the undrained Young’s modulus (Eu) of the cohesive soil layer is estimated using Equation (1).
Eu = k Cu (1)
where k is evaluated using Duncan chart (Duncan, (1976)) [47].
Table 1. Soil layers engineering parameters.
Soil Layers Made Silty Middle Cobbles and Upper Sand Gravel Lower Sand Ground Clay Sand Boulders Parameter Thick. (m) 4.00 5.00 11.00 1.50 1.50 6.50 Extended Unit weight (kN/m3) 17 17.67 19.5 20 19.5 21 19.5 ◦ Friction angle ( ) 27 ϕu = 0 36 36 35 36 34
Cohesion (kPa) 0 Cu = 111 0 0 0 0 0 Lateral earth pressure 0.546 1 0.412 0.384 0.384 0.412 0.384 coefficient (-)
Poisson’s ratio (-) 0.3 νu = 0.3 0.3 0.3 0.3 0.3 0.3 Dilatancy angle (◦) 0 0 6 6 5 6 4 Triaxial loading stiffness E 50 4 27.75 15.33 100 16.48 19.61 19.61 (MPa) Oedometer loading stiffness 4 27.75 15.33 100 16.48 19.61 19.61 Eoed (MPa) Triaxial unloading stiffness 12 83.25 45.98 300 49.43 58.84 58.84 Eur (MPa)
Additionally, for the sandy soil layers, the secant modulus of elasticity (E50) is esti- mated using the SPT original (N-values) according to the Egyptian code of practice, ECP (202/3 (2005)) [48]. In most cases, (Eur) is set to three times (E50), and (Eoed) is taken to be equal to (E50)[46]. For soil layers, dilatancy angle (ψ) typically equal to be zero for undrained analysis and (ψ = ϕ − 30◦) for drained analysis [49]. According to the geological conditions at the site location, the over-consolidation ratio (OCR) was estimated to be equal to 1.0. In addition, the coefficient of lateral earth pressure at rest (ko) is estimated by Mayne and Kulhawy (1982) [50] using Equation (2).
sin ϕ ko = (1 − sin ϕ)OCR (2)
On the other hand, a linear elastic model was used to simulate the piles, pile caps, tunnel lining, and shield machine. This model requires the input of two main parameters, i.e., Young’s modulus (E) and Poisson’s ratio (υ) to describe the stress–strain relationship. Structural properties adopted in the numerical analysis are taken as given in Table2. Symmetry 2021, 13, 426 8 of 22
Table 2. Structural properties adopted in the numerical analysis.
Parameters Pile Pile Cap Lining Shield Grouting Elasticity modulus (MPa) 3.45 × 104 1.4 × 104 1.4 × 104 2 × 104 2 × 104 Unit weight (kN/m3) 25 25 25 78 22.5 Possion’s ratio (-) 0.15 0.15 0.15 0.3 0.3
3.3. Numerical Analysis Procedure The same material properties of the soil layers and structural elements listed in Tables1 and2 , respectively, were employed in three-dimensional models. The shield tunnel lining construction consists of connecting a series of concrete ring segments, of about 1.5 m long for each segment (two segments of 1.5 m are erected in one calculation stage). In order to more realistically reflect the situation of shield excavation, the model sets the drilling pressure applied on the shield excavation face; jack thrust is applied in front of the segment face; shield external pressure and segment external pressure are applied around the tunnel. A 3D model’s analysis was performed on the 46 stages including the initial stage. The following modeling sequence is followed: 1. The initial stage set up the initial stress and boundary conditions at-rest earth pressure coefficient of 0.5. 2. The first stage starts with changing the properties of the piles to concrete material as soil material replacement. At this stage, the caps are activated. 3. The second stage includes applying the building loads to pile caps using eight in- cremental loadings. At this stage, the displacements of the initial and first stages of analysis were reset to zero in order to facilitate the study of the influence of shield tunneling on pile cap behavior. 4. The third stage simulates the advancement of the tunnel and the excavation of the first ring and replaced it with the shield every 3 m. The drilling pressure and shield external pressure are activated. 5. Stages from 4 to 6: shield advancement, application of the drilling pressure and the shield external pressure, erecting the first ring of the segment inside the shield and applying the jacking force on it. 6. Stages from 7 to 10: Erecting four rings behind the shield and applying the segment external pressure. 7. Stage 11: erecting the next ring and the grout is considered hardened by changing the material properties. 8. Stages from 12 to 46: Repeat stages (3–7) and continue digging until all segments are completed. Table3 reveals the activation (Install element) and the re-activation (Remove element) of the structural elements during tunnel construction stages by using Midas stage definition wizard, from stage 1 to stage 10, as they are done in the Midas GTX NX Software to prepare the 3D FEM model.
Table 3. Tunnel construction stages by using Midas–Wizard analysis.
Set Name Prefix S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 A:5 A:6 A:7 A:8 A:9 A:10 Shield A:1 A:2 A:3 A:4 R:1 R:2 R:3 R:4 R:5 R:6 Segment A:1 A:2 A:3 A:4 A:5 A:6 A:7 Drilling pressure A:1 A:2 A:3 A:4 A:5 A:6 A:7 A:8 A:9 A:10 A:2 A:3 A:4 A:5 A:6 A:7 Jack thrust A:1 R:1 R:2 R:3 R:4 R:5 R:6 Shield external pressure A:1 A:2 A:3 A:4 A:5 A:6 A:7 A:8 A:9 A:10 Segment external pressure A:1 A:2 A:3 A:4 A:5 A:6 Hard grout A:1 A:2 A:3 Where S: Stage Number; A: Activated; R: Re-activated. Symmetry 2021, 13, x FOR PEER REVIEW 9 of 23 Symmetry 2021, 13, 426 9 of 22
4. Verification4. Verification of of the the Numerical Numerical ModelModel ThereThere are are five five field field measurements measurements (SSP. (SSP. B, B, SSP. SSP. C, SSP. SSP. D, SSP. E,E, andand SSP.SSP. F)F) ofof lon- gitudinallongitudinal surface surface settlement settlement that thathad hadbeen been monitored monitored which which were were located located near near the the Garage El-GarageAttaba El-Attababuilding buildingas shown as in shown Figure in Figure2. To 2ensure. To ensure the validity the validity of ofthe the numerical numerical model results,model a results,comparison a comparison has been has conducted been conducted between between the field the field measurements measurements of ofthese these points withpoints numerical with numerical results resultsas shown as shown in the in following the following Figure Figure 7, 7and, and the the comparison comparison hashas indi- catedindicated a good a agreement good agreement between between the thenumerical numerical and and the the measured measured values.
Distance of the tunnel face to the point B, m Distance of the tunnel face from the point C, m
-45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 0 0
-2 -2
-4 -4
mm mm -6 -6
-8 -8
-10 -10 Field Measurments Field Measurements Longitodinal Surface Settlement, Settlement, Surface Longitodinal -12 Numerical -12 Numerical
-14 mm settlement, surface longitodinal -14
Distance of the tunnel face from the point D, m Distance of tunnel face from the point E , m -45 -35 -25 -15 -5 5 15 25 35 45 55 -35 -25 -15 -5 5 15 25 35 45 55 65 0 0 -2 -2
-4 -4
-6 -6
mm mm -8 -8
-10 Field Measurements -10 Field Measurments -12 Numerical -12
Numerical Longitodinal surface settlement, settlement, surface Longitodinal -14 settlement, surface Longitodinal -14
Distance of the tunnel face from the point F, m -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 0 -2 -4 -6
mm -8 -10 Field Mesurements -12 numerical Longitodinal surface settlement, settlement, surface Longitodinal -14
FigureFigure 7. The 7. The longitudinal longitudinal surface surface settlement settlement at different points points relative relative to tunnelto tunnel advancement. advancement.
5. Numerical Results and Discussion 5.1. Influence of the Tunnel Excavation on the Piles Caps Foundations In order to study the behavior of piles caps due to tunneling construction, the axial settlement of 17 piles that connect with four caps was measured before and after tunnel construction as shown in Figure 8. As expected, due to the stress release caused by the
Symmetry 2021, 13, 426 10 of 22
5. Numerical Results and Discussion 5.1. Influence of the Tunnel Excavation on the Piles Caps Foundations In order to study the behavior of piles caps due to tunneling construction, the axial Symmetry 2021, 13, x FOR PEER REVIEW 10 of 23 settlement of 17 piles that connect with four caps was measured before and after tunnel construction as shown in Figure8. As expected, due to the stress release caused by the tunnel construction, the pile settlement becomes larger than before tunneling. In addition, thetunnel results construction, indicate thatthe pile the settlement nearest pile becomes cap to larger the tunnel than before (PC1) tunneling. was affected In addition, by the tunnel progressthe results and indicate the larger that the settlement nearest pile occurring cap to the tunnel on it by (PC1) about was60% affected to 70%. by the After tunnel that, the pilesprogress settlements and the larger are roughly settlement independent occurring on of it their by about locations 60% to relative 70%. After to the that, tunnel the route. Therefore,piles settlements the following are roughly sections independent have concerned of their locations with the relative pile (PC1) to the only.tunnel route.
Therefore, the following sections have concerned with the pile (PC1) only.
PC1.a PC1.b PC1.c PC1.d PC1.e PC2.a PC2.b PC3.a PC3.b PC3.c PC3.d PC4.a PC4.b PC4.c PC4.d PC4.e PC4.f 0
-2
-4
-6
-8
-10
-12
-14 axial axial pile settlement,mm -16 Settlement Before Tunnel Construction Settlement After Tunnel Construction -18
-20
FigureFigure 8.8. TheThe pile axial axial settlement settlement before before and and after after tunnel tunnel construction construction..
5.2.5.2.Response Response of an Existing Existing Pile Pile Cap Cap Foundation Foundation (PC1) (PC1) to Tunneling to Tunneling-Induced-Induced Ground Ground Movements withMovements Different with Construction Different Construction Stages Stages TheThe axialaxial settlement, lateral lateral deflection, deflection, axial axial force, force, and and bending bending moment moment behaviors behaviors of theof th pilese piles cap cap foundation foundation (PC1) (PC1) during during differentdifferent construction stages stages are are discussed. discussed. In In this this study, different construction stages are (Y = −2Dtun, Y = 0, Y = +2Dtun, and Y = +4Dtun), study, different construction stages are (Y = −2Dtun, Y = 0, Y = +2Dtun, and Y = +4Dtun), where Y is the distance between the tunnel face and center of PC1, and Dtun is the diameter where Y is the distance between the tunnel face and center of PC1, and D is the diameter of the tunnel. Fundamental to note that the pile near to the tunnel is titled the “Near”tun pile of the tunnel. Fundamental to note that the pile near to the tunnel is titled the “Near” pile and the pile further away from the tunnel is the “Rear” pile, while the pile between them andis the the “Middle pile further” pile. away from the tunnel is the “Rear” pile, while the pile between them is the “Middle”Figure 9 shows pile. the behavior of the axial settlement of the Near, Middle, and Rear pilesFigure for the9 showsPC1 foundation the behavior that adjacent of the axial to the settlement tunnel at ofdifferent the Near, tunnel Middle, constructio and Rearn piles forstages. the PC1The results foundation indicate that that adjacent the axial to settlement the tunnel behavior at different is the tunnel same in construction all the con- stages. Thestruction results stages indicate for Near, that Middle, the axial and settlement Rear piles. behaviorMeanwhile, is the the maximum same in allsettlement the construction is stagesmeasured for Near,at the Middle,pile head andand Rearreduced piles. slightly Meanwhile, at the pile the tip maximum located above settlement the tunnel. is measuredIn ataddition, the pile the head axial and settlement reduced of slightly the Near at pile the is pile higher tip than located that aboveobserved the for tunnel. the Middle In addition, theand axial Rear settlement piles in all ofconstruction the Near pilestages. is higherOverall, than when that the observedtunnel face for is theat (Y Middle = −2Dtun and) Rear from the PC1, the axial settlement of the pile is approximately uniform along the pile side piles in all construction stages. Overall, when the tunnel face is at (Y = −2Dtun) from the due to the strong stiffness of the pile [51]. After that, there is a significant increase in the PC1, the axial settlement of the pile is approximately uniform along the pile side due to axial settlement when the tunnel face approaches the center of the PC1 (Y = 0), while it the strong stiffness of the pile [51]. After that, there is a significant increase in the axial moreover increases when the tunnel passes away from the PC1 (Y = +2Dtun) and (Y = settlement when the tunnel face approaches the center of the PC1 (Y = 0), while it moreover +4Dtun). Finally, the pile settlement increase becomes negligible. increases when the tunnel passes away from the PC1 (Y = +2Dtun) and (Y = +4Dtun). Finally, the pile settlement increase becomes negligible.
Symmetry 2021, 13, 426 11 of 22 Symmetry 2021, 13, x FOR PEER REVIEW 11 of 23 Symmetry 2021, 13, x FOR PEER REVIEW 11 of 23
axial settlement, mm axial settlement, mm axial settlement, mm axial settlement, mm axial settlement, mm 0 -2 -4 -6 -8 -10 -12 -14 0 -2axial-4 settlement,-6 -8 -10 mm-12 -14 0 -2 -4 -6 -8 -10 -12 -14 0 -2 -4 -6 -8 -10 -12 -14 0 -2 -4 -6 -8 -10 -12 -14 0 -2 -4 -6 -8 -10 -12 -14 0 0 0 0 0 0 -2 -2 -2 -2 -2 -2 -4 -4 -4 -4 -4 -4 -6 -6 -6 -6 -6 -6 -8 -8 -8 -8 -8 -8 -10 -10 -10
-10 -10 m depth, pile -10
pile depth, m depth, pile pile depth, m depth, pile
-12 -12 m depth, pile -12 pile depth, m depth, pile -12 m depth, pile -12 -12 -14 -14 -14 -14 -14 -14 -16 -16 -16 -16 -16 -16 -18 -18 -18 -18 -18 -18 -20 -20 -20 -20 -20 -20 -2D zero -2D zero -2D zero -2D zero -2D zero +2D +4D +2D +4D -2D+2D zero+4D +2D +4D +2D +4D +2D +4D (a) (b) (c) (a) (b) (c) Figure 9. Axial settlement with a depth of (a) Near, (b) Middle, and (c) Rear piles at different construction stages. Figure 9. Axial settlement with a depth of ( a) Near, (b) Middle, and ((c)) RearRear pilespiles atat different constructionconstruction stages.stages. In order to understand the lateral deflection of the PC1 foundation due to the tunnel In order to understand the lateral deflection deflection of the PC1 foundationfoundation due to the tunnel excavationexcavation at different different construction construction stages stages,, Figure Figure 10 10 presents presents the the variations variations of lateral of lateral de- excavation at different construction stages, Figure 10 presents the variations of lateral de- deflectionflection behaviors behaviors of of the the Near, Near, Middle, Middle, and and Rear Rear piles piles for for PC1. The results indicate thatthat flection behaviors of the Near, Middle, and Rear piles for PC1. The results indicate that thethe laterallateral deflectiondeflection behavior behavior is is the the same same in in all all the the construction construction stages stages for for all piles,all piles and, and the the lateral deflection behavior is the same in all the construction stages for all piles, and maximumthe maximum lateral lateral deflection deflection occurs occurs at the at pilethe headpile head and graduallyand gradually decreases decreases along along the pile the the maximum lateral deflection occurs at the pile head and gradually decreases along the depthpile depth to be to smaller be smaller at the at pile the tip. pile Again, tip. Again, the measured the measured lateral lateral deflection deflection of the Nearof the pile Near is pile depth to be smaller at the pile tip. Again, the measured lateral deflection of the Near notedpile is tonoted be higher to be thanhigher that than observed that observed from others, from andothers, this and can this be attributed can be attributed to the volume to the pile is noted to be higher than that observed from others, and this can be attributed to the lossvolume induced loss induced around the around tunnel the when tunnel the when distance the fromdistance the tunnelfrom the decreases. tunnel decreases. In addition, In volume loss induced around the tunnel when the distance from the tunnel decreases. In itaddition, can be noted it can thatbe noted when that the when tunnel the face tunnel is reaching face is thereaching PC1 foundation, the PC1 foundation, there is only there a addition, it can be noted that when the tunnel face is reaching the PC1 foundation, there slightis only translation a slight tran of theslation pile of (Y the = − pile2Dtun (Y). = While −2Dtun at). (YWhile = 0), at there (Y = is 0) a, significant there is a amountsignificant of is only a slight translation of the pile (Y = −2Dtun). While at (Y = 0), there is a significant lateralamount deflection of lateral of deflection the pile. Afterof the that, pile. when After the that, tunnel when face the is tunnel further face away is fromfurther the away PC1 amount of lateral deflection of the pile. After that, when the tunnel face is further away atfrom (Y =the +2D PC1tun atand (Y = Y +2D = +4Dtun andtun), Y the = +4D piletun deflection), the pile increases.deflection Finally, increases. the Finally, lateral deflectionthe lateral from the PC1 at (Y = +2Dtun and Y = +4Dtun), the pile deflection increases. Finally, the lateral isdeflection roughly stagnating.is roughly stagnating. deflection is roughly stagnating.
lateral deflection, mm lateral deflection, mm lateral deflection, mm lateral deflection, mm lateral deflection, mm lateral deflection, mm -1 0 1 2 3 4 -1 0 1 2 3 4 -1 0 1 2 3 4 -1 0 1 2 3 4 -1 0 1 2 3 4 -1 0 1 2 3 4 0 0 0 0 0 0 -2 -2 -2 -2 -2 -2 -4 -4 -4 -4 -4 -4 -6 -6 -6 -6 -6 -6 -8 -8 -8 -8 -8 -8 -10 -10 -10 -10
pile depth, m depth, pile -10 -10 pile depth, m depth, pile pile depth, m depth, pile -12
pile depth, m depth, pile -12
pile depth, m depth, pile -12 pile depth, m depth, pile -12 -12 -12 -14 -14 -14 -14 -14 -14 -16 -16 -16 -16 -16 -16 -18 -18 -18 -18 -18 -20 -18 -20 -20 -20 -2D zero -20 -20 -2D zero -2D zero -2D zero -2D zero -2D zero +2D +4D +2D +4D +2D +4D +2D +4D +2D +4D +2D +4D (a) (b) (c) (a) (b) (c) Figure 10. Lateral deflection with a depth of (a) Near, (b) Middle, and (c) Rear piles at different construction stages. Figure 10. Lateral deflection deflection with a depth of ( a) Near, (b) Middle, and ((cc)) RearRear pilespiles atat differentdifferent constructionconstruction stages.stages. Figure 11 presents the behavior of the axial force of Near, Middle, and Rear piles of Figure 11 presents the behavior of the axial force of Near, Middle, and Rear piles of PC1. It can be realized that axial force for the Near pile approximately equal at the pile PC1. It It can be realized that axial force for the Near pile approximately equal at the pile head at different stages and increases up to its maximum value at the pile depth (16 m) head at different stages and increases up to its maximum value at the pile depth (16 m) followed by a decrease due to the ground movement caused by the tunnel excavation. In followed by a decrease due to the ground movement caused byby thethe tunneltunnel excavation.excavation. In general, when the tunnel face is reaching the PC1 foundation, there is only a small amount general, when the tunnel face is reaching the PC1 foundation, there is only a small amount of axial force induced in the pile (Y = −2Dtun). After that, when the tunnel face reaches the of axial force induced in the pile (Y = −2Dtun). After that, when the tunnel face reaches the center of the PC1 (Y = 0), there is a slight increase in axial force. Moreover, it can be seen center of the PC1 (Y = 0), there is a slight increase in axial force. Moreover, it can be seen
Symmetry 2021, 13, 426 12 of 22
Symmetry 2021,, 13,, xx FORFOR PEER REVIEW 12 of 23
of axial force induced in the pile (Y = −2Dtun). After that, when the tunnel face reaches the center of the PC1 (Y = 0), there is a slight increase in axial force. Moreover, it can be seen also that the maximum axial force is detected when the tunnel face is further away from also thatthat thethe maximummaximum axialaxial forceforce isis detecteddetected whenwhen thethe tunneltunnel faceface isis furtherfurther awayaway fromfrom the PC1 at (Y = +2Dtun). After the passage of the tunnel face the PC1 at (Y = +4Dtun), there thethe PC1PC1 atat (Y(Y == +2D+2Dtuntun).). AfterAfter thethe passagepassage ofof thethe tunneltunnel faceface thethe PC1PC1 atat (Y(Y == +4D+4Dtuntun),), therethere is a decrease of the axial force. Again, the measured axial force of the Near pile is higher isis aa decreasedecrease ofof thethe axialaxial forceforce.. Again,Again, thethe measuredmeasured axialaxial forceforce ofof thethe NearNear pilepile isis higherhigher than that observed from others. thanthan thatthat observedobserved fromfrom others.others.
axial force, kN axial force, kN axial force, kN 500 400 300 200 100 0 -100-100-200-200 200 100 0 -100-100 -200-200 100 0 -100-100 -200-200 -300-300 -400-400 0 0 0 -2-2 -2-2 -2-2 -4-4 -4-4 -4-4 -6 -6-6 -6-6 -6 -8 -8-8 -8-8 -8 -10
-10-10 -10-10 -10
pile depth, m depth, pile
pile depth, m depth, pile m depth, pile
pile depth, m depth, pile pile depth, m depth, pile pile depth, m depth, pile -12 -12-12 -12-12 -12 -14 -14-14 -14-14 -14 -16 -16-16 -16-16 -16 -18 -18-18 -18-18 -18 -20 -20-20 -20-20 -20 -2D zero -2D zero -2D-2D zerozero -2D-2D zerozero +2D +4D +2D +4D +2D +4D +2D +4D
((a)) ((b)) ((c)) Figure 11. Axial force with a depth of ( (a)) Near, (((bb)) Middle,Middle, andand (((cc))) RearRearRear pilespilespiles atatat differentdifferent constructionconstruction stages.stages.
Additionally, Figure 1212,, illustratesillustrates thethe behaviorbehavior ofof thethe bendingbending momentmoment alongalong thethe Near, Middle, and Rear piles of the PC1 foundation during different construction stages. stages. The results results point point to to the the maximum maximum bending bending moment moment occur occurringring almost almost at the at the bottom bottom of the of pilesthe piles due dueto the to large the large lateral lateral soil displacement soil displacement around around the tunnel. the tunnel. Meanwhile, Meanwhile, the meas- the uredmeasured bending bending moment moment of the of Near the Near piles pilesis double is double the value the value observed observed for the for Middle the Middle and Rearand Rearpiles. piles. In general, In general, the bending the bending moment moment along alongthe pile the length pile length isis almost is almost straight straight when when the tunnel reached (Ytun = −2D ), while there is a significant amount of bending thethe tunneltunnel reachedreached (Y(Y == −2Dtun)),, wwhiletun there is a significant amount of bending moment inducedmomentinduced inducedinin thethe pilepile in the tiptip pile atat thethe tip center atcenter thecenter ofof PC1PC1 of (Y(Y PC1 == (Y0).0). = TheThe 0). Themaximummaximum maximum bendingbending bending momentmoment moment isis is detected almost tripled when the tunnel face is further away from the PC1 at (Y = +2D ). detected almost tripled when the tunnel face is further away from the PC1 at (Y = +2Dtuntuntun).). After that, little change in maximum bending moment occurs at (Y = +4Dtun ). After that, little change in maximum bending moment occurs at (Y = +4Dtun).).
bending moment, kN.m bending moment, kN.m bending moment, kN.m -90 -70 -50 -30 -10 10 30 50 -90-90 -70-70 -50-50 -30-30 -10-10 10 30 50 -90-90 -70-70 -50-50 -30-30 -10-10 10 30 50 -90 -70 -50 -30 -10 10 30 50 0 0 0 0 -2 -2-2 -2-2 -2 -4 -4-4 -4-4 -4 -6 -6-6 -6-6 -6 -8 -8-8 -8-8 -8 -10
-10-10 -10-10 -10
pile depth, m depth, pile
pile depth, m depth, pile
pile depth, m depth, pile
pile depth, m depth, pile pile depth, m depth, pile pile depth, m depth, pile -12 -12-12 -12-12 -12 -14 -14-14 -14-14 -14 -16 -16-16 -16-16 -16 -18 -18-18 -18-18 -18 -20 -20-20 -20-20 -20 -2D zero -2D zero -2D zero -2D-2D zerozero -2D zero +2D +4D +2D +4D +2D +4D +2D +4D +2D +4D ((a)) ((b)) ((c)) Figure 12. Bending moment with a depth of (a) Near, (b) Middle, and (c) Rear piles at different construction stages. Figure 12. Bending moment with a depth of ( a) Near, (b) Middle, and ((cc)) RearRear pilespiles atat different constructionconstruction stages.stages.
5.3. Parametric Studies A series of parametric studies are investigated by varying the tunnel--pile distance (X(Xpile),), thethe diameterdiameter ofof thethe tunneltunnel (D(Dtuntun)) atat differentdifferent tunneltunnel axisaxis (H).(H). TheThe wholewhole studystudy isis categorized into two cases; deep tunnel where the tunnel axis is located below the tip,
Symmetry 2021, 13, 426 13 of 22
Symmetry 2021, 13, x FOR PEER REVIEW5.3. Parametric Studies 13 of 23
A series of parametric studies are investigated by varying the tunnel-pile distance Symmetry 2021, 13, x FOR PEER REVIEW 13 of 23 (Xpile), the diameter of the tunnel (Dtun) at different tunnel axis (H). The whole study is (Lp/Hcategorized < 1) and into shallow two cases; tunnel deep where tunnel the wheretunnel theaxis tunnel is located axis above is located the tip below (Lp/H the > tip,1). Figure(Lp/H 13 < 1)shows and shallowthe flowchart tunnel of where the parametric the tunnel studies. axis is located above the tip (Lp/H > 1). Figure(Lp/H 13< 1) shows and shallow the flowchart tunnel w ofhere the the parametric tunnel axis studies. is located above the tip (Lp/H > 1). Figure 13 shows the flowchart of the parametric studies. Parametric Studies Parametric Studies Deep Tunnel, Shallow Tunnel, Deep Tunnel, Shallow Tunnel, Lp/H˃1 Lp/H˂1 Lp/H˃1 Lp/H˂1 H=26m H=14m H=26m H=14m
X1=6.45m X2=14m X3=18m X1=6.45m X2=14m X3=18m X1=6.45m X2=14m X3=18m X1=6.45m X2=14m X3=18m
DD1=9.15m1=9.15m DD22=7.5m=7.5m D3D=6m3=6m D1=9.15mD1=9.15m D2=7.5mD2 =7.5m D3=6m D3=6m
Figure 13. Flowchart of the parametric studies. Figure 13. FlowchartFlowchart of the the parametric studies. 5.3.1. Axial Settlement of the Piles 5.3.1. Axial Axial Settlement Settlement of of the Piles Figures 14 and 15 illustrate the axial settlement amount of the Near, Middle, and Rear FigureFiguress 14 and 15 illustrateillustrate the the axial axial settlement settlement am amountount of the Near, Near, Middle, and Rear piles for deep and shallow tunnel respectively at various Xpile (6.45, 14, and 18) m with a piles for deep and shallow tunnel respectively at various Xpilepile (6.45, 14, and 18) m with pilesconstant for deep diameter and Dshallowtun of 9.15 tunnel m. The respectively results indicate at variousthat in the X axial (6.45, settlement 14, and for 18) both m with a constantacases constant, the diameter deep diameter and D shallowtun D tunof 9.15of tunnel 9.15 m. rThe m.eaches Theresults the results peak indicate value indicate thatwhen thatin the the inpile axial the offset axialsettlement about settlement 6.45 for both for casesbothm because, cases, the deep the the tunnel deepand shallow andeffect shallow decreases tunnel tunnel wreacheshen reachesdistance the peak theincreases peakvalue, valueand when finally when the the pile the tunnel offset pile effect offset about about 6.45 m6.45fades because m when because the the tunnel pile the tunnelis effectat a distance effect decreasesdecreases of about when twice when distance the distance diameter increasesincreases, of the, and tunnel. finally and The finally the increase tunnel the tunnel effect fadeseffectof the when fades axial setthe whentlement pile the is is at pile due a distance isto atthe a additional distance of about ofsettlement twice about the twice resulting diameter the during diameter of the the tunnel. construction of the The tunnel. increase The ofincreaseof the the axial tunnel. of set the tlementM axialeanwhile, settlement is due the to axial the is settlementadditional due to the in settlement additionalthe case of resulting the settlement deep tunnelduring resulting is the approxi- construction during the ofconstructionmately the tunnel. three oftimes M theeanwhile, the tunnel. settlement Meanwhile,the axial in the settlement shallow the axial tunnel. in settlement the Moreover, case inof the thein the casedeep case of tunnel theof the deep deep is approxi- tunnel is tunnel, the axial settlement is approximately uniform while in the shallow tunnel the max- matelyapproximately three times three the times settlement the settlement in the shallow in the tunnel. shallow Moreover, tunnel. Moreover, in the case in of the the case deep of theimum deep axial tunnel, settlement the axial is noted settlement at the pile is approximately head and gradually uniform decreased while to in reach the shallow a mini- tunnel tunnel,mum value the axial at the settlement pile tip due is to approximately the tunneling effect uniform only onwhile the upperin the portionshallow of tunnel the pile. the max- imumthe maximum axial settlement axial settlement is noted isat notedthe pile at thehead pile and head gradually and gradually decreased decreased to reach toa mini- reach aIn minimum general, for value both atcases, the the pile axial tip settlement due to the of tunneling the Near, Middle, effect onlyand Rear on thepiles upper increases portion of mumas the value distance at the between pile tip the due pile to andthe tunnelingthe tunnel effectdecreases. only The on theresults upper indicate portion a good of the pile. the pile. In general, for both cases, the axial settlement of the Near, Middle, and Rear piles Inagreement general, for with both the cases,findings the of axial [13,52] settlement. of the Near, Middle, and Rear piles increases increases as the distance between the pile and the tunnel decreases. The results indicate a as the distance between the pile and the tunnel decreases. The results indicate a good axial settlement,good mm agreement with theaxial settlement, findings mm of [13,52]. axial settlement, mm -4 -6 -8agreement-10 -12 -14 with the -4findings-6 -8 of -10[13,52]-12 . -14 -4 -6 -8 -10 -12 -14 0 0 0 -2 axial settlement, mm -2 axial settlement, mm -2 axial settlement, mm -4-4 -6 -8 -10 -12 -14 -4 -4 -6 -8 -10 -12 -14 -4 -4 -6 -8 -10 -12 -14 -6 -6 -6 0 0 -8 -80 -8 -2 -10 -10-2 -10 -2
-4 -12 -12-4 -12 -4
pile depth, m depth, pile pile depth, m depth, pile -6 -14 m depth, pile -14-6 -14 -6 -8 -16 -16-8 -16 -8 -10 -18 -18-10 -18 -10
-12 -20 -20-12 -20 -12
pile depth, m depth, pile pile depth, m depth, pile -14 X1=6.45m X2=14m m depth, pile -14 X1=6.45m X2=14m -14X1=6.45m X2=14m X3=18m X3=18m -16 -16 -16X3=18m -18 (a) -18 (b) -18 (c) -20 -20 -20 Figure 14. AxialX1=6.45m settlement at a depthX2=14m of (a) Near, (b) X1=6.45mMiddle, and (c) RearX2=14m piles with differentX1=6.45m Xpile for the deepX2=14m tunnel (H = 26 m). X3=18m X3=18m X3=18m (a) (b) (c)
Figure 14. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H Figure 14. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel = 26 m). (H = 26 m).
Symmetry 2021, 13, 426 14 of 22 Symmetry 2021, 13, x FOR PEER REVIEW 14 of 23
Symmetry 2021, 13, x FOR PEER REVIEW 14 of 23
Symmetry 2021, 13, x FOR PEER REVIEW 14 of 23
axial settlement, mm axial settlement, mm axial settlement, mm 0 -1 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -4 axial settlement, mm axial settlement, mm axial settlement, mm 0 0 -1 -2 -3 -4 0 0 -1 -2 -3 -4 0 0 -1 -2 -3 -4 -2 axial settlement, mm -2 axial settlement, mm -2 axial settlement, mm 0 0 0 -4 0 -1 -2 -3 -4 -4 0 -1 -2 -3 -4 -4 0 -1 -2 -3 -4 -2 -2 -2 -60 -60 -60 -4 -4 -4 -2-8 -2-8 -2-8 -6 -6 -6 -10-4 -10-4 -10-4 -8 -8 -8 -12-6 -12-6 -6
pile depth, m depth, pile -12 pile depth, m depth, pile pile depth, m depth, pile -10 -10 -10 -14-8 -14-8 -8 -12 -12 -14
pile depth, m depth, pile -12 pile depth, m depth, pile pile depth, m depth, pile -10 -10-16 -10 -16 -14 -16 -12-14 -12 -14
-18 m depth, pile -12 pile depth, m depth, pile pile depth, m depth, pile -18 -18 -16 -16 -16 -14-20 -14-20 -14-20 -18 -18 -16-18 X1=6.45m X2=14m -16 X1=6.45m X2=14m -16 X1=6.45m X2=14m -20 -20 -18-20 -18 X3=18m -18 X3=18m X1=6.45mX3=18m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m -20 -20 -20 X3=18m X3=18m (X1=6.45maX3=18m) X2=14m X1=6.45m(b) X2=14m X1=6.45m (cX2=14m) (X3=18ma) X3=18m(b) X3=18m (c) Figure 15. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel Figure 15. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (H = 14 m). (a) (b) (c) (HFigure = 14 m). 15. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel Figure(H = 14 15. m). Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (H = 14 m). OnOn the the other other hand, hand, Figures Figures 16 16 and and 17 17 illustrate illustrate thethe axialaxial settlementsettlement of the Near, Near, Mid- Middle, dle, andOn theRear other piles hand, for the Figure deeps and 16 and shallow 17 illustrate tunnel, therespectively axial settlement, at various of the Dtun Near, (9.15, Mid- 7.5, and Rear piles for the deep and shallow tunnel, respectively, at various Dtun (9.15, 7.5, dle,and and6)On m theRear with other piles constant hand, for the distanceFigure deeps and 16Xpile and shallow of 176.45 illustrate m.tunnel For ,both therespectively axia cases,l settlement it ,can at various be seenof the D that tunNear, (9.15, the Mid-axial 7.5, and 6) m with constant distance Xpile of 6.45 m. For both cases, it can be seen that the dle,andsettlement and6) m Rear with of pilesthe constant Near, for the distanceMiddle, deep and Xandpile shallow ofR ear6.45 piles m.tunnel For is almost,both respectively cases, higher it ,can atwhen various be seenDtun D=thattun 9.15 (9.15, the m axial and7.5, axial settlement of the Near, Middle, and Rear piles is almost higher when Dtun = 9.15 m andsettlementdecreases 6) m with withof theconstant the Near, decreases distanceMiddle, in Xandthepile oftunnelR ear6.45 piles m.diameter. For is almostboth This cases, higher result it can when well be seenagreesDtun that= 9.15with the m thoseaxial and and decreases with the decreases in the tunnel diameter. This result well agrees with settlementdecreasesconducted with ofby the [52] the Near,. Indecreases addition, Middle, in the andthe axial tunnelRear settlement piles diameter. is almost of Thisthe higher pileresult occurred when well agreesD uniformlytun = 9.15with m alongthose and those conducted by [52]. In addition, the axial settlement of the pile occurred uniformly decreasesconductedits length owingwith by [52] the to. Indecreasesthe addition, high stiffness in thethe axialtunnel of the settlement pilediameter. in the of This casethe pileofresult the occurred deepwell agreestunnel uniformly withwhile thosealong non- along its length owing to the high stiffness of the pile in the case of the deep tunnel while conducteditsun iformlength in owing bythe [52] case to. In theof addition,the high shallow stiffness the tunnel. axial of the settlement pile in the of casethe pile of the occurred deep tunnel uniformly while along non- nonuniform in the case of the shallow tunnel. itsun iformlength in owing the case to theof the high shallow stiffness tunnel. of the pile in the case of the deep tunnel while non- axial settlement,uniform mm in the case of theaxial shallow settlement, tunnel. mm axial settlement, mm 0 -2 -4 -6 -8 -10 -12 -14 0 -2 -4 -6 -8 -10 -12 -14 0 -2 -4 -6 -8 -10 -12 -14 axial settlement, mm axial settlement, mm axial settlement, mm 0 0 -2 -4 -6 -8 -10 -12 -14 0 0 -2 -4 -6 -8 -10 -12 -14 0 0 -2 -4 -6 -8 -10 -12 -14 -2 axial settlement, mm -2 axial settlement, mm -2 axial settlement, mm 0 0 0 -4 0 -2 -4 -6 -8 -10 -12 -14 -4 0 -2 -4 -6 -8 -10 -12 -14 -4 0 -2 -4 -6 -8 -10 -12 -14 -2 -2 -2 -60 -60 -60 -4 -4 -4 -2-8 -2-8 -2-8 -6 -6 -6 -10-4 -10-4 -10-4 -6-8 -6-8 -6-8
pile depth, m depth, pile -12 -12 -12 pile depth, m depth, pile -10 m depth, pile -10 -10 -14-8 -14-8 -14-8
pile depth, m depth, pile -12 -12 -12 pile depth, m depth, pile -10 m depth, pile -10-16 -10-16 -14-16 -14 -14
pile depth, m depth, pile -12 -12-18 -12-18 pile depth, m depth, pile -18 m depth, pile -16 -16 -16 -14-20 -14-20 -14-20 -18 -18 -18 -16 D1=9.15m D2=7.5 m -16 D1=9.15m D2=7.5 m -16 D1=9.15m D2=7.5 m -18-20 -18-20 -18-20 D3=6 m D1=9.15mD3=6 m D2=7.5 m D1=9.15mD3=6 m D2=7.5 m -20 D1=9.15m D2=7.5 m -20 -20 D3=6 m D3=6 m D1=9.15mD3=6(a) m D2=7.5 m D1=9.15m (b) D2=7.5 m D1=9.15m D2=7.5(c) m D3=6(a) m D3=6 m (b) D3=6 m (c) Figure 16. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H (a) (b) (c) Figure= 26 m). 16. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H Figure 16. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel = 26 m). (HFigure = 26 m). 16. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H = 26 m). axial settlement, mm axial settlement, mm axial settlement, mm 0 -1 -2 -3 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -4 axial settlement, mm axial settlement, mm axial settlement, mm 0 0 -1 -2 -3 -4 0 0 -1 -2 -3 -4 0 0 -1 -2 -3 -4 -2 axial settlement, mm -2 axial settlement, mm axial settlement, mm 0 0 -20 -4 0 -1 -2 -3 -4 -4 0 -1 -2 -3 -4 0 -1 -2 -3 -4 -2 -2 -4 -60 -60 -20 -4 -4 -6 -2-8 -2-8 -2-4 -6 -6 -8 -10-4 -10-4 -4-6
-8 -8 -10-8 pile depth, m depth, pile pile depth, m depth, pile -12-6 -12-6 -6 -10 -10 m depth, pile -12 -14-8 -14-8 -10-8 pile depth, m depth, pile -14 pile depth, m depth, pile -12 -12 -10-16 -10-16 m depth, pile -12 -14 -14 -10-16 pile depth, m depth, pile -14 pile depth, m depth, pile -12-18 -12-18 -16 -16 m depth, pile -12-18 -14 -14-20 -16 -20 -18 -14-20 -16-18 D1=9.15m D2=7.5 m -16 D1=9.15m D2=7.5 m -18 -20 -16 D1=9.15m D2=7.5 m -20 -18 -18 D1=9.15mD3=6 m D2=7.5 m D1=9.15mD3=6 m D2=7.5 m -18-20 D3=6 m -20 -20 D1=9.15m D2=7.5 m D1=9.15mD3=6 m D2=7.5 m D3=6 m -20 (a) D1=9.15m(b) D2=7.5 m D1=9.15mD3=6 m (cD2=7.5) m (aD3=6) m D3=6 m(b) D3=6 m (c) Figure 17. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel (a) (b) (c) Figure(H = 14 17. m). Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel
Figure(H = 14 17. m). Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel Figure 17. Axial settlement at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel (H = 14 m). (H = 14 m).
Symmetry 2021, 13, 426 15 of 22 Symmetry 2021, 13, x FOR PEER REVIEW 15 of 23
Symmetry 2021, 13, x FOR PEER REVIEW 15 of 23
Finally, it can be be concluded concluded that that for for all all cases, cases, the the axial axial settlement settlement of ofthe the Near Near piles piles is higheris higherFinally, than than the it can theMiddle be Middle concluded and and Rear Rear thatpiles. piles.for Furthermore, all Furthermore,cases, the it axial can it besettlement can noted be noted tha oft inthe that the Near incase the piles of case the is highershallowof the shallowthan tunnel the tunnel(Lp/HMiddle < (Lp/H and1) the Rear
-10-8 -10-8 -10-8
pile depth, m depth, pile pile depth, m depth, pile
-10-12 -10-12 m depth, pile -10-12 pile depth, m depth, pile -14 m depth, pile -14 -14 -12 -12 m depth, pile -12 -14-16 -14-16 -14-16 -16-18 -16-18 -16-18 -18-20 -18-20 -18-20 X1=6.45m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m -20 -20 -20 X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X3=18m(a) X3=18m(b) X3=18m (c) (a) (b) (c) pile Figure 18. Lateral deflectiondeflection at a depth of (a)) Near,Near, ((bb)) Middle,Middle, andand ((cc)) RearRear pilespiles withwith differentdifferent XXpile for the deep tunnel Figure(H = 26 18. m). Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H = 26 m). lateral deflection, mm lateral deflection, mm lateral deflection, mm 6 4 2 0 -2 lateral deflection, mm 6 lateral4 deflection,2 mm0 -2 6 lateral4 deflection,2 mm0 -2 0 6 4 2 0 -2 0 6 4 2 0 -2 0 6 4 2 0 -2 -2 0 -20 -20 -4 -2 -2-4 -2-4 -6 -4 -4-6 -4-6 -8 -6 -6-8 -6-8 -10 -8 -10-8 -10-8 -10-12 -12 m depth, pile pile depth, m depth, pile -10 -10-12 -12-14 m depth, pile -14 -14
-12 m depth, pile pile depth, m depth, pile -12 -16 -14 m depth, pile -14-16 -14-16 -18 -16 -16-18 -16-18 -20 -18 -18-20 -18-20 -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X3=18m(a) X3=18m(b) X3=18m (c) (a) (b) (c) Figure 19. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel Figure 19. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (HFigure = 14 19.m).Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (H(H = 14 14 m). m). Moreover, Figures 20 and 21 show the lateral deflection behavior of the Near, Middle, and RearMoreover,Moreover, piles Figurefor Figures thes deep20 and and 2121 showshallowshow the the tunnellateral lateral deflectionat deflection various behavior behaviorDtun (9.15, of of 7.5,the the Near,and Near, 6) Middle, Middle,m and andconstantand Rear Rear distance piles piles for for X th thepilee of deep 6.45 andm. As shallow expected, tunnel an increase at various in the Dtun tunnel (9.15,(9.15, diameter7.5, 7.5, and and 6)causes 6) m m and and an constantincreaseconstant distance in distance the lateral X Xpilepile of deflectionof 6.45 6.45 m. m. As Asdue expected, expected, to tunneling an anincrease increase induced in the in ground the tunnel tunnel movementdiameter diameter causes and causes thean increasestressan increase relea in se the in which the lateral lateral in deflectionturn deflection affect due the due topiles.to tunneling tunneling The results induced induced indicate ground ground a good movement movement agreement and and with the the stressthestress work relea release ofse [52] whichwhich. inin turnturn affect affect the the piles. piles. The The results results indicate indicate a gooda good agreement agreement with with the thework work of [ 52of ].[52].
Symmetry 2021, 13, 426 16 of 22 Symmetry 2021, 13, x FOR PEER REVIEW 16 of 23
Symmetry 2021, 13, x FOR PEER REVIEW 16 of 23
lateral deflection, mm lateral deflection, mm lateral deflection, mm 6 lateral4 deflection,2 0 mm -2 6 lateral4 deflection,2 0 mm -2 6 lateral4 deflection,2 mm0 -2 0 6 4 2 0 -2 0 6 4 2 0 -2 0 6 4 2 0 -2 -20 -20 -20 -4-2 -4-2 -4-2 -6-4 -6-4 -6-4 -8-6 -8-6 -8-6 -10 -8 -10-8 -10-8
-12 m depth, pile pile depth, m depth, pile pile depth, m depth, pile -10 -12-10 -12-10 -14
-12 m depth, pile -14 -14m depth, pile pile depth, m depth, pile -12 -12 -16 -14 -16-14 -16-14 -18 -16 -18 -18-16 -20 -16 -18 -20-18 -20-18 -20 D1=9.15m D2=7.5m -20 D1=9.15m D2=7.5m -20 D1=9.15m D2=7.5m D3=6mD1=9.15m D2=7.5m D3=6mD1=9.15m D2=7.5m D3=6mD1=9.15m D2=7.5m (a) D3=6m D3=6m(b) D3=6m (c) (a) (b) (c) Figure 20. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel Figure 20. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel Figure 20. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H = 26 26 m). m). (H = 26 m). lateral deflection, mm lateral deflection, mm 6 lateral4 deflection,2 mm0 -2 6 lateral4 deflection,2 mm0 -2 0 6 4 2 0 -2 0 6 4 2 0 -2 -20 -20 -4-2 -4-2 -6-4 -6-4 -8-6 -8-6
-10-8 -10-8 pile depth, m depth, pile
pile depth, m depth, pile -12-10 -12-10 pile depth, m depth, pile pile depth, m depth, pile -14-12 -14-12 -16-14 -16-14 -18-16 -18-16 -20-18 -20-18 D1=9.15m D2=7.5m D1=9.15m D2=7.5m -20 -20 D3=6mD1=9.15m D2=7.5m D3=6mD1=9.15m D2=7.5m D3=6m D3=6m (a) (b) (c) (a) (b) (c) Figure 21. Lateral deflection at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel (HFigure = 14 21.m). Lateral deflectiondeflection at a depth of (a)) Near,Near, ((bb)) Middle,Middle, andand ((cc)) RearRear pilespiles withwith differentdifferent DDtuntun for the shallow tunnel (H(H = 1 144 m m).). 5.3.3. Axial Force of the Piles 5.3.3.The Axial developing Force of the axial Piles force distribution along with the Near, Middle, and Rear piles at variousThe developing pile position axialaxials Xpile forceforce (6.45, distributiondistribution 14, and 18) along along m relative with with the the to Near, theNear, deep Middle, Middle, and andshallow and Rear Rear tunnels piles piles at at various pile positions Xpile (6.45, 14, and 18) m relative to the deep and shallow tunnels withvarious a constant pile positions diameter Xpile Dtun(6.45, of 9.15 14, andm are 18) demonstrated m relative to in the Figure deeps and 22 and shallow 23. For tunnels both with a constant diameter Dtun of 9.15 m are demonstrated in Figures 22 and 23. For both cases,with athe constant axial force diameter at the D uppertun of 9.15part mof arethe demonstratedpile does not affect in Figures by the 22 tunnel and 23 excavation. For both whilecases, thethe effectaxial force increases at the more upper significantly part of the at pile the does middle not and affect lower by the partition tunnel of excavation the pile. Inwhile addition, the effecteffect an increasesincreaseincreases in more more the significantly distancesignificantly between at at the the middlethe middle pile and andand lower thelower tunnel partition partition does of theofnot the pile. cause pile. In muchInaddition, addition, variation an increasean inincrease the inaxial the in distanceforce.the distance Furthermore, between between the there pilethe andispile a significant theand tunnel the tunnel doeseffect notdoes in the cause not amount muchcause ofmuchvariation axial variation force in the at the axialin the Near force. axial pile Furthermore,force. while Furthermore, a small there effect is there aat significant the is Middlea significant effect and inRear effect the piles amount in the in theamount of axialcase ofofforce theaxial at shallow force the Near at tunnel.the pile Near while However, pile a while small the a effect small induced at effect the maximum Middle at the Middle and axial Rear and force piles Rear at in thepiles the Near casein the pile of case the is largerofshallow the than shallow tunnel. that tunnel.of However, the Middle However, the inducedand theRear induced maximum pile for maximumthe axial deep force and axial at shallow the force Near attunnel. pile the is Near This larger pileresult than is wellargerthatl agrees of than the Middlewiththat ofthe andthe findings Middle Rear pile of and [52,53] for Rear the. deeppile for and the shallow deep and tunnel. shallow This tunnel. result wellThis agreesresult withwell agrees the findings with the of [findings52,53]. of [52,53]. On the other hand, Figures 24 and 25 illustrate the axial force behavior for Near, Middle, and Rear piles located at a specific distance of about 6.45 m from the deep and shallow tunnel with various Dtun (9.15, 7.5, and 6) m. Again, the axial force increases as the tunnel diameter increases. Moreover, the axial force increases by about 75% and 90% in the deep and shallow tunnel, respectively, with D = 9.15 m. This is due to the increase in ground movement around the tunnel construction. As in the case of the shallow tunnel, the axial force at the Near pile is significantly more affected. However, it can be concluded that higher-diameter tunnels induce a higher axial force on the piles. The axial force at the Near pile is larger than that of the middle and Rear pile for the deep and shallow tunnel. In
Symmetry 2021, 13, 426 17 of 22
general, additional axial forces can be induced in a pile due to tunnel construction, based Symmetry 2021, 13, x FOR PEER REVIEWon the location of piles relative to the tunnel. These results are similar to those obtained17 of 23 Symmetry 2021, 13, x FOR PEER REVIEW 17 of 23 by [44,52,53].
axial force, kN axial force, kN axial force, kN 400 200axial 0force,-200 kN -400 -600 400 200axial force,0 -200 kN -400 -600 400 axial200 force,0 kN-200 -400 -600 400 200 0 -200 -400 -600 0400 200 0 -200 -400 -600 0400 200 0 -200 -400 -600 0 -20 -20 -20 -2-4 -2-4 -2-4 -4-6 -4-6 -4-6 -6-8 -6-8 -6-8
-10-8 -10-8 -10-8 pile depth, m depth, pile -10 m depth, pile -10
pile depth, m depth, pile -12 -10-12 -12
pile depth, m depth, pile pile depth, m depth, pile pile depth, m depth, pile -12-14 -12-14 -12-14 -14-16 -14-16 -14-16 -16-18 -16-18 -16-18 -18-20 -18-20 -18-20 -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X3=18m X3=18m X3=18m (a) (b) (c) (a) (b) (c) FigureFigure 22.22. AxialAxial forceforce atat depthdepth ofof ((aa)) Near,Near, ( (bb)) Middle, Middle, and and ( c(c)) Rear Rear piles piles with with different different X Xpilepile forfor deepdeep tunneltunnel (H(H == 2626 m). Figure 22. Axial force at depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for deep tunnel (H = 26 m). axial force, kN axial force, kN axial force, kN 500 -500axial force,-1500 kN -2500 500 axial-500 force,-1500 kN -2500 500 axial-500 force, -1500kN -2500 0500 -500 -1500 -2500 0500 -500 -1500 -2500 0500 -500 -1500 -2500 -20 -20 -20 -2-4 -2-4 -2-4 -4-6 -4-6 -4-6 -6-8 -6-8 -6-8 -10-8 -10-8 -10-8
-10-12 -10-12 -10-12
pile depth, m depth, pile pile depth, m depth, pile
-12-14 m depth, pile -12-14 -12-14
pile depth, m depth, pile pile depth, m depth, pile -14-16 m depth, pile -14-16 -14-16 -16-18 -16-18 -16-18 -18-20 -18-20 -18-20 -20 -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m X1=6.45m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X3=18m X3=18m X3=18m (a) (b) (c) (a) (b) (c) Figure 23. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H = 26 Symmetry 2021, 13, x FOR PEER REVIEW 18 of 23 Figure 23. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H = 26 Figurem). 23. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H = 26 m). m). On the other hand, Figures 24 and 25 illustrate the axial force behavior for Near, Mid- axial force,dle, kN andOn theRear other piles hand, locate Figuredaxial at a force, sspecific 24 kNand distance25 illustrate of about the axial 6.45axial forceforce,m from kNbehavior the deep for and Near, shallow Mid- 400 300 200 100dle,0 and-100 Rear-200 piles locate400 300d at200 a 100specific0 -100 distance-200 of about400 3006.45200 m from100 0 the-100 deep-200 and shallow tunnel with various Dtun (9.15, 7.5, and 6) m. Again, the axial force increases as the tunnel 0 0 tunnel with various0 Dtun (9.15, 7.5, and 6) m. Again, the axial force increases as the tunnel -2 diameter increase-2s. Moreover, the axial force increases-2 by about 75% and 90% in the deep -4 diameterand shallow increase tunnel-4s. Moreover,, respectively the, axialwith forceD = 9.15 increases m.-4 This by is about due to75% the and increase 90% in in the ground deep -6 -6 -6 andmovement shallow around tunnel the, respectively tunnel construction., with D = 9.15As in m. the This case is of due the to shallow the increase tunnel, in the ground axial -8 movement around-8 the tunnel construction. As in the-8 case of the shallow tunnel, the axial
-10 force at the Near-10 pile is significantly more affected.-10 However, it can be concluded that
pile depth, m depth, pile pile depth, m depth, pile -12 forcehigher at-diameter the Near-12 tunnels pile is significantlyinduce a higher more axial affected. m forcedepth, pile -12 However,on the piles. it can The be axial concluded force at that the -14 higher-diameter -14tunnels induce a higher axial force-14 on the piles. The axial force at the -16 Near pile is larger-16 than that of the middle and Rear pile for the deep and shallow tunnel. Near pile is larger than that of the middle and Rear-16 pile for the deep and shallow tunnel. -18 In general, additional-18 axial forces can be induced-18 in a pile due to tunnel construction, -20 In general, additional-20 axial forces can be induced-20 in a pile due to tunnel construction, D1=9.15m basedD2=7.5m on the location of piles relative to the tunnel. These results are similar to those ob- based on the location ofD1=9.15m piles relative D2=7.5mto the tunnel. TheseD1=9.15m results are similarD2=7.5m to those ob- D3=6m tained by [44,52,53]. D3=6m D3=6m (a) tained by [44,52,53]. (b) (c)
FigureFigure 24.24. AxialAxial forceforce at at a a depth depth of of (a ()a Near,) Near, (b )(b Middle,) Middle, and and (c) ( Rearc) Rear piles piles with with different different Dtun Dfortun thefor deepthe deep tunnel tunnel (H = (H 26 = m 26). m).
axial force, kN axial force, kN axial force, kN 500 -500 -1500 -2500 500 -500 -1500 -2500 500 -500 -1500 -2500 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10
pile depth, m depth, pile pile depth, m depth, pile -12 -12 m depth, pile -12 -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 D1=9.15m D2=7.5m D1=9.15m D2=7.5m D1=9.15m D2=7.5m D3=6m D3=6m D3=6m (a) (b) (c)
Figure 25. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel (H = 14 m).
5.3.4. Bending Moment of the Piles Figures 26 and 27 show the comparison of the bending moment behavior of the Near, Middle, and Rear piles at various Xpile (6.45, 14, and 18) m and constant Dtun of 9.15 m for the deep and shallow tunnel, respectively. It can be seen that the bending moment in both cases increased as the distance from the tunnel decreased due to lateral soil movement. This result is in good agreement with the work of [44,52]. For more details, the bending moment of the pile increases significantly as the tunnel construction reaching to the pile tip [54]. As expected, the pile that is closer to the tunnel is affected more by tunnel con- struction. In general, very little change in the bending moment may be noted at the dis- tance Xpile = 14 m and 18 m. Finally, it can be concluded that the maximum bending mo- ment of the shallow tunnel (Lp/H > 1) is more than that of the deep tunnel (Lp/H < 1) [53].
Symmetry 2021, 13, x FOR PEER REVIEW 18 of 23
axial force, kN axial force, kN axial force, kN 400 300 200 100 0 -100 -200 400 300 200 100 0 -100 -200 400 300 200 100 0 -100 -200 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10
pile depth, m depth, pile pile depth, m depth, pile -12 -12 m depth, pile -12 -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 D1=9.15m D2=7.5m D1=9.15m D2=7.5m D1=9.15m D2=7.5m D3=6m D3=6m D3=6m Symmetry 2021, 13, 426 (a) (b) (c) 18 of 22
Figure 24. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H = 26 m).
axial force, kN axial force, kN axial force, kN 500 -500 -1500 -2500 500 -500 -1500 -2500 500 -500 -1500 -2500 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10
pile depth, m depth, pile pile depth, m depth, pile -12 -12 m depth, pile -12 -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 D1=9.15m D2=7.5m D1=9.15m D2=7.5m D1=9.15m D2=7.5m D3=6m D3=6m D3=6m (a) (b) (c)
Figure 25. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel (H = Figure 25. Axial force at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the shallow tunnel 14 m). (H = 14 m). 5.3.4. Bending Moment of the Piles 5.3.4. Bending Moment of the Piles Figures 26 and 27 show the comparison of the bending moment behavior of the Near, Middle,Figures and 26 Rear and piles 27 show at various the comparison Xpile (6.45, 14, of and the 18) bending m and constant moment D behaviortun of 9.15 ofm thefor Near, Middle,the deep and and Rear shallow piles tunnel at various, respectively. Xpile (6.45, It can 14, be and seen 18) that m the and bending constant moment Dtun ofin both 9.15 m for thecases deep increased and shallow as the tunnel, distance respectively. from the tunnel It can decreased be seen due that to the lateral bending soil movement. moment in both casesThis increased result is in as good the distance agreement from with the the tunnel work decreased of [44,52]. dueFor more to lateral details, soil the movement. bending This resultmom isent in goodof the agreementpile increases with significantly the work as of the [44 ,tunnel52]. For construction more details, reaching the bending to the pile moment of thetip [54] pile. increasesAs expected, significantly the pile that as is the closer tunnel to the construction tunnel is affected reaching more to by the tunnel pile tip con- [54]. As expected,struction. the In pilegeneral, that very is closer little change to the tunnelin the bending is affected moment more may by be tunnel noted construction. at the dis- In tance Xpile = 14 m and 18 m. Finally, it can be concluded that the maximum bending mo- general, very little change in the bending moment may be noted at the distance Xpile = 14 m ment of the shallow tunnel (Lp/H > 1) is more than that of the deep tunnel (Lp/H < 1) [53]. Symmetry 2021, 13, x FOR PEER REVIEWand 18 m. Finally, it can be concluded that the maximum bending moment of19 the of shallow23
Symmetry 2021, 13, x FOR PEER REVIEWtunnel (Lp/H > 1) is more than that of the deep tunnel (Lp/H < 1) [53]. 19 of 23
bemding moment, kN.m Bending moment, kN.m bending moment, kN.m 50 0 -50 -100 50 0 -50 -100 bemding moment, kN.m Bending moment, kN.m 50bending moment,0 -50 kN.m -100 0 0 50 0 -50 -100 50 0 -50 -100 0 50 0 -50 -100 -2 -2 0 0 -20 -4 -4 -2 -2 -2-4 -6 -6 -4 -4 -4-6 -8 -6-8 -6 -6-8 -10
-10-8 -8 -10-8 pile depth, m depth, pile
-12 m depth, pile -12 -12 -10 -10 m depth, pile -10 -14 -14 pile depth, m depth, pile -14 -12 m depth, pile -12 -12 -16 m depth, pile -16 -14-16 -14 -14 -18 -18 -16-18 -16 -16 -20 -18-20 -18-20 -18 X1=6.45m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m -20 -20 -20 X3=18m X3=18m X1=6.45mX3=18m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m X3=18m X3=18m (a)X3=18m (b) (c) (a) (b) (c) Figure 26. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H Figure 26. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel Figure= 26 m). 26. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H (H = 26 m). = 26 m). bending moment, kN.m bending moment, kN.m bending moment, kN.m 100 50 0 -50 50 0 -50 -100 bending moment, kN.m bending moment, kN.m 50bending0 moment,-50 kN.m -100 0100 50 0 -50 0 50 0 -50 -100 0 50 0 -50 -100 -20 -20 -20 -2-4 -2-4 -2-4 -4-6 -4-6 -4-6 -6-8 -6-8 -6-8
-10-8 -10-8 -10-8 pile depth, m depth, pile pile depth, m depth, pile -12 -12 -12 -10 -10 m depth, pile -10
-14 -14 -14 pile depth, m depth, pile
pile depth, m depth, pile -12 -12 -12 pile depth, m depth, pile -14-16 -14-16 -14-16 -16-18 -16-18 -16-18 -18-20 -18-20 -18-20 X1=6.45m X2=14m -20 -20 X1=6.45m X2=14m -20 X1=6.45m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m X1=6.45mX3=18m X2=14m (a)X3=18m X3=18m(b) X3=18m (c) (a) (b) (c) Figure 27. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel Figur(H = 14e 27 m).. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel Figure 27. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (H = 14 m). (H = 14 m). On the other hand, Figures 28 and 29 show the bending moment profiles at various Dtun (9.15,On the 7.5, other and hand, 6) m Figureand a sconstant 28 and 29Xpile show of 6.45 the bendingm for the moment deep and profiles shallow at varioustunnel, Drespectively.tun (9.15, 7.5, It andcan be6) seenm and that a anconstant increase Xpile in theof 6.45 diameter m for of the the deep tunnel and causes shallow an increase tunnel, respectively.in bending moment It can be [52] seen. Moreover, that an increase the maximum in the diameter bending of moment the tunnel occurs causes at anthe increase bottom inpartition bending of moment the piles. [52] Again,. Moreover, the bending the maximum moment at bending the Near moment pile is larger occurs than at the that bottom of the partitionMiddle and of the Rear piles. pile Again, for the the deep bending and shallow moment tunnel. at the Generally, Near pile isvery larger little than change that ofin the Mmaximumiddle and bending Rear pile moment for the deepcan be and noted shallow for both tunnel. cases. Generally, very little change in the maximum bending moment can be noted for both cases. bending moment, kN.m bending moment, kN.m bending moment, kN.m 50 0 -50 -100 50 bending0 moment,-50 kN.m -100 bending moment, kN.m 50 bending0 moment,-50 kN.m-100 0 50 0 -50 -100 0 50 0 -50 -100 0 50 0 -50 -100 -20 -20 -20 -2-4 -2-4 -2-4 -6 -4 -4-6 -4-6 -8 -6 -6-8 -6-8 -10
-8 -10-8 -10-8 pile depth, m depth, pile
-12 m depth, pile -10 -10m depth, -12pile -10-12
pile depth, m depth, pile -14 -14 -14
-12 m depth, pile pile depth, m depth, -12pile -12 -14-16 -16 -16 -18 -14 -14 -16 -16-18 -16-18 -18-20 -20 -20 D1=9.15m D2=7.5m -18 D1=9.15m D2=7.5m -18 D1=9.15m D2=7.5m -20 -20 -20 D1=9.15m D3=6m D2=7.5m D1=9.15m D3=6m D2=7.5m D1=9.15m D3=6m D2=7.5m (a) D3=6m D3=6m (b) D3=6m (c) (a) (b) (c) Figure 28. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H Figure= 26 m ).28. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H = 26 m).
Symmetry 2021, 13, x FOR PEER REVIEW 19 of 23
bemding moment, kN.m Bending moment, kN.m bending moment, kN.m 50 0 -50 -100 50 0 -50 -100 50 0 -50 -100 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10 pile depth, m depth, pile
-12 m depth, pile -12 -12 pile depth, m depth, pile -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 X1=6.45m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m X3=18m X3=18m X3=18m (a) (b) (c)
Figure 26. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the deep tunnel (H = 26 m).
bending moment, kN.m bending moment, kN.m bending moment, kN.m 100 50 0 -50 50 0 -50 -100 50 0 -50 -100 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10 pile depth, m depth, pile
pile depth, m depth, pile -12 -12 -12 pile depth, m depth, pile -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 X1=6.45m X2=14m X1=6.45m X2=14m X1=6.45m X2=14m X3=18m X3=18m X3=18m Symmetry 2021, 13, 426 (a) (b) (c) 19 of 22
Figure 27. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Xpile for the shallow tunnel (H = 14 m). On the other hand, Figures 28 and 29 show the bending moment profiles at various On the other hand, Figures 28 and 29 show the bending moment profiles at various Dtun (9.15, 7.5, and 6) m and a constant Xpile of 6.45 m for the deep and shallow tunnel, Dtun (9.15, 7.5, and 6) m and a constant Xpile of 6.45 m for the deep and shallow tunnel, respectively. It can be seen that an increase in the diameter of the tunnel causes an increase respectively. It can be seen that an increase in the diameter of the tunnel causes an increase in bending moment [52]. Moreover, the maximum bending moment occurs at the bottom in bending moment [52]. Moreover, the maximum bending moment occurs at the bottom partition of the piles. Again, the bending moment at the Near pile is larger than that of the partition of the piles. Again, the bending moment at the Near pile is larger than that of the Middle and Rear pile for the deep and shallow tunnel. Generally, very little change in the Middle and Rear pile for the deep and shallow tunnel. Generally, very little change in the maximum bending moment can be noted for both cases. maximum bending moment can be noted for both cases.
bending moment, kN.m bending moment, kN.m bending moment, kN.m 50 0 -50 -100 50 0 -50 -100 50 0 -50 -100 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8
-10 -10 -10 pile depth, m depth, pile
-12 m depth, pile pile depth, m depth, -12pile -12 -14 -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 D1=9.15m D2=7.5m D1=9.15m D2=7.5m D1=9.15m D2=7.5m D3=6m D3=6m D3=6m (a) (b) (c)
Figure 28. Bending moment at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel (H SymmetryFigure 2021 28., 13,Bending x FOR PEER moment REVIEW at a depth of (a) Near, (b) Middle, and (c) Rear piles with different Dtun for the deep tunnel20 of 23
(H= 26 = m 26). m).
bending moment, kN.m bending moment, kN.m bending moment, kN.m 150 100 50 0 -50 -100 50 0 -50 -100 50 0 -50 -100 0 0 0 -2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8 -10 -10 -10 -12
-12 m depth, pile -12 pile depth, m depth, pile -14 m depth, pile -14 -14 -16 -16 -16 -18 -18 -18 -20 -20 -20 D1=9.15m D2=7.5m D1=9.15m D2=7.5m D1=9.15m D2=7.5m D3=6m D3=6m D3=6m (a) (b) (c)
tun Figure 29. BendingBending moment at a depth of ( a) Near, (b) Middle, and ((c)) Rear pilespiles withwith differentdifferent DDtun forfor the the shallow shallow tunnel tunnel (H = 1 144 m m).).
6.6. Conclusions Conclusions AA series series of of 3D 3D finite finite element element model modellingslings have have been been conducted conducted using using Midas Midas GTS GTS--NX softwareNX software to study to study the behavior the behavior of pile of cap pile foundation cap foundation for Garage for Garage El-Attaba El-Attaba building building dur- ingduring the theshield shield advancement advancement of the of the Greater Greater Cairo Cairo Metro Metro Line Line 3 3-Phase-Phase 1 1 using using Modified Modified MohrMohr–Coulomb–Coulomb constitutive model.model. InvestigationInvestigation ofof thethe pilepile responses, responses, including including the the axial ax- ialsettlement, settlement, lateral lateral deflection, deflection, bending bending moment, moment, and and additional additional axial axial forceforce byby the tunnel constructionconstruction stages stages were were discussed. discussed. The The present present study study shows shows that that the the pile pile responses are influencedinfluenced by by tunneling. tunneling. In In addition, addition, variou variouss factors factors on on the the pile pile response response were were studied in whichwhich the the following factors were included: the the distance distance between between the the pile pile and the tunnel andand the the diameter diameter of of the the tunnel tunnel with with two two different different tunnel tunnel axes axes,, deep deep and and shallow shallow tunnel. tunnel. TheThe following following findings findings have been drawn from the study: 1. TheThe tunnel tunnel depth depth has has an an adverse adverse influence influence on on the the response response of of piles. piles. As As the the depth depth of thethe tunnel tunnel increases, increases, the the response response of of the the piles piles decreases. decreases. However, However, to to avoid avoid serious damage to the adjacent pile foundation and structures, the tunnel depth and distance between the piles and the tunnel must be taken into consideration, being important to control effectively the piles responses. 2. For both cases, deep and shallow tunnel, increasing the tunnel diameter causes the pile to increase the axial settlement and lateral deflection more as well as induce more additional axial force and bending moment. 3. Decreasing the distance between the tunnel and the pile does cause a significant ef- fect on pile response. However, the behavior of the variation is the same for Near, Middle, and Rear piles. 4. For the deep tunnel (tunnel axis is located below the tip) and shallow tunnel (tunnel axis is located above the tip), the maximum bending moment and axial force occurred at the pile tip while the maximum axial settlement and lateral deflection occurred at the pile head. 5. Larger variation to the pile axial force and bending moment were observed in the case of the shallow tunnel. However, the depth of the tunnel axis has much signifi- cant effect on pile response. Hence, the shallow tunnel does cause a greater response on piles more than the deep tunnel.
Author Contributions: Conceptualization, M.A., H.Q., and X.Z.; formal analysis, M.A.; investiga- tion, M.A., H.Q., and X.Z.; writing—original draft preparation, M.A. and H.Q.; supervision, H.Q., and X.Z. All authors have read and agreed to the published version of the manuscript. Funding: The publishing of this paper is financially supported by the National Natural Science Foundation of China (No. 11672215). Institutional Review Board Statement: Not applicable
Symmetry 2021, 13, 426 20 of 22
damage to the adjacent pile foundation and structures, the tunnel depth and distance between the piles and the tunnel must be taken into consideration, being important to control effectively the piles responses. 2. For both cases, deep and shallow tunnel, increasing the tunnel diameter causes the pile to increase the axial settlement and lateral deflection more as well as induce more additional axial force and bending moment. 3. Decreasing the distance between the tunnel and the pile does cause a significant effect on pile response. However, the behavior of the variation is the same for Near, Middle, and Rear piles. 4. For the deep tunnel (tunnel axis is located below the tip) and shallow tunnel (tunnel axis is located above the tip), the maximum bending moment and axial force occurred at the pile tip while the maximum axial settlement and lateral deflection occurred at the pile head. 5. Larger variation to the pile axial force and bending moment were observed in the case of the shallow tunnel. However, the depth of the tunnel axis has much significant effect on pile response. Hence, the shallow tunnel does cause a greater response on piles more than the deep tunnel.
Author Contributions: Conceptualization, M.A., H.Q., and X.Z.; formal analysis, M.A.; investigation, M.A., H.Q., and X.Z.; writing—original draft preparation, M.A. and H.Q.; supervision, H.Q., and X.Z. All authors have read and agreed to the published version of the manuscript. Funding: The publishing of this paper is financially supported by the National Natural Science Foundation of China (No. 11672215). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conflicts of Interest: The authors declare no conflict of interest.
References 1. Attewell, P.B.; Farmer, I.W. Ground disturbance caused by shield tunnelling in a stiff, overconsolidated clay. Eng. Geol. 1974, 8, 361–381. [CrossRef] 2. Basile, F. Effects of tunnelling on pile foundations. Soils Found. 2014, 54, 280–295. [CrossRef] 3. Al-Omari, R.R.; Al-Soud, M.S.; Al-Zuhairi, O.I. Effect of Tunnel Progress on the Settlement of Existing Piled Foundation. Stud. Geotech. Mech. 2019, 41, 102–113. [CrossRef] 4. Wang, H.; Leung, C.F.; Yu, J.; Huang, M. Axial response of short pile due to tunnelling-induced soil movement in soft clay. Int. J. Phys. Model. Geotech. 2019, 20, 71–82. [CrossRef] 5. Li, Y.; Zhang, W. Investigation on passive pile responses subject to adjacent tunnelling in anisotropic clay. Comput. Geotech. 2020, 127, 103782. [CrossRef] 6. Simic-Silva, P.T.; Martínez-Bacas, B.; Galindo-Aires, R.; Simic, D. 3D simulation for tunnelling effects on existing piles. Comput. Geotech. 2020, 124, 103625. [CrossRef] 7. Jacobsz, S.W.; Standing, J.R.; Mair, R.J.; Hagiwara, T.; Sugiyama, T. Centrifuge modelling of tunnelling near driven piles. Soils Found. 2004, 44, 49–56. [CrossRef] 8. Franza, A.; Marshall, A.M. Centrifuge modeling study of the response of piled structures to tunneling. J. Geotech. Geoenviron. Eng. 2018, 144, 4017109. [CrossRef] 9. Lee, C.J. Numerical analysis of the interface shear transfer mechanism of a single pile to tunnelling in weathered residual soil. Comput. Geotech. 2012, 42, 193–203. [CrossRef] 10. Franza, A.; Marshall, A.M. Centrifuge and real-time hybrid testing of tunneling beneath piles and piled buildings. J. Geotech. Geoenviron. Eng. 2019, 145, 4018110. [CrossRef] 11. Soomro, M.A.; Hong, Y.; Ng, C.W.W.; Lu, H.; Peng, S. Load transfer mechanism in pile group due to single tunnel advancement in stiff clay. Tunn. Undergr. Space Technol. 2015, 45, 63–72. [CrossRef] 12. Soomro, M.A.; Ng, C.W.W.; Liu, K.; Memon, N.A. Pile responses to side-by-side twin tunnelling in stiff clay: Effects of different tunnel depths relative to pile. Comput. Geotech. 2017, 84, 101–116. [CrossRef] 13. Loganathan, N.; Poulos, H.G.; Xu, K.J. Ground and pile-group responses due to tunnelling. Soils Found. 2001, 41, 57–67. [CrossRef] Symmetry 2021, 13, 426 21 of 22
14. Soomro, M.A.; Bangwar, D.K.; Soomro, M.A.; Keerio, M.A. 3D Numerical Analysis of the Effects of an Advancing Tunnel on an Existing Loaded Pile Group. Eng. Technol. Appl. Sci. Res. 2018, 8, 2520–2525. [CrossRef] 15. Huang, M.; Zhang, C.; Li, Z. A simplified analysis method for the influence of tunneling on grouped piles. Tunn. Undergr. Space Technol. 2009, 24, 410–422. [CrossRef] 16. Mroueh, H.; Shahrour, I. A full 3-D finite element analysis of tunneling-adjacent structures interaction. Comput. Geotech. 2003, 30, 245–253. [CrossRef] 17. Lee, G.T.K.; Ng, C.W.W. Effects of Advancing Open Face Tunneling on an Existing Loaded Pile. J. Geotech. Geoenviron. Eng. 2005, 131, 193–201. [CrossRef] 18. Jongpradist, P.; Kaewsri, T.; Sawatparnich, A.; Suwansawat, S.; Youwai, S.; Kongkitkul, W.; Sunitsakul, J. Development of tunneling influence zones for adjacent pile foundations by numerical analyses. Tunn. Undergr. Space Technol. 2013, 34, 96–109. [CrossRef] 19. Lueprasert, P.; Jongpradist, P.; Jongpradist, P.; Suwansawat, S. Numerical investigation of tunnel deformation due to adjacent loaded pile and pile-soil-tunnel interaction. Tunn. Undergr. Space Technol. 2017, 70, 166–181. [CrossRef] 20. Loganathan, N. An Innovative Method for Assessing Tunnelling-Induced Risks to Adjacent Structures; Parsons Brinckerhoff: New York, NY, USA, 2011. 21. Burland, J.B.; Wroth, C.P. Settlement of Buildings and Associated Damage. In Settlement of Structures; Pentech Pr.: London, UK, 1974; pp. 611–654. 22. Boscardin, M.D.; Cording, E.J. Building response to excavation-induced settlement. J. Geotech. Eng. 1989, 115, 1–21. [CrossRef] 23. Burland, J.B. Assessment of Risk of Damage to Buildings due to Tunnelling and Excavation; Imperial College of Science, Technology and Medicine: London, UK, 1995. 24. Mair, R.J.; Taylor, R.N.; Burland, J.B. Prediction of Ground Movements and Assessment of Risk of Building Damage due to Bored Tunnelling. In Proceedings of the Geotechnical aspects of Underground Construction in Soft Ground, London, UK, 15–17 April 1996; pp. 713–718. 25. Bolton, M.D.; Lu, Y.C.; Sharma, J.S. Centrifuge models of tunnel construction and compensation grouting. Geotech. Asp. Undergr. Constr. Soft Ground 1996, 15–17, 471–477. 26. Loganathan, N.; Poulos, H.G.; Stewart, D.P. Centrifuge model testing of tunnelling-induced ground and pile deformations. Geotechnique 2000, 50, 283–294. [CrossRef] 27. Franza, A.; Marshall, A.M.; Haji, T.; Abdelatif, A.O.; Carbonari, S.; Morici, M. A simplified elastic analysis of tunnel-piled structure interaction. Tunn. Undergr. Space Technol. 2017, 61, 104–121. [CrossRef] 28. Abdullah, M.H.; Taha, M.R. A review of the effects of tunneling on adjacent piles. Electron. J. Geotech. Eng. 2013, 18, 2739–2762. 29. Vakili, K.N.; Lavasan, A.A.; Schanz, T.; Datcheva, M. The Influence of the Soil Constitutive Model on the Numerical Assessment of Mechanized Tunneling. In Proceedings of the 8th European Conference on Numerical Methods in Geotechnical Engineering, Delft, The Netherlands, 18–20 June 2014; pp. 889–894. 30. Zidan, A.F.; Ramadan, O.M.O. Three dimensional numerical analysis of the effects of tunnelling near piled structures. KSCE J. Civ. Eng. 2015, 19, 917–928. [CrossRef] 31. Lee, C.J.; Jacobsz, S.W. The influence of tunnelling on adjacent piled foundations. Tunn. Undergr. Space Technol. 2006, 21, 430. [CrossRef] 32. Lee, C.J. Three-dimensional numerical analyses of the response of a single pile and pile groups to tunnelling in weak weathered rock. Tunn. Undergr. Space Technol. 2012, 32, 132–142. [CrossRef] 33. National Authority for Tunnel. “Tunnel from Attaba to Geish Shaft Monitoring Measurements”, Contract N 49/Metro, Phase 1"; National Authority for Tunnel: Cairo, Eqypt, 2010; pp. 270–271. 34. Mocarthy Brothers Company. A Division of Design and Management, Consultant of Attaba Parking Garage; Mocarthy Brothers Company: Cairo, Egypt, 1984. 35. Hamza Associates. Geotechnical Investigation Report; Hamza Associates: Cairo, Egypt, 2002. 36. Ayasrah, M.; Qiu, H.; Zhang, X.; Daddow, M. Prediction of Ground Settlement Induced by Slurry Shield Tunnelling in Granular Soils. Civ. Eng. J. 2020, 6, 2273–2289. [CrossRef] 37. Hejazi, Y.; Dias, D.; Kastner, R. Impact of constitutive models on the numerical analysis of underground constructions. Acta Geotech. 2008, 3, 251–258. [CrossRef] 38. Fu, Y.; He, S.; Zhang, S.; Yang, Y. Parameter Analysis on Hardening Soil Model of Soft Soil for Foundation Pits Based on Shear Rates in Shenzhen Bay, China. Adv. Mater. Sci. Eng. 2020, 2020, 7810918. [CrossRef] 39. Surarak, C.; Likitlersuang, S.; Wanatowski, D.; Balasubramaniam, A.; Oh, E.; Guan, H. Stiffness and strength parameters for hardening soil model of soft and stiff Bangkok clays. Soils Found. 2012, 52, 682–697. [CrossRef] 40. Potts, D.M.; Zdravkovic, L.; Zdravkovi´c,L. Finite Element Analysis in Geotechnical Engineering: Application; Thomas Telford: London, UK, 2001. 41. Potts, D.M.; Addenbrooke, T.I. A structure’s influence on tunnelling-induced ground movements. Proc. Inst. Civ. Eng. Geotech. Eng. 1997, 125, 109–125. [CrossRef] 42. Mašín, D.; Tamagnini, C.; Viggiani, G.; Costanzo, D. Directional response of a reconstituted fine-grained soil—Part II: Performance of different constitutive models. Int. J. Numer. Anal. Methods Geomech. 2006, 30, 1303–1336. [CrossRef] 43. Obrzud, R.F. On the use of the Hardening Soil Small Strain model in geotechnical practice. Numer. Geotech. Struct. 2010, 16, 15–32. Symmetry 2021, 13, 426 22 of 22
44. Yang, M.; Sun, Q.; Li, W.; Ma, K. Three-dimensional finite element analysis on effects of tunnel construction on nearby pile foundation. J. Cent. South Univ. Technol. 2011, 18, 909. [CrossRef] 45. Çelik, S. Comparison of Mohr-Coulomb and Hardening Soil Models’ Numerical Estimation of Ground Surface Settlement Caused by Tunneling Tünel Kazısından Dolayı Zemin Yüzeyindeki Oturmaların Mohr- Coulomb ve Pekle¸senZemin Modelleriyle Nümerik Tahminlerinin Kar¸sıla¸st. I˘gdırUniv. J. Inst. Sci. Technol. 2017, 7, 95–102. [CrossRef] 46. Teo, P.L.; Wong, K.S. Application of the Hardening Soil model in deep excavation analysis. IES J. Part A Civ. Struct. Eng. 2012, 5, 152–165. [CrossRef] 47. Duncan, J.M.; Buchignani, A. An Engineering Manual for Settlement Studies; University of California: Oakland, CA, USA, 1976. 48. The Housing and Building Research Center (HBRC). ECP 202/3, Egyptian Code for Soil Mechanics—Design and Construction of Foundations. Part 3, Shallow Foundation; The Housing and Building Research Center (HBRC): Cairo, Egypt, 2005. 49. Zhao, C.Y.; Lavasan, A.A.; Barciaga, T.; Zarev, V.; Datcheva, M.; Schanz, T. Model validation and calibration via back analysis for mechanized tunnel simulations—The Western Scheldt tunnel case. Comput. Geotech. 2015, 69, 601–614. [CrossRef] 50. Mayne, P.W.; Kulhawy, F.H. K0-OCR relationships in soil. J. Geotech. Eng. 1982, 108, 851–872. 51. Cheng, C.Y.; Dasari, G.R.; Leung, C.F.; Chow, Y.K.; Rosser, H.B. 3D numerical study of tunnel-soil-pile interaction. Tunn. Undergr. Space Technol. 2004, 19, 381–382. 52. Chen, L.T.; Poulos, H.G.; Loganathan, N. Pile Responses Caused by Tunneling. J. Geotech. Geoenviron. Eng. 1999, 125, 207–215. [CrossRef] 53. Mroueh, H.; Shahrour, I. Three-dimensional finite element analysis of the interaction between tunneling and pile foundations. Int. J. Numer. Anal. Methods Geomech. 2002, 26, 217–230. [CrossRef] 54. Lee, C.J.; Chiang, K.H. Responses of single piles to tunneling-induced soil movements in sandy ground. Can. Geotech. J. 2007, 44, 1224–1241.