Numerical investigations of the installation process of giant deep-buried circular open caissons in undrained clay

Computers and Geotechnics 118 (2020) 103322

Contents lists available at ScienceDirect

Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo

Research Paper

Numerical investigations of the installation process of giant deep-buried circular open caissons in undrained clay

T

⁎

Fengwen Laia,b, Songyu Liua,b, , Yongfeng Denga,b, Yanxiao Suna,b, Kai Wua,b, Hanxiang Liuc a

Institute of Geotechnical Engineering, Southeast University, Nanjing 211189, China Jiangsu Key Laboratory of UrbanUnderground Engineering & Environmental Safety, Southeast University, Nanjing 211189, China c State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Sichuan 610059, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Coupled Eulerian-Lagrangian approach Giant deep-buried circular open caisson Hypoplastic model Installation mechanism Deformation characteristic

Numerical investigations of the whole installation process of giant deep-buried circular open (GDCO) caissons in undrained clay were conducted using 3D large deformation finite-element (LDFE) method performed by the Coupled Eulerian-Lagrangian (CEL) approach. This study was focused on the installation mechanism and soil deformation characteristics of GDCO caissons. A kinematic and continuous numerical technique based on the CEL approach accounting for the synchronous coupling between the penetration and excavation was first introduced to simulate real installation process of GDCO caissons. An advanced user-defined hypoplastic (HP) constitutive model was applied to match the clay behaviors realistically. The measured values of penetration resistance and ground surface settlement were compiled from centrifuge tests available to validate the proposed numerical technique and show the superiorities of HP model. The plastic zone, deformed soil flow, stress distribution and penetration resistance developed in clay were effectively captured to investigate the installation mechanism. Furthermore, the soil deformation including ground surface settlement and radial displacement around the caisson were examined. The simplified semi-empirical equations were then proposed to predict the ground surface settlement pattern and maximum value.

1. Introduction With the development of urbanization, industrialization and modernization in the developing countries, especially in China, the extensive water collecting wells need to be constructed inevitably in residential areas in order to effectively alleviate the water shortage, meet the demand of water for fire protection and sewage collection [1–4]. Giant deep-buried open caissons (diameter or width D ⩾ 15 m and depth H ⩾ 30 m) are widely used as collecting wells or deep shield tunnel shafts since the caissons with the smaller footprint and larger internal space are excellent in integrity and stability. In practical engineering, Open caissons are generally circular in plane for the tunneling, pump station and public works [5–11]; those used in the bridge construction and harbor engineering works are typically square or rectangular in cross-section [1,2,12–14], as shown in Fig. 1. Open caissons subjected to external forces and gravity need to be penetrated to a pre-designed depth by excavating the inside soil. The current construction technology and design methods of giant deepburied caissons are mostly deduced and given based on those of large

diameter open-ended piles or bucket foundations. The engineering problems (e.g., slow sinking, sudden sinking, tilting, or deflection) might be ignored during the installation of open caissons due to the complicated geological conditions and huge plane sizes [15]. Thus, the installation controllability and ground disturbance effect have yet to be improved. Extensive field monitoring, experimental and numerical works have been conducted, focusing on the evaluation of the mechanical responses and deformation characteristics of the surrounding soil induced by the installation of open caissons. The distribution law of external skin friction of open caissons obtained by field monitoring was reported by Chen et al. [16] and Jiang et al. [17], the corresponding semi-empirical calculation equations were given via curve fitting. The results suggested that the external skin friction first linearly increased to the certain value then decreased nonlinearly after it due to stress relaxation effect. Furthermore, laboratory experimental studies on the external skin friction of the open caissons penetration in sandy soil were also conducted by Wang et al. [18] and Zhou et al. [19]. Zhao et al. [20] presented that the earth pressure near the blades of rectangular open caissons was significantly affected by the soil arching effect and

⁎

Corresponding author. E-mail addresses: [email protected] (F. Lai), [email protected] (S. Liu), [email protected] (Y. Deng), [email protected] (Y. Sun), [email protected] (K. Wu), [email protected] (H. Liu). https://doi.org/10.1016/j.compgeo.2019.103322 Received 16 July 2019; Received in revised form 24 September 2019; Accepted 23 October 2019 0266-352X/ © 2019 Elsevier Ltd. All rights reserved.

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

Nomenclature

βr

The following symbols are used in this paper:

χ

Δtcrit Le cd Fp dp kp h v T H R s d σ̇ ε̇ L N fs fd N λ∗ κ∗ ϕc′ Ag μ

Re

critical time step size characteristic element length dilatational wave speed contact force penetration distance penalty stiffness penetration depth penetration velocity calculation time total height of the caisson internal radius of the caisson bottom width of caisson blades radial distance to the caisson Jaumann stress rate tensor Jaumann strain rate tensor fourth-order tensors second-order tensors scalar factor describing the effect of barotropy scalar factor describing the effect of pyknotropy position of the isotropic normal compression line slope of the isotropic normal compression line slope of the unloading–reloading line critical internal friction angle parameter controlling the stiffness magnitude parameter controlling the shear stiffness at medium- to largestrain levels size of the elastic range

mt mr

G0 pr p γ′ e K0 k E υ ρ Gs c Su ϕ Rint er σr F A δv δ vm α δr

parameter controlling the rate of degradation of the stiffness with strain parameter controlling the rate of degradation of the stiffness with strain parameter controlling the initial shear modulus upon 180° strain path reversal parameter controlling the initial shear modulus upon 90° strain path reversal initial shear modulus at small strain level reference stress of 1 kPa mean principal stress effective unit weight initial void ratio coefficient of earth pressure at rest permeability Young’s modulus Poisson’s ratio density specific gravity of soil solids cohesion undrained soil strength internal friction angle friction coefficient of caisson-soil interface radial stress of the soil penetration resistance cross-section area of the caisson above the blade ground surface settlement maximum ground surface settlement ground surface settlement factor radial displacement along the caisson

Fig. 1. Schematic diagram of open caissons in practical engineering: (a) Circular caisson; (b) Rectangular caisson.

addition, the real three-dimensional installation mechanisms of giant deep-buried open caissons and deformation characteristics of the surrounding soil are not yet fully understood. The aim of this study is to investigate the whole installation process of giant deep-buried circular open (GDCO) caissons in undrained clay using 3D large deformation finite-element (LDFE) analysis performed by the Coupled Eulerian-Lagrangian (CEL) approach. To reveal real installation mechanism of GDCO caissons, an axisymmetric numerical model was thus established by the proposed kinematic numerical technique based on the CEL approach with the implementation of coupled excavation-penetration. The small-strain and hardening characteristics of clay depended on the stress-strain path were considered using an advanced user-defined hypoplastic (HP) constitutive model. The key parameters during the installation of GDCO caissons (i.e., plastic zones, deformed soil flow and stress distribution and penetration resistance) were examined. In addition, the quantitative evaluation of soil deformation characteristics induced by the installation was conducted by capturing ground surface settlement and radial deformation

rotation of principal stress by laboratory experiments. There also have been numerous investigations on spatial stress-state of blades of open caissons by field measurements [14,21,22]. However, the summarized results of above works were rather limited because of the only sandy soil, dimensional effect and a few measuring points. It is noted that the numerical simulation can reflect relatively real stress-strain state in the installation process of open caissons in soil. To examine the ground deformation characteristics induced by the installation of open caisson, Peng et al. [12] proposed a discontinuous mechanical model incorporating the finite element (FE) programs for the rectangular open caissons based on plane strain condition. Nevertheless, the calculation accuracy of soil deformation for this model was dependent on the imposed mechanical boundary conditions (e.g., external skin friction, endbearing resistance). In fact, the installation of open caissons in soil should be a continuous, complicated, kinematic and coupled process between the penetration and excavation, but this process was ignored frequently in current FE methods; and little attention was paid to threedimensional kinematic numerical modeling for the present works. In 2

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

moving of four sets of mud rushing and sucking systems placed inside the GDCO caisson. The mud sucked by the air was discharged into the slurry pond. Mud rushing and sucking system mainly includes high pressure pump chambers, flow pipes, air supply pipes, air pockets and mudding pipes, of which operating principle was described in Fig. 2b. When the high pressure pumps were working, the compressed air entered the air pocket along the air supply pipes; a mixture of gas-watermud with a bulk density of less than 1.0 was then formed. If the compressed air was sufficient and the air pocket was below the groundwater level at a certain depth, gas-water-mud mixtures would be discharged out of the caisson along mudding pipe under the action of internal and external difference. Therefore, the more compressed air supplies, the smaller bulk density of the gas-water-mud mixture. The greater pressure difference and deeper groundwater, the better effect of mud suction. However, excessive compressive air would reduce the effective amount of suction mud per unit volume of air, resulting in the prolonged construction period, higher project cost and worse effect of soil excavating.

around caissons. 2. Description of undrained construction technology 2.1. Undrained excavating method Multi-segment concrete shaft connection and penetration step by step are generally required to conduct during the installation process of GDCO caissons. How to successfully excavate soil in the ultra-deep underground water under the condition of ultra-high pressure is a significant process to ensure the complete installation of GDCO caissons, which is also one of the construction difficulties. To deal with these problems, a novel undrained excavation and penetration system was presented to apply in the installation process of GDCO caissons, which mainly includes soil breaking system, mud rushing and sucking system (hoisting and crushing equipment), gyro floating platform system and penetration aid system, as show in Fig. 2a. Soil breaking system was used to crush the soil inside the GDCO caissons under the undrained and ultra-high pressure conditions, and then the crushed soil (mud) was removed from the caissons by mud rushing and sucking system. The steel poles need to be first installed on the side walls for lifting and

Fig. 2. New undrained construction technology: (a) Undrained excavation and penetration system; (b) Operating principle of soil breaking system. 3

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

2.2. Auxiliary measures for GDOC caissons penetration

3. Numerical simulation

In the early stage of penetration, GDCO caissons are only required to rely on self-weight combined with lubrication of slurry sleeve; the disturbance induced by the installation of the caisson on the surrounding soil could be significantly reduced. Nevertheless, when the caisson was penetrated to a certain depth, the bottom soil stratum might be over-stiff, and it is much difficult to continue penetrating under the action of self-weight. An auxiliary measure for GDOC caissons penetration, vertical jacking method, was thus introduced in China [3,23]. The vertical jacking method is contributed to control penetration-verticality of the caisson, improve installation efficiency and shorten construction period. In addition, the disturbance effect can be weakened because it can ensure that there is a certain height of soil plugging (about 2–2.5 m) inside the caisson. According to the plane size of GDCO caisson, even number of bored cast-in-place piles should be uniformly and symmetrically driven in foundation soil around the caisson as reaction devices. Simultaneously, a reinforced ring beam need to be set on the outer walls of the caisson as the bracing structures of piercing jacks, as sketched in Fig. 3a. The detailed operational process of vertical jacking method was depicted in Fig. 3b–d. First, the working and substitutional drawbars were installed according to the pre-designed depth of the GDCO caisson. In the installation process of GDCO caisson, the anchor nuts on the jack cylinders were activated, the induced tension was transferred to the bored piles through the drawbars. Then, the ring beam subjected to down forces caused that the caisson penetrate to a specified depth. The oil cylinder of jacks would be retracted after the caisson was penetrated to one oil cylinder stroke (about 0.2 m); the fixed anchor nuts were further screwed and locked. Note that the upper and lower nuts connecting each drawbar were unable to pass through the holes reserved in ring beam due to the larger size, it was thus necessary to remove a section of substitutional drawbars (about 1.7 m in length) when the caisson penetrated to a depth of 1.7 m. Simultaneously, the upper and lower drawbars were manually connected. The above operations were repeated until the specified penetration depth was reached.

3.1. CEL approach with coupled excavation-penetration Using traditional FE method based on the Lagrangian formulation to analyze the penetration problems (i.e., large deformation problems) in geotechnical engineering frequently leads to the contact problems and FE-mesh distortion, further causing the non-convergence of the numerical simulation. Therefore, the key to ensure the calculation accuracy in this field is to adopt the appropriate numerical approach. The current LDFE analysis techniques mainly includes Arbitrary Lagrangian-Eulerian (ALE), Re-meshing and Interpolation Technique with Small Strain (RITSS) and Coupled Eulerian-Lagrangian (CEL) approach. The CEL approach combines the advantages of the Lagrangian formulation with those of the Eulerian formulation, which is well suited to solve geotechnical penetration problems involving caissons [5,24], piles [25–29], offshore structures [30–34] and cone penetration test [35–37], etc. Therefore, the numerical investigations of the whole installation process of the GDCO caissons were conducted in this study using 3D LDFE technique based on CEL approach. The CEL approach that attempts to capture the advantages both of the Lagrangian and Eulerian formulations can be used to describe two different relationships correlating the mesh and time. The Lagrangian formulation describes the motion of the continuum as a function of material coordinates and time. Lagrangian mesh nodes move together with materials in the process of calculation. Thus, the kinematic continuum interface could be precisely specified and tracked in this formulation, which is widely used in the mechanical response analyses of the solid structures using the traditional FE method. However, the deformed element with the larger deformation during the simulation might lead to the mesh distortion. Contrary to the Lagrangian formulation, the Eulerian formulation describes the motion of the continuum as a function of spatial coordinates and time. The elements that cannot be deformed are not affected by the movement of the materials since the mesh nodes are fixed in the materials. Simultaneously, undeformed elements can track the flow of materials within the Eulerian mesh to capture the motion of continuum. Obviously, the advantage of Eulerian mesh is that the material can flow through the mesh in the case

Note Anchor nuts; Piercing jacks; Working drawbars; Substitutional drawbars; Reaction devices; Cast-in-place piles; caisson walls; Bracket; Counterweight steel plate; Suspension centre; Symmetry axis. Fig. 3. Detailed operational process of vertical jacking method for GDCO caisson: (a) Plane view; (b) Installation of drawbars; (c) Penetration by jacking; (d) Removing of substitutional drawbars. 4

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

of Eulerian elements are filled by void elements, i.e., EVF < 1. However, the Lagrangian domains are not allowed to be invaded by the Eulerian elements. The Eulerian elements are created independently of the contact surface since the Eulerian elements can be occupied by the Lagrangian elements. In fact, the principle of penalty contact is similar to hard pressure–overclosure behavior, which allows the small amount of Eulerian materials penetration into the Lagrangian domain. The normal contact force Fp between surfaces can be expressed as a linear function of the penetration distance dp and penalty stiffness kp :

Fp = kp dp

Note that the penalty stiffness based on a representative stiffness of the underlying elements is chosen automatically by Abaqus/Explicit for hard penalty contact, depending on the Lagrangian and Eulerian material properties. A scale factor is used to this representative stiffness to set the default penalty stiffness. Consequently, the penetration distance will typically be greater than the parent elements' elastic deformation normal to the contact interface. This scaling may affect the automatic time increment. Using a large scale factor is likely to increase the computational time required for an analysis because of the reduction in the time increment that is necessary to maintain numerical stability. Furthermore, the basic Coulomb friction model can be introduced to defines the critical shear stress (i.e., skin friction resistance, f ), at which sliding of the surfaces starts as a fraction of the contact force Fp between the surfaces (i.e., f = Rint er Fp ).The fraction Rint er is known as the friction coefficient of the interfaces. The CEL approach is well suited to investigate the penetration problem, but the function of “model change” implemented in Abaqus/ Standard cannot be used for CEL approach in the explicit mode, leading to the incapability for simple simulation of excavating process of GDCO caissons. Furthermore, most of the numerical works need to be discretized step by step, i.e., a discontinuous mechanical model with imposed boundary conditions is established. It is thus difficult to truly reflect the kinematic synchronous coupling process between penetration and excavation of GDCO caissons. To deal with these problems, the relationship between penetration depth h and calculation time T is first established by controlling penetration velocity v , that is, h = vT . The numerical relationship between the time and soil coordinates (r , z ) in excavating zone is then set up by modifying user-defined Hypoplasticity-Vumat material subroutine. Simultaneously, the field variables are defined for the strength parameter (i.e., critical internal friction angle ϕc′) and deformation parameter in HP model (i.e., parameter controlling the stiffness magnitude Ag ) that need to be modified. The specified parameter value of excavated soil zone is further defined by StateNEW function (i.e., ϕc′ = 1.0°, Ag = 1.0) to cause the failed elements of the specific zone. The above method can simulate the process of soil breaking, namely, material failure. Finally, the symmetric lateral boundary near the excavation zone is opened (i.e., vr ≠ 0 ), the failed soil would flow out of the excavation zone along the lateral velocity boundary to simulate the process of mud sucking. The kinematic synchronous coupling process between penetration and excavation of GDCO caissons can be realized by adopting the above steps. The detailed flowchart was drawn in Fig. 4. It is worth noting that the presented CEL approach with coupled excavation-penetration is also applicable and easier to implement when the soil is simulated by the material constitutive models incorporated in Abaqus commercial software such as Mohr-Coulomb model and Modified Cam-clay model. The failed materials can be simulated only by modifying the specified soil parameters in the excavation zone via modifying the Keyword files based on the Field function. Note that the soil weight and deformation parameters would affect the outflow speeds of the failed elements. If the soil weight is too small or the modified deformation parameters are too large, the failed soil might not be completely removed in specific zone. In addition, the phenomenon of obvious stress concussion could occur during the numerical simulation for the smaller soil weight, leading to the non-convergence of numerical result.

Fig. 4. Flowchart for the implementation of CEL approach with coupled excavation-penetration.

of no mesh distortion during LDFE analysis. The CEL method tracks the flow paths of the materials within the Eulerain mesh by defining the Eulerian volume fraction (EVF). Each Eulerian element is specified as a percentage, indicating that the portion of that element filled with a material. EVF = 1 represents that the Eulerian element is completely filled with the materials, while EVF = 0 describes that there is no filled materials in the mesh. The “Lagrangeplus-remap” algorithm is adopted in CEL approach to the integration of Eulerian time, and the solution is further given by explicit dynamic analysis. Note that the numerical stability can be guaranteed if the time step size Δt is lower than the critical value of Δtcrit . In each time step, the critical time step size can be represented as

Δtcrit = Le / cd

(2)

(1)

where Le is the characteristic element length and cd is the dilatational wave speed. The contact between the Eulerian domain and the Lagrangian domain is automatically identified using general contact algorithm based on penalty function. The nonlinear contact behavior can be thus captured in LDFE analyses. The Eulerian materials would be extruded by the Lagrangian structures during the penetration process, while the rest 5

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

soil constitutive model requires being able to reflect strain-dependent and path-dependent soil stiffness (cycle process of loading-unloading). The degradation in soil stiffness from very small to large strain and the incrementally non-linear behaviors of clay have been extensively in the existing studies [40,41]. These behaviors would evidently affect the accuracy of disturbance effect assessment [12]. However, these behaviors cannot be capture using conventional elasto-plastic constitutive models, such as Modified Cam-clay, wherein the admissible states and behaviors inside the model are reversible for the yield surface in stress space bounds. It is instead necessary to introduce irreversible strain within the state boundary surface due to extremely limited elastic range of clay. Thus, an advanced constitutive model with hypoplasticity concept beyond the conventional elasto-plasticity was developed to model the clay. Mašín & Herle [42] developed a basic HP model to predict the clay behavior from medium to large strain. The basic HP model was further improved by Mašín [43] via introducing the concept of inter-granular strain [44] to consider strain-dependent and path-dependent soil stiffness at small strain level. Najser et al. [45] applied the improved HP model to predict the deformation of soft clay subjected to embankment loads, and the calculated results were in reasonable agreement with the measured results. Ragni et al. [31,32] further modeled the consolidation effect of clay on the jack-up spudcan penetration using the improved HP model, and the satisfactory agreement between the numerical results and centrifuge test data was found. Wang et al. [46], Rott et al. [47] and Soomro et al. [48] illustrated the highlighted advantages of the HP clay model in calculating strain-dependent and path-dependent soil stiffness under the conditions of non-linear, inelastic and small strain. The yield surface and plastic potential surface do not need to be considered in HP model that is different from the elastic-plastic model. In addition, the elasticity and plasticity of clay are also not distinguished due to the introduced concept of strain rate. The general form of HP model can be expressed as

3.2. Geometry, mesh and boundary conditions The installation mechanism and soil deformation characteristics of GDCO caissons in undrained clay were investigated using presented CEL approach with coupled penetration-excavation incorporated in the commercial software package Abaqus/Explicit (Version 2017) [38]. The homogeneous kaolin clay and caisson of reinforced concrete were selected in this study. The geometric schematic of the GDCO caisson with the height H and radius R penetration to the specific depth h in undrained clay was shown in Fig. 5, where the thickness of caisson steining is s , the bottom width of caisson blades is s/3 and width of caisson groove is s + 0.2 m. Note that the value of s was generally constant and set to 1.5 m in this study because the rigidity of the steining is much larger than that of surrounding soils. In addition, the heights of caisson blade and groove are 2.5 m and 4.5 m, respectively; the controlling soil plugging is remained at 2.0 m during the penetration process. The axial symmetry of the circular caisson was considered to improve the computational efficiency, only 1/8 model (i.e., 45°) was established in LDFE simulation, as shown in Fig. 6. The kaolin clay domain was extended to 4R horizontally and 4H vertically to avoid the boundary effect, which could simulate a large expanse of a single layer of clay in the field. The Eulerian domain for kaolin clay was divided into two layers, i.e., the clay layer of EVF = 1 and void layer of EVF = 0 with the height of H/3. This guaranteed that the clay could be heaved and moved to the void element. The clay was discretized into 190282 eight-node Eulerian brick elements with reduced integration and hourglass control (denoted as EC3D8R in Dassault Systems), where the number of nodes is 204705 eight-node. 1744 Lagrangian brick elements with reduced integration and hourglass control (termed as C3D8R in Dassault Systems) were used to model the GDCO caisson, while the number of corresponding nodes is 2686. The fine mesh sizes, 0.025R of minimum element size for the surrounding clay and 0.02 s for the caisson penetration zone, were adopted in specific zone nearby the caisson (around 2R × 2H ) to achieve a compromise between computational effort and accuracy according to the previous studies [30,35,39]. Furthermore, the advanced user-defined HP model was used to simulate the kaolin clay; the caisson was deemed as a rigid body, and was not allowed to tilt in the process of penetration. The constant penetration velocity of 0.5 m/s (z direction) for the caisson was input. The velocity as a variable was used for controlling the initial boundary conditions of the axisymmetric model. The zero flow velocity normal to two planes of symmetry (t direction) was imposed. The bottom boundary condition was vertically constrained against flow in z direction, while the top boundary was free. The zero radial flow velocity of far-field boundary was ascribed on the curved face. Tracer Particle technique was introduced to track the movement of material nodes, realizing that quantitatively evaluation of soil deformation characteristics nearby the caisson during the penetration process, that is, capturing the ground surface settlement and radial displacement induced by the installation of GDCO caissons. This technique requires that the some parent node sets are established on the Abaqus/CAE interface. The flow paths of the initial nodes would be traced by the defined particles after the deformed soil separated from the parent nodes, which overcomes the disadvantage of incapability of outputting the material displacement for CEL approach. A series of tracer particle sets for specified nodes located on the ground surface and deep clay (d/ H = 1/6, 1/3, 1/2) were defined in this study to capture the surface settlement and radial displacement.

σ̇ = fs (L: ε ̇ + fd N ∥ε∥̇ )

(3)

where σ̇ and ε ̇ represent the Jaumann stress rate tensor and strain rate tensor, respectively. L and N are fourth-order and second-order tensors, fs and fd are scalar factors describing the effect of barotropy and pyknotropy. The stiffness prediction of clay is determined by the tensor L , while the strength and general asymptotic response are governed by the combination of tensor L and N . Earlier HP models, such as those presented by Von Wolffersdorff [49] and Mašín [43], were not allowed to do any modification for tensor L ; otherwise undesirable prediction of asymptotic states might occur in the model. Mašín [50] proposed an approach by introducing the asymptotic state boundary surface independently from tensors to overcome this hypoplasticity limitation.

3.3. HP constitutive model and model parameters GDCOC caisson installation is a kinematic and repeated process with synchronous and coupled penetration-excavation. The soil around the caisson blades is repeatedly subjected to compaction (shear loading), unloading caused by excavation and stress relaxation effect, resulting in the extremely complicated stress mechanism. Therefore, the adopted

Fig. 5. Problem definition under the axisymmetric condition. 6

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

Fig. 6. Numerical model for CEL analysis of GDCO caisson.

intersection was allowed. The friction coefficient Rint er of the caissonsoil interface was set to 0.40 by referring to the pile-soil contact [27,53]. Note that the value of friction coefficient of the caisson-soil interface is closely related to the soil behaviors, caisson materials and auxiliary measures for the caisson penetration.

The feasibility of this approach was then validated by presenting a simple and hypoplastic equivalent of the Modified Cam-clay model. Mašín [51] developed an advanced HP clay model based on this approach, which was adopted in the present work as an updated version of a user subroutine in explicit scheme by combining UMAT with VUMAT interface [52]. The basic HP model requires five parameters: ϕc′, N , λ∗, κ ∗ and ν . N , λ∗ and κ ∗ represent the parameter expressing the compressibility of clay in the plane of ln(1 + e ) -ln(p′ ) . Model parameters N and λ∗ denote the position and slope of the isotropic normal compression line, respectively. Parameter κ ∗ controls the slope of the isotropic unloading line in the same plane of ln(1 + e ) -ln(p′ ) . ϕc′ is the critical state friction angle, which is identical to that of soil model based on any other critical state. The parameter μ denotes the soil stiffness at medium strain to large strain. To predict the small strain behavior of clay, another set of parameters related to the concept of inter-granular strain was required, namely R e , βr , χ , mrat , Ag and ng . The parameter R e is the size of the elastic range. βr and χ are the parameter controlling the rate of degradation of the stiffness with strain. The parameter mrat is the ratio of parameter mt controlling the initial shear modulus upon 90° strain path reversal to parameter mr controlling the initial shear modulus upon 180° strain path reversal. The parameter controls the value of initial shear modulus G0 at small strain level, and the parameter is the slope of G0 − p curve. The model can be calibrated to describe the initial shear modulus G0 at small strain level:

3.4. Validations against centrifuge test data As of concern, there are no relevant tests or measured data from GDCO caissons by continuously penetration-excavation in clay, as also noted in the introduction. Therefore, the numerical model based on CEL approach with coupled excavation-penetration was validated against the centrifuge tests on the open caissons by penetration-excavation in silty sand [19] and suction caissons by only jacking in kaolin clay [54]. The test was conducted on the super-fine silty sands commonly used for testing by TLJ-2 geotechnical centrifuge at Southwest Jiaotong University in China, and the properties of which was adopted in the validated model [19]. The test was performed at 90 g on an open caisson with prototype dimension of 72 m × 63 m × 45 m (i.e., length × width × height). The equivalent penetration depth of the caisson was 27 m. The thickness and height of caisson blades with 45°inclined angle were 0.9 m and 7.2 m, respectively; the equivalent width of the caisson groove was 0.9 m. For the purpose of validating the CEL approach with coupled excavation-penetration, the axisymmetric numerical model was established according to the equivalent size, and the silty sand was modeled using Mohr-Coulomb (MC) constitutive model, the detailed model parameters was listed in Table 3. Keyword files of the model were modified using Field function to redefine the model parameter (i.e., ϕ = 1°, E = 1 MPa), resulting in the soil failing. The additional details were similar to the Section 3.1. Note that the value of Rint er was 0.472 according to the results of interface friction tests [19]. Furthermore, Chen and Randolph [54] carried out a series of centrifuge tests on suction caisson in normally consolidated kaolin clay at 120 g to reveal the changes law of external skin friction of the caissons by jacking and suction respectively. The adopted caisson with the wall thickness of 0.06 m was 14.4 m long and 3.6 m in diameter in prototype dimensions. The normalized external skin friction f / γH for the caisson penetration to the specified depth from the CEL analysis was compared with the theoretical results by the current calculation methods and centrifuge test data in Fig. 7a. It can be found from the centrifuge test data

ng

p G0 = pr Ag ⎛⎜ ⎞⎟ p ⎝ r⎠

(4)

where pr is reference stress of 1 kPa, and p is the mean principal stress. Four out of eleven parameters defined in HP constitutive model for kaolin clay have been extensively investigated and reported. Based on these four known parameters, the other seven model parameters that control soil stiffness at medium strain to large strain (i.e., μ ) and at small strain level of the kaolin clay could be calibrated or deduced from the existing experimental data. The detailed values of model parameters and some additional physical parameters were summarized in Table 1. Apart from kaolin clay, the linear elastic constitutive model was used to simulate caissons, and the model parameters are given in Table 2. The general contact with penalty algorithm was used to simulate the interface interactions between the caisson and kaolin clay. The normal contact was defined as hard contact to ensure that no 7

Computers and Geotechnics 118 (2020) 103322 Deduced from Wang et al. [46] Data from Wang et al. [46] Deduced from Jáky [74] Data from Al-Tabbaa [75] kN/m3 – – m/s 7.4 1.15 0.54 1e−9

γ′ e K0 k

Deduced from Rott et al. [47] 5300 0.5 Ag ng

– –

Deduced from Atkinson [73] – –

Table 2 Concrete parameters adopted in 3D LDFE analyses. Description

Symbol

Value

Unit

Reference

Young’s modulus Poisson’s ratio Density

E υ ρ

35 0.3 2400

GPa – kg/m3

Data from Soomro et al. [48]

Table 3 Model parameters of silty sand and kaolin clay modeled by MC model in the validations. Description

Symbol

Silty sand

Cohesion Undrained strength Internal friction angle Poison’s ratio Unit weight Young’s modulus

c Su φ ν γ E

0.3 – 36.2 0.30 19.84 12.9

a b 1 2

a,1

Kaolin clay – 18 0 0.49 17.00 9.0

b,2

Unit kPa kPa ° – kN/m3 MPa

Drained condition. Undrained condition. Data from Zhou et al. [19]. Data from Hossain et al. [76].

Effective unit weight Initial void ratio Coefficient of earth pressure at rest Permeability

that the external skin friction for the open caisson by penetration-excavation first linearly increases to the certain value then nonlinearly decreases as the normalized embedded depth z / H increases, which is caused by the stress relaxation effect. However, for the jacking caisson without excavation, the value of f / γH increase linearly with increasing the value of z / H , to a first approximation. This indicates that the excavation activities inside the open caisson would cause the reduction in the external skin friction near the caisson blade due to stress relaxation effect. The established numerical models (v = 0.5, 1.0 m/s) using the CEL approach with coupled excavation-penetration could provide the reasonable prediction for the external skin friction, especially for the penetration velocity of v = 0.5 m/s. The coupling effect of penetrationexcavation can be well demonstrated by comparing the centrifuge results from Chen and Randolph [54]. Additionally, the code by MOHURD [55] presented that the external skin friction increases linearly to the maximum value (i.e., ultimate friction resistance of soil) for z ⩽ 5 m, and then remains at the maximum value for z > 5 m. The active and passive earth methods are based on the assumption that the external skin friction is the product of earth pressure and friction coefficient. The calculation results of both the code and active earth pressure method have a tendency to be unsafe, and the cases of penetration difficulties might be ignored. The passive earth pressure method is more suitable for the case of the tilted sinking of open caissons. Therefore, the whole installation process of GDCO caissons in kaolin clay would be investigated using the proposed CEL approach with coupled excavationpenetration, and the penetration velocity of the caisson was fixed at 0.5 m/s for the following numerical simulations. To further validation and show the advantages of HP model, The proposed CEL approach with coupled excavation-penetration was performed to obtain the normalized ground surface settlements (δ v / H ), which were compared with the values compiled from the published centrifuge tests [7,56] and empirical prediction methods [57,58]. Divall and Goodey [7] developed an apparatus for centrifuge modeling of a GDCO caisson construction, the short-term caisson installation induced ground settlements in kaolin clay strata was measured at an acceleration level of 100g. The prototype dimensions of GDCO caisson used were 78 m in diameter and 100 m in depth, respectively. According to this centrifuge test, the numerical model of GDCO caisson was established using the proposed CEL approach, then the whole installation process was simulated. The HP model parameters of kaolin clay can be directly adopted in light of Table 1. The undrained kaolin clay modeled as Tresca material using the elastic-perfectly plastic Mohr–Coulomb

Physical parameters

Parameter controlling the rate of degradation of the stiffness with strain Ratio of parameter mt controlling the initial shear modulus upon 90° strain path reversal to parameter mr controlling the initial shear modulus upon 180° strain path reversal Parameter controlling the stiffness magnitude Curvature of the G0 − p line

0.7 0.7

Calibrated based on Benz [72] – – 1e−5 0.1 Intergranular strain concept parameters

Initial size of the elastic range Parameter controlling the rate of degradation of the stiffness with strain

Re βr χ mrat

Data from Mašín [71] ° – – – – 27.5 0.065 0.01 0.918 0.35

λ∗ k∗ N μ slope of the isotropic normal compression line in the ln(1 + e ) − ln p plane slope of the isotropic unloading line in the ln(1 + e ) − ln p plane position of the isotropic normal compression line in the ln(1 + e ) − ln p plane shear modulus the the the the controlling controlling controlling controlling

critical state friction angle

Parameter Parameter Parameter parameter

Basic parameters

ϕc

Reference Unit Value Symbol Description Category

Table 1 Model parameters of kaolin clay adopted in 3D LDFE analyses.

F. Lai, et al.

8

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

IȖH 0.0 0.0

0.2

0.4

0.6

0.8

(a)

1.2

1.4

1.6

1.8

the obvious soil compaction effect, causing the radial expansion of the surrounding soil. Simultaneously, the soil outside the caisson and above the blades is towed by down force during the penetration process. In addition, the soil inside the caisson subjected to strongly unloading due to the excavation would result in vertical heaving, showing the obviously unloading effect. The discrepancies in soil depth and earth pressure between inside and outside the caisson increase with increasing in penetration depth. The soil around the caisson blade gradually reaches the yield strength under the action of shear force, then the local soil flows into the caisson and the stress relaxation effect occurs. Fig. 8(a–i) illustrate the evolution of plastic zone around the GDCO caisson for the different normalized radius R/H during the whole installation process. The plastic zone of surrounding soil could be divided into inside-caisson and outside-caisson, respectively. The plastic zone inside the caisson is mainly distributed within the soil plugging and the shallow soil at the base of the caisson, and the soil nearby the blades is obviously accompanied with plastic failure. The plastic zone inside the caisson decreases gradually along the direction from the blade to the symmetry axis of the caisson. The plastic zone of the soil outside the caisson induced by caisson penetration is distributed vertically and uniformly along the caisson shaft rather than expanding continuously, which is different from the cavity expansion theory caused by pile foundation penetration [59]. Furthermore, the radius of vertical plastic zone of soil outside the caisson is extremely small. This phenomenon is because the soil compaction effect is greatly weakened and transferred under the combined action of the unloading and soil relaxation effect during the installation process. In fact, the uniform soil plastic zone nearby the soil-caisson interface was caused by uniform towing due to the down forces. Accordingly, the vertical extent of the soil plastic zone inside the caisson is almost unchanged and that outside the caisson uniformly increases along the penetration depth at a given value of R/ H . The soil plastic zone inside the caisson increases along the radial direction with increasing the value of R/ H when the GDCO caisson penetrate to a specified depth, the soil near the symmetry axis of the caisson is loosened locally due to the only unloading effect, and the depth of the soil plastic zone inside the caisson is fairly limited and almost unchanged. It is concluded that the evolution of the plastic zone is not affected basically by penetration depth, because the installation of caisson is the repeated and kinematic process with the synchronous coupling between excavation and penetration. Note that the majority of soil outside the caisson is within the range of elasticity at small strain level, indicating that the significance of adopting HP model to evaluate the deformation characteristics of soil during the installation process of GDCO caisson.

2.0

CEL(v=0.5m/s) CEL(v=1.0m/s) Active earth pressure method Passive earth pressure method Normalized unit weight Code (MOHURD, 2016) Fitting equation (Zhou et al., 2019) Centrifuge test (Zhou et al., 2019) Centrifuge test (Chen & Randolph 2007)

0.1 0.2 0.3 0.4 h/H

1.0

0.5

Open caisson with penetration-excavation

0.6 0.7

Jacked-in caisson without excavation

0.8 0.9 1.0

d/H 0.0 0.0

0.3

0.6

0.9

1.2

1.5

(b) 0.1 0.2

0.4

v

/ H (%)

0.3

0.5 0.6 0.7

Centrifuge test (Right side) (Divall & Goodey, 2016) Centrifuge test (Left side) (Divall & Goodey, 2016) Centrifuge test (Lade et al.,1981) Empirical prediction (New & Bowers 1994) Empirical prediction (Gaba et al. 2003) This study (HP Model) This study (MC Model)

0.8 Fig. 7. Validations against centrifuge test data and current calculation methods: (a) External skin friction; (b) Ground surface settlements.

4.2. Deformed soil flow

failure criteria was further introduced to make a comparison with HP model. The adopted MC model parameters were shown in Table 3. Lade et al. [56] also carried out centrifuge tests on circular shafts in dry sand, the measured normalized ground surface settlement was depicted in Fig. 7b which contains the test data, numerical results and the predictions from New and Bowers [57] and Gaba et al.[58]. The variation in δ v / H along the normalized radial distance d/ H predicted by CEL approach incorporating with HP model are found to be in good agreement with the centrifuge test data and empirical predictions (see Fig. 7b). The advantages of HP model capable of capturing the nonlinear soil stiffness depended on stress path from the very small to large strain levels was demonstrated by comparing with MC model which overestimates the ground surface settlement.

Fig. 9(a–c) shows the deformed soil flow (instantaneous (result) velocity vector and contour plots) induced by the GDCO caissons penetrating to the specified depth (h/ H = 1) for the different values of R/ H . Note that the instantaneous velocity vector plots are not the same as for the actual Lagrangian material, but the representation of the deformed soil flow in the Eulerian elements [33,53,60]. The instantaneous velocity vector plots clearly indicate that: (1) For the smaller value of R/H (R/ H ⩽ 1/3), the soil outside the caisson and above excavation base is mainly subjected to towage and compaction effect, leading to soil subsidence and movement away from the caisson. The phenomenon of “ground loss” becomes more and more obvious with an increase in the value of R/ H (R/ H ⩾ 1/2 ). The instantaneous velocity vectors of the soil surrounding the caisson shaft point to the caisson. In addition to towage and soil compaction effect, the soil outside the caisson also bears the obvious unloading effect for R/ H ⩾ 1/2 . (2) The soil outside caisson and below the excavation base is mainly subjected to soil compaction and unloading effect, thus the soil heaves and moves away from the caisson. (3) It is found from both

4. GDCO caisson installation mechanism 4.1. Plastic zone The soil nearby the blades of the caisson subjected to cutting shows 9

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

Fig. 8. Evolution of plastic zone distribution around the GDCO caisson for the different normalized radius R/ H during the whole installation process.

comparing Fig. 9a with Fig. 9c, the relative extent of this domain decreases gradually with an increase in the value of R/ H , which indicates that there is a critical influence extent within the zone affected by stress relaxation effect at the base of excavation, and the corresponding critical range is equal to H/3 approximately (see Fig. 9b). The explanation

instantaneous velocity vector and contour plots that there exist significantly stress relaxation effect in the soil near the caisson blade, causing that the soil outside the caisson flows into the interior. It is also found that the domain affected by the stress relaxation effect concentrates on the base excavation for R/ H = 1/6 (see Fig. 9a). By 10

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

Fig. 9. Deformed soil flow induced by the GDCO caisson installation for the different normalized radius R/H.

1) with smooth and rough interface. Theoretically, the radial stress of the homogeneous saturated clay along the caisson should increase linearly under the action of self-weight. However, when z / H < h/ H , the obvious stress reduction due to unloading effect resulted from the excavation occurs in the deep soil along the caisson; while the value of σr / γ ′H of the soil below the caisson increases significantly, the corresponding influence range is about 0.3H . Therefore, when z / H < h/ H + 0.3H , the value of σr / γ ′H along the caisson is approximately distributed in “S” shape, that is, the value of σr / γ ′H increases and then decreases nonlinearly along the caisson in the range of z / H < h/ H + 0.3H during the installation process. Furthermore, this trend is more obvious for the larger value of R/ H . Also, the phenomenon of principal stress rotation might occur in the deep soil subjected to compaction and unloading effect along the caisson, i.e., the value of σr / γ ′H around the smooth interface is larger than that around the rough interface. At a given value of h/ H , the value of σr / γ ′H in the soil at the specified depth increases basically with an increase in the value of R/ H for z / H < h/ H + 0.3H , but this trend is contrary to the range of z / H ⩾ h/ H + 0.3H . In fact, the installation of GDCO caisson is extremely complicated process with synchronous coupling between the penetration and the excavation. It is therefore difficult to accurately evaluate the quantitative relationship correlating the soil compaction, unloading and stress relaxation effect. In the initial stage of caisson installation, the radial stress of the shallow soil around the caisson is firstly subjected to the radial expansion induced by the soil compaction effect, and the radial compressive stress increases. Simultaneously, towage action on the soil due to penetration is also stronger, resulting in an increase of vertical shear stress of the soil, the radial stress further increases. However, the unloading effect due to the excavation appears gradually with increasing the penetration depth, resulting in a rapid reduction in the radial compressive stress of soil above the caisson blade. Therefore, it is quite difficult to quantitatively evaluate the influence of various stress mechanisms on the soil around the caisson under the different degrees of unloading, compaction and stress relaxation effects.

of stress relaxation phenomenon would be further indicated in the following vertical stress contour plots. (4) There is also noticeable unloading effect in the soil inside the caisson due to the excavation at the base of the caisson, and the upheaval deformation occurs in the soil inside the caisson. Note that this phenomenon was not described in too much detail in this paper because it was similar to that of foundation pits.

4.3. Stress distribution 4.3.1. Radial stress The radial stress state of the soil around the caisson has an essential influence on the bearing capacity of the caisson. Fig. 10(a–c) illustrate the variation in normalized radial stress σr / γ ′H developed in ground surface along the radial distance for the different normalized radius (R/ H = 1/6, 1/3, 1/2) during the installation process of GDCO caisson (h/ H = 1/3, 2/3, 1) with the smooth and rough interface. At a given value of h/ H = 1/3, the ground surface soil near the caisson is subjected to compressive stress under the action of compaction and towage, but the radial stress of the ground surface soil away from caisson is almost zero (the initial vertical stress is zero). The compressive stress of the ground surface soil near caisson (d/ H ⩽ 0.5) increases approximately in parabolic shape with increasing the value of h/ H , and the value of d/ H is about 0.2 when the compressive stress is maximum. On the contrary, the ground surface soil away from the caisson (d/ H > 0.5) is subjected to tensile stress with an increase in the value of h/ H . This is because the undrained installation technology was adopted for GDCO caisson and the kaolin clay is deemed to be incompressible. It can also be predicted from the radial stress distribution that a parabolic-settlement pattern might be formed in the ground surface soil near the caisson, while the soil away from the caisson might be slightly heaved during the installation process. This predicted phenomenon is consistent with the results of field monitoring conducted by Peng et al. [12] and Xu et al. [3]. When the value of R/ H is smaller, the absolute value of σr / γ ′H near the caisson with the smooth interface is theoretically smaller than the case of rough interface (see Fig. 10a). It is interesting that the above phenomenon is opposite with increasing the value of R/ H , namely, the absolute value of σr / γ ′H around the caisson with smooth interface is larger than the rough case for the larger value of R/ H , as shown in Fig. 10(b and c). The key cause is that the principal stress rotation resulted from the larger vertical shear stress at the rough interface induced by down-force. In other words, the soil compaction and unloading effect would be stronger for the rough interface with an increase in the value of R/ H , radial stress of ground surface is no longer principal stress in this case. Note that the main deformation modes are the vertical shearing, radial expansion and base soil flow due to stress relaxation in the case of rough interface, while the latter two deformation modes are dominant in the case of smooth interface. Fig. 11(a–c) plot the variation of the normalized radial stress σr / γ ′H of the deep soil along the caisson (d/ H = 1/6) for the different values of R/ H during the installation process of GDCO caisson (h/H = 1/3, 2/3,

4.3.2. Vertical stress Fig. 12(a–i) show the contour plots of vertical stress of the soil around the GDCO caisson with the different normalized radius (R/ H = 1/6, 1/3, 1/2) during the installation process (h/ H =1/3, 2/3, 1). It is found that the dense closed stress contours appear around the caisson blades during the penetration process, which shows that the existed phenomenon of stress concentration. The concept of “stress concentration zone” was introduced in this study according to the numerical work by Li et al. [61], as shown in Fig. 12e. In addition, the vertical stress of the soil outside the deep-buried caisson is approximately equal to that of the shallow soil, indicating that vertical stress reduction, i.e., stress relaxation effect (see Fig. 12i). The stress relaxation effect becomes more and more significant with increasing the penetration depth. At a given value of R/ H , the vertical stress increases with an increase in the value of d/ H for a certain range of soil above the 11

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

0.0

(a) h/H=1/3

Unloading effect 0.2

Penetration depth

0.4

Soil compaction effect

0.3H

0.6 R/H=1/6 (Smooth interface) R/H=1/3 (Smooth interface) R/H=1/2 (Smooth interface) R/H=1/6 (Rough interface) R/H=1/3 (Rough interface) R/H=1/2 (Rough interface)

z/H

0.8 1.0 d r

1.2 y

R

H

1.4

r h

1.6

x

1.8 z

2.0

2

0

-2

-4

-6 H

-8

r/

0.0

-10

-12

-14

(b) h/H=2/3

0.2

Unloading effect

0.4 Penetration depth

0.6

Soil compaction effect

z/H

0.8

0.3H

1.0 d r

1.2

1.8 2.0

0

-2

-4

-6

0.0

r/

r h

R/H=1/6 (Rough interface) R/H=1/3 (Rough interface) R/H=1/2 (Rough interface) R/H=1/6 (Smooth interface) R/H=1/3 (Smooth interface) R/H=1/2 (Smooth interface)

1.6

y

R

H

1.4

x

z

-8 H

-10

-12

-14

(c) h/H=3/3

0.2

d r

0.4

Unloading effect

y

R

H

r h

0.6

x

z/H

0.8 Penetration depth

1.0

Soil compaction effect

1.2 1.4

1.8 2.0

caisson blade. Note that this is contrary to the influence of pile penetration on the stress distribution described by Zhou et al. [19], indicating that the stress relaxation effect of soil around the caisson is more obvious than soil compaction effect during the installation process of GDCO caisson. Furthermore, the larger the value of R/ H is, the denser the stress contours of soil outside the caisson are, and the more obvious the stress relaxation effect is. It is noted that the “passive concave arch” [62,63] is found in the domain from soil plugging to the

0.3H

R/H=1/6 (Smooth interface) R/H=1/3 (Smooth interface) R/H=1/2 (Smooth interface) R/H=1/6 (Rough interface) R/H=1/3 (Rough interface) R/H=1/2 (Rough interface)

1.6

Fig. 10. Variation in normalized radial stress σr / γ ′H along the normalized radial distance d/ H to the GDCO caisson with smooth and rough interface for (a) R/ H = 1/6 ; (b) R/ H = 1/3; (c) R/ H = 1/2 .

z

0

-1

-2

-3

-4

-5

-6

r/

H

-7

-8

-9

-10 -11 -12

Fig. 11. Variation in normalized radial stress σr / γ ′H developed in deep soil along the caisson shaft with smooth and rough interface for (a)h/ H = 1/3; (b) h/ H = 2/3; (c) h/ H = 3/3.

12

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

4.0 3.5 3.0

R/H=1/6 (Smooth interface) R/H=1/3 (Smooth interface) R/H=1/2 (Smooth interface) R/H=1/6 (Rough interface) R/H=1/3 (Rough interface) R/H=1/2 (Rough interface) Fitting line (Smooth interface) Fitting line (Rough interface)

d r y

R

H

r h

F/ HA

2.5 2.0

x

z

1.5

increase in concave shape

1.0 0.5 0.0 0.0

0.1

0.2

0.3

0.4

0.5 h/H

0.6

0.7

0.8

0.9

1.0

Fig. 13. Variation in normalized penetration resistance F / γ ′HA of GDCO caisson shaft with smooth and rough interface for (a) R/ H = 1/6 ; (b)R/ H = 1/3; (c) R/ H = 1/2 .

4.4. Penetration resistance The variation in normalized penetration resistance F / γ ′HA with the different normalized radius (R/ H = 1/6, 1/3, 1/2) of GDCO caisson for the smooth and rough interface was sketched in Fig. 13, where the parameter A represents the cross-section area of the caisson above the blade. The value of F / γ ′HA increases approximately in a concave curve with increasing the value of h/ H for the given value of R/ H . The rate of increase in the value of F / γ ′HA is more sensitive for the larger value of R/ H due to the more significant soil compaction effect. The penetration resistance of GDCO caisson can be divided into two parts, namely, the end-bearing resistance of the caisson blade edge and skin friction resistance of caisson shaft. The end-bearing resistance of the caisson blade edge depended on ultimate bearing capacity of the base soil below the blade is constant approximately since the excavation work for the homogeneous soil inside the GDCO caisson is accompanied in the whole installation process. The total skin friction resistance of the caisson shaft yet increases with increasing the penetration depth, leading to the further increase of the value of F / γ ′HA . Therefore, the above increase trend in the concave curve of penetration resistance is similar to the given variation law of outside shaft resistance of open-ended pile (corresponding to skin friction for caisson) using discrete element method by Li et al. [61], but not the same as that of convex curve of total penetration resistance of piles [27,36], spudcans [30,64] and CPT [65,66]. Additionally, the significant discrepancy in F / γ ′HA can be found for the smooth and rough interfaces. This further shows the significant effect of the skin friction of the caisson shaft on the total penetration resistance. It should be emphasized that investigating the effect of different values of Rint er on the total penetration resistance and surrounding ground movements is desired, and many parametric studies are required in future for such purpose.

Fig. 12. Contour plots of vertical stress around the GDCO caisson for the different normalized radius R/ H during the whole installation process

soil below the caisson blade due to the favored reorientation of major principal stress (vertical stress) to resist the upward pushing force. The passive concave arch is supported by the stress concentration zone below the caisson blade which is corresponding to the triangle zone near the pile tip plotted by Li et al. [61]. This is explained by the fact that the shear stress of caisson-soil interface prevents the formation of major principal stress along the passive arch. It is also found in Fig. 12 that the vertical stress trajectory within the soil plugging inside the caisson gradually tends to flatten with increasing the value of R/ H similar to the aspect ratio of trapdoor, then the phenomenon “passive concave arch” would disappear gradually.

5. Soil deformation characteristics 5.1. Ground surface settlement The installation of GDCO caisson would result in the ground movements including the ground surface settlement and radial displacement along the caisson and disturbance to adjacent buildings and underground pipelines. The ground surface settlement is the key factor endangering the surrounding environment. It is of great significance to investigate the values, influence extents, distribution patterns and 13

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

maximums of ground surface settlement for evaluating the environmental effect during the installation process of GDCO caisson. Fig. 14(a–c) show the distribution of the normalized ground surface settlement δ v / H along radial distance induced by the installation of GDCO caisson for different values of h/ H = 0.2, 0.4, 0.6, 0.8, 1.0, respectively. Three values of normalized caisson radius (R/ H = 1/6, 1/3, 1/2) are considered in the analysis for a given value of Rint er = 0.4 . It is found that the value of δ v / H first increases then decreases rapidly and eventually approaches to zero as the value of d/ H increases. As expected, the pattern of ground surface settlement around the caisson is in approximately parabolic shape. The corresponding normalized radial distance to the caisson for the maximum value of δ v / H is in the range of 0.2 < d/ H < 0.3, not near the caisson-soil interface. This is consistent with the ground surface settlement caused by the excavation proposed by Heish and Ou [67] and Kung et al. [68]. In the early stage of the caisson installation, the surface soil away from the caisson is slightly heaved, which is mainly due to the action of tensile stress, the detailed explanation was given in Section 4.3.1. In addition, at a given value of R/H, the value of δ v / H gradually increases with increasing the value of h/ H for a constant value of d/ H due to the larger down-force, thus the bound of surface settlement gradually moves down. Fig. 15 further summarizes the variation in maximum normalized ground surface settlement δ vm/ H around the GDCO caisson with the different value of R/ H during the installation process. It can be clearly found that the value of δ vm/ H nonlinearly increases with increasing of the values of R/ H and h/ H . The calculation equation of the value δ vm/ H considering simultaneously penetration depth and caisson radius is obtained by the optimal nonlinear fitting, which can be expressed as

δ vm h 1.730 R 2.355 (%) = −0.023 + 0.423 ⎛ ⎞ + 0.268 ⎛ ⎞ . H H H ⎝ ⎠ ⎝ ⎠

Zone II:

δv 10(α − 1) d (10 − 3α ) d = + for 0.3 ⩽ ⩽ 1.0 δ vm 7H 7 H

(6b)

Zone III:

δv d = α for 1.0 ⩽ ⩽ 2.0 δ vm H

(6c)

Zone IV:

δv α d d =− + 2α for 2.0 ⩽ ⩽ 4.0 δ vm 2H H

(6d)

where the surface settlement factor α is depended on the value of R/ H . The relationship between R/H and α was obtained by the linear fitting -0.1

(a)R/H=1/6 Ground surface

0.0

v/H

(%)

0.1

h/H=0.2 h/H=0.4 h/H=0.6 h/H=0.8 h/H=1.0

0.2 0.3

d r y

R

H

r h

0.4

x

Maximum value 0.5 z

0.6 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

d/H

-0.1

(b)R/H=1/3 Ground surface

0.0

(5) 0.1

Zone I:

δv d = 1 for 0 ⩽ ⩽ 0.3 δ vm H

v/H

(%)

The numerical relationship between dimensionless ground surface settlement δ v / δ vm and the normalized radial distance d/ H to the caisson was established in Fig. 16 to examine the ground surface settlement pattern induced by the installation of GDCO caisson. Furthermore, extensive field monitoring data was gathered, including the ground surface settlement cause by the deep cylindrical excavations [69], rectangular pneumatic caisson [12] and jacked open caisson [3]. The some typical ground surface settlement envelops induced by the excavation were also depicted in Fig. 16. The numerical results are larger than field monitoring data due to the caisson with the obvious towage compared with the excavation and the neglectful auxiliary measures of mud lubrication in numerical study. The bilinear settlement distribution bound was proposed for the for excavations in soft to medium clay by Clough and O’Rourke [70], and the influence extent of settlement was further divided into the maximum settlement and transition zone. The trilinearrelationship between δ v / δ vm and d/ H by the average measurement of the excavations in the soft soil was plotted in Fig. 16 by Hsieh and Ou [67], and the concepts of the primary influence and secondary influence zone was also introduced. It was considered that the value of d/ H corresponding to the maximum value of δ v / δ vm is 0.5 according to extensive engineering cases in the works by Kung et al. [68]. The fine zones of the surface settlement induced by the GDCO caisson were presented in this study based on the above and numerical results. The primary influence zone was denoted as Zone I (0 ⩽ d/ H ⩽ 0.3), the secondary influence zone was defined as Zone II (0.3 ⩽ d/ H ⩽ 1.0 ), the slight influence zone was represented as Zone III (1.0 ⩽ d/ H ⩽ 2.0 ) and the possible influence zone was abbreviated as Zone IV (2.0 ⩽ d/ H ⩽ 4.0 ).The four-linear settlement envelopes in the multilevel trapezoid shape were further given by considering the influence of GDCO caisson radius, and the expressions are as follows:

0.2

h/H=0.2 h/H=0.4 h/H=0.6 h/H=0.8 h/H=1.0

0.3 0.4

d r y

R

H

r h x

0.5

Maximum value z

0.6 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

d/H

-0.1

(c)R/H=1/2 Ground surface

0.0 0.1

v/H

(%)

0.2 0.3

h/H=0.2 h/H=0.4 h/H=0.6 h/H=0.8 h/H=1.0

0.4 0.5

Maximum value 0.6 0.0

0.2

0.4

d r y

R

H

r h x

z

0.6

0.8

1.0

1.2

d/H

Fig. 14. Variation in normalized ground surface settlement δ v / H along the normalized radial distance d/ H to the GDCO caisson during the whole installation process for (a) R/ H = 1/6 ; (b) R/ H = 1/3; (c) R/ H = 1/2 .

(6a)

14

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

are more significant for the larger values of R/ H and h/ H , indicating that the more obvious soil compaction and unloading effect. For a given value of d/ H = 1/6, the inflection points of the radial displacement curve of the soil increases from two to three with increasing the values of R/ H and h/ H , and the top-down displacement mode of soil evolves from “inner -outer convexes” to “inner-outer-inner convexes”. This is mainly because the obvious movement trend toward the caisson of deep soil below the blade due to the stronger unloading effect. For the value of d/ H = 1/3, the deep soil mainly shows the soil compaction effect. The unloading effect is more and more noticeable with increasing the excavation depth or width, especially for the soil below the caisson blades. The inflection points increases from one to two with increasing the values of R/ H and h/ H , thus the top-down displacement mode evolves from “outer convex” to “outer-inner convexes”. However, the radial displacement mode of deep soil along the caisson shaft is the single bulging with a convex shape for the value of d/ H = 1/2 because of the weaker unloading effect. It can be found in Fig. 17a that the value of δr / H is more than zero for R/ H = 1/6 and h/ H = 0.2 , showing that the GDCO caisson is mainly subjected to the compaction effect in the early stage of installation. When R/ H = 1/6 and h/ H = 1.0 , the value of δh/ H is basically less than zero (see Fig. 17e), which illustrates that the unloading effect is stronger with an increase in excavation depth. The value of radial displacement of the soil near the blade edge with the trend of moving away from the caisson (outer convex shape) is yet less than zero, it is thus concluded that the radial displacement mode of the soil around the caisson mainly shows unloading effect. It is also found from the comparison to Figs. 17–19 that the rate of variation in δr / H is more sensitive for the larger values of R/ H and h/ H .

Fig. 15. Variation in maximum normalized ground surface settlement δ vm/ H with the normalized penetration depth h/ H for the different normalized radius R/H .

6. Discussion The CEL approach with coupled excavation-penetration was first introduced to investigate the installation process of GDCO caisson in undrained clay. Tracer Particle technique was then used to capture the ground movements. However, there are some deficiencies in this study due to the limitation of calculation time and efficiency. Noted that the response of HP model parameters (e.g., Ag and ϕc ), thickness of caisson shaft and controlled height of soil plugging on soil behaviors were ignored in numerical simulation. General contact for caisson-soil interface was used in Abaqus/CEL, only the two extreme situations (rough and smooth) were used to investigate the installation mechanism, and the nonlinear behaviors of caisson-soil interface have not been fully taken into account. Furthermore, only a constant value of Rinter = 0.4 was adopted in the analysis of soil deformation characteristics, and the effect of different friction coefficients of interface was ignored. The GDCO installation mechanisms and induced ground movements in multi-layer soils also needs to be further investigated by experimental, numerical and analytical methods. However, the conducted numerical simulation provides a basis for performing the more sophisticated analyses considering nonlinear behaviors of the caisson-soil interface, soil properties and caisson geometry in the future.

Fig. 16. The proposed pattern and prediction of ground surface settlement induced by the GDCO caisson installation for different normalized radius R/ H .

according the numerical results, as shown in Table 4. The corresponding equation could be expressed as:

α = 0.169 + 0.255

R for R/ H ⩾ 0.167 H

(7)

5.2. Radial displacement Figs. 17–19 show respectively the variation in normalized radial displacement δr / H along the caisson shaft with three values of the normalized radial distance to the caisson (d/ H =1/6, 1/3, 1/2) for h/ H = 0.2, 0.4, 0.6, 0.8 and 1.0. Three values of normalized radius of the caisson (R/ H =1/6, 1/3, 1/2) were compared in the numerical simulation. The soil outside the caisson above the blade (z / H < h/ H ) moves toward the caisson under the action of unloading effect during the caisson installation process. A certain depth range of h/ H ⩽ z / H < h/ H + 0.3H of soil outside the caisson below the blade moves away from the caisson due to the soil compaction effect. The soil is mainly subjected to the unloading effect for z / H ⩾ h/ H + 0.3H , namely, the deformation mode of the soil is moving toward the caisson. Note that the above deformation modes for soil at the different depth

7. Concluding remarks A CEL approach with coupled excavation-penetration was first Table 4 Numerical relationship between normalized radius and settlement factor.

15

Normalized radius, R/ H

Settlement factor, α

Fitting equation

0.167 0.333 0.500

0.215 0.247 0.300

α = 0.169 + 0.255

R H

(Coefficient of

determination = 0.98)

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

0.0

0.0

(a)h/H=0.2

0.2 0.4

0.0

(b)h/H=0.4

0.0

(c)h/H=0.6

0.0

(d)h/H=0.8

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

z/H

z/H

0.8 1.0

1.0

1.0

z/H

points

z/H

0.6

z/H

Inflection

1.0

1.0

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.6

1.8

1.8

1.8

1.8

1.6 1.8

d/H=1/6 d/H=1/3 d/H=1/2

2.0 -0.04 0.00 0.04 0.08 0.12 įr /H (%)

2.0 -0.04

0.00 0.04 įr /H (%)

2.0 -0.08 -0.04 0.00 0.04 įr /H (%)

0.08

2.0 -0.12

0.08

-0.06 0.00 įr /H (%)

(e)h/H=1.0

2.0 -0.16 -0.08 0.00 0.08 įr /H (%)

0.06

0.16

Fig. 17. The variation in normalized radial displacement δr / H along the GDCO caisson shaft with different normalized radial distance d/ H for R/ H = 1/6 during the whole installation process.

0.2H corresponding to the maximum radial compressive stress, while the normalized penetration resistance increases in concave curve during the installation process. The radial stress of the soil at a certain range of depth along the caisson shaft is approximately distributed in “S” shape under the coupling effect of unloading and compaction. The phenomenon of principal stress rotation is more obvious with an increase in the caisson radius. Furthermore, the approximate influence range of compaction effect is from the specified penetration depth to 0.3H below. (3) The pattern of ground surface settlement around the caisson induced by the installation is approximately distributed in parabolic shape. The settlement bound gradually moves down and the influence extent also enlarges as the penetration depth increases. The equation for predicting the maximum surface settlement accounting for the penetration depth and caisson radius was given, and the four-linear settlement enveloping lines considering the influence of GDCO caisson radius were also given according to the proposed fine zones based on the extensive field monitoring data and existing empirical formulas. The main top-down radial displacement mode around the caisson shaft evolves from “inner-outer convexes” to “inner-outer-inner convexes” with increasing the penetration depth and caisson radius, while that away from the caisson shaft shows the single bulging with a convex shape.

proposed to investigate the whole installation process of GDCO caisson in undrained clay modeled by a user-defined constitutive model with hypoplasticity concept. The validation, in terms of skin friction resistance and ground surface settlement, against the centrifuge test data was further conducted. The plastic zone, deformed soil flow, stress distribution and deformation parameters developed in the clay and penetration resistance were systematically studied to investigate the real installation mechanism and soil deformation characteristics for GDCO caissons. The main conclusions can be drawn as follows: (1) In the process of GDCO caisson installation, the soil inside the caisson mainly bears the unloading effect due to the excavation, and the stress relaxation effect appears near the caisson blade edge, while the soil outside the caisson is primarily subjected to the compaction and unloading effect. The plastic zone inside the caisson is distributed within the controlled soil plugging and shallow base soil under the comprehensive action of various stress mechanisms, which is primarily concentrated near the blade. The soil outside the caisson is basically in the range of elasticity at small strain level, and the radius of the plastic zone is very small. (2) The radial compressive stress of ground surface around the caisson increases approximately in parabolic shape with increasing the penetration depth, and the radial distance to the caisson is about 0.0

0.0

(a)h/H=0.2

0.2 0.4

0.0

(c)h/H=0.6

0.0

(d)h/H=0.8

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4 0.6

0.8

0.8

0.8

1.0

1.0

1.0

1.0

1.0

z/H

0.6

z/H

0.6

0.8

points

z/H

0.6

0.8 z/H

z/H

0.6

Inflection

0.0

(b)h/H=0.4

(e)h/H=1.0

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.6

1.8

1.8

1.8

1.8

2.0 -0.04 0.00 0.04 0.08 0.12 įr /H (%)

2.0 -0.08 -0.04 0.00 0.04 0.08

2.0 -0.16 -0.08 0.00 0.08 0.16 įr /H (%)

2.0 -0.24 -0.16 -0.08 0.00 0.08 įr /H (%)

1.6 1.8

d/H=1/6 d/H=1/3 d/H=1/2

2.0 -0.04 0.00 0.04 0.08 0.12 įr /H (%)

įr /H (%)

Fig. 18. The variation in normalized radial displacement δr / H along the GDCO caisson shaft with different normalized radial distance d/ H for R/ H = 1/3 during the whole installation process. 16

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

0.0

0.0

(a)h/H=0.2

0.2 0.4

0.0

(c)h/H=0.6

0.0

(d)h/H=0.8

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4 0.6

0.8

0.8

1.0

1.0

1.0

1.0

1.0

z/H

z/H

0.6

0.8

z/H

0.6

0.8

points

z/H

0.6

0.8

0.6

z/H

Inflection

0.0

(b)h/H=0.4

(e)h/H=1.0

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.6

1.8

1.8

1.8

1.8

2.0 -0.04 0.00 0.04 0.08 0.12 įr /H (%)

2.0 -0.16

2.0 -0.24 -0.16 -0.08 0.00 0.08 įr /H (%)

2.0 -0.24 -0.16 -0.08 0.00 0.08 įh/H (%)

1.6 1.8

d/H=1/6 d/H=1/3 d/H=1/2

2.0 -0.04 0.00 0.04 0.08 0.12 įr /H (%)

-0.08

0.00

įr /H (%)

0.08

Fig. 19. The variation in normalized radial displacement δr / H along the GDCO caisson shaft with different normalized radial distance d/ H for R/H = 1/2 during the whole installation process.

Declaration of Competing Interest

[17] Jiang BN, Ma JL, Zhu JL, Li MH, Li JT, Xu L. On-site monitoring of lateral pressure of ultra-deep large and subaqueous open caisson during construction. Rock Soil Mech 2019;40(4):1551–60. [in Chinese]. [18] Wang J, Liu Y, Zhang Y. Model test on sidewall friction of open caisson. Rock Soil Mech 2013;34(3):659–66. [in Chinese]. [19] Zhou HX, Ma JL, Zhang K, Luo CY, Yang B. Study on sinking resistance of large and deep caisson based on centrifugal model test. Rock Soil Mech 2019;40(10):1–8. [in Chinese]. [20] Zhao X, Xu J, Mu B, et al. Macro-and meso-scale mechanical behavior of caissons during sinking[J]. J Test Eval 2014;43(2):1–13. [21] Yan FY, Guo YC, Liu SQ. The bearing capacity analyses of soil beneath the blade of circular cassion. Adv Mater Res 2011;250–253:1794–7. [22] Wang HL, Peng FL, Tan Y. Site monitoring and development of real-time monitoring program for new pneumatic caisson construction. In: Proceedings of Geo-Frontiers 2011: Advances in Geotechnical Engineering, Geo-Institute of ASCE, Dallas, Texas; 2011. p. 182–91. [23] Luo YF, inventor; Shanghai Foundation Engineering Group Co., Ltd., assignee. Reaction system of jacked open caisson. Chinese patent CN 104032764 A. 2014 Sep 10. [in Chinese]. [24] Andresen L, Petter Jostad H, Andersen KH. Finite element analyses applied in design of foundations and anchors for offshore structures. Int J Geomech 2010;11(6):417–30. [25] Pucker T, Bienen B, Henke S. CPT based prediction of foundation penetration in siliceous sand. Appl Ocean Res 2013;41(41):9–18. [26] Hamann T, Qiu G, Grabe J. Application of a coupled Eulerian-Lagrangian approach on pile installation problems under partially drained conditions. Comput Geotech 2015;63:279–90. [27] Ko J, Jeong S, Lee JK. Large deformation FE analysis of driven steel pipe piles with soil plugging. Comput Geotech 2016;71:82–97. [28] Grabe J, Heins E. Coupled deformation–seepage analysis of dynamic capacity tests on open-ended piles in saturated sand. Aata Geotech. 2017;12(1):211–23. [29] Chen F, Lin Y, Dong Y, Li D. Numerical investigations of soil plugging effect inside large-diameter, open-ended wind turbine monopiles driven by vibratory hammers. Mar Georesour Geotechnol 2019;9:1–14. [30] Tho KK, Leung CF, Chow YK, Swaddiwudhipong S. Eulerian finite-element technique for analysis of jack-up spudcan penetration. Int J Geomech 2012;12(1):64–73. [31] Ragni R, Wang D, Mašín D, Bienen B, Cassidy MJ, Stanier SA. Numerical modelling of the effects of consolidation on jack-up spudcan penetration. Comput Geotech 2016;78:25–37. [32] Ragni R, Bienen B, Wang D, Mašín D, Cassidy MJ. Numerical modelling of the effects of consolidation on the undrained spudcan capacity under combined loading in silty clay. Comput Geotech 2017;86:33–51. [33] Jun M, Kim Y, Hossain M, Cassidy M, Hu Y, Sim J. Numerical investigation of novel spudcan shapes for easing spudcan-footprint interactions. J Geotech Geoenviron Eng 2018;144(9):04018055. [34] Li Y, Liu Y, Lee F, Goh S, Zhang X, Wu J-F. Effect of sleeves and skirts on mitigating spudcan punch-through in sand overlying normally consolidated clay. Géotechnique 2019;69(4):283–96. [35] Qiu G, Grabe J. Explicit modeling of cone and strip footing penetration under drained and undrained conditions using a visco-hypoplastic model. geotechnik 2011;34(3):205–17. [36] Wang D, Bienen B, Nazem M, Tian Y, Zheng J, Pucker T, et al. Large deformation finite element analyses in geotechnical engineering. Comput Geotech 2015;65:104–14. [37] Susila E, Hryciw RD. Large displacement FEM modelling of the cone penetration test (CPT) in normally consolidated sand. Int J Numer Anal Methods Geomech 2003;27(7):585–602.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The financial support from the National Key R&D Program of China (Grant No. 2016YFC0800201) and Fundamental Research Funds for the Central Universities (Grant No. 2242019) are gratefully acknowledged. References [1] Sun Y, Shen S, Xu Z, Xia X. Prediction of lateral displacement of soil behind the reaction wall caused by pipe jacking operation. Tunnel Undergr Space Technol 2014;40:210–7. [2] Sun Y, Su JB, Xia XH, Xu ZL. Numerical analysis of soil deformation behind the reaction wall of an open caisson induced by horizontal parallel pipe-jacking construction. Can Geotech J 2015;52(12):1–9. [3] Xu PF, Li YL, Xu W. Field measurement and analysis of influence of jacked open caisson construction on environments. Rock Soil Mech 2014;35(4):1084–94. [in Chinese]. [4] Tomlinson MJ, Boorman R. Foundation design and construction. Pearson Education; 2001. [5] Hossainm S, Lehaneb M, Hu Y, Gao Y. Soil flow mechanisms around and between stiffeners of caissons during installation in clay. Can Geotech J 2012;49:442–59. [6] Schwamb T. Performance monitoring and numerical modelling of a deep circular excavation PhD thesis Cambridge, UK: University of Cambridge; 2014. [7] Divall S, Goodey RJ. An apparatus for centrifuge modelling of a shaft construction in clay. In: Proceedings of Eurofuge2016, 3rd European Conf on Physical Modelling in Geotechnics. France: Nantes, 2016. [8] Chavda J, Dodagoudar G. Finite element modelling of extent of failure zone in c-ϕ soil at the cutting edge of open caisson, Numerical Methods in Geotechnical Engineering IX, London: Taylor & Francis Group; 2018. p. 999–1007. [9] Chavda JT, Mishra S, Dodagoudar GR. Experimental evaluation of ultimate bearing capacity of the cutting edge of an open caisson. Int J Phys Model Geo 2019:1–14. [10] Abdrabbo FM, Gaaver KE. Applications of the observational method in deep foundations. Alex Eng J 2012;51(4):269–79. [11] Abdrabbo F, Gaaver K. Challenges and uncertainties relating to open caissons. DFI J –J Deep Found Inst 2012;6(1):21–32. [12] Peng FL, Wang HL, Tan Y, Xu ZL, Li YL. Field measurements and finite-element method simulation of a tunnel shaft constructed by pneumatic caisson method in shanghai soft ground. J Geotech Geoenviron Eng 2011;137(5):516–24. [13] Peng FL, Dong YH, Wang HL, Jia JW, Li YL. Remote-control technology performance for excavation with pneumatic caisson in soft ground. Autom. Constr. 2019;105:102834. [14] Yea GG, Kim TH. Vertical cutting edge forces measured during the sinking of pneumatic caisson. Mar Georesour Geotechnol 2012;30(2):103–21. [15] Yao Q, Yang XG, Li HT. Construction technology of open caisson for oversize surge shaft in drift gravel stratum. Electr J Geotech Eng 2014;19:5725–38. [16] Chen XP, Qian PY, Zhang ZY. Study on penetration resistance distribution characteristic of sunk shaft foundation. Chin J Geotech Eng 2005;27(2):148–52. [in Chinese].

17

Computers and Geotechnics 118 (2020) 103322

F. Lai, et al.

trial tunnel. Tunnelling’94. Boston: Springer, 1994. p. 301–29. [58] Gaba A, Simpson B, Beadman D, Powrie W. Embedded retaining walls: guidance for economic design. In: Proceedings of the Institution of Civil Engineers-Geotechnical Engineering. London: CIRIA; 2003. [59] Randolph MF. Science and empiricism in pile foundation design. Géotechnique 2003;53(10):847–75. [60] Kim Y, Hossain M, Wang D, Randolph M. Numerical investigation of dynamic installation of torpedo anchors in clay. Ocean Eng 2015;108:820–32. [61] Li L, Wu W, El Naggar MH, Mei G, Liang R. DEM analysis of the sand plug behavior during the installation process of open-ended pile. Comput Geotech 2019;109:23–33. [62] Paikowsky SG, Whitman RV, Baligh MM. A new look at the phenomenon of offshore pile plugging. Mar Georesour Geotechnol 1989;8(3):213–30. [63] Paikowsky SG, Whitman RV. The effects of plugging on pile performance and design. Can Geotech J 1990;27(4):429–40. [64] Kim Y, Hossain M, Edwards D, Wong P. Penetration response of spudcans in layered sands. Appl Ocean Res 2019;82:236–44. [65] Lim YX, Tan SA, Phoon K-K. Application of press-replace method to simulate undrained cone penetration. Int J Geomech 2018;18(7):04018066. [66] Moug DM, Boulanger RW, DeJong JT, Jaeger RA. Axisymmetric simulations of cone penetration in saturated clay. J Geotech Geoenviron Eng 2019;145(4):04019008. [67] Hsieh PG, Ou CY. Shape of ground surface settlement profiles caused by excavation. Can Geotech J 1998;35(6):1004–17. [68] Kung GT, Juang CH, Hsiao EC, Hashash YM. Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays. J Geotech Geoenviron Eng 2007;133(6):731–47. [69] Tan Y, Wang D. Characteristics of a large-scale deep foundation pit excavated by the central-island technique in Shanghai soft clay. I: Bottom-up construction of the central cylindrical shaft. J Geotech Geoenviron Eng 2013;139(11):1875–93. [70] Clough GW, O'Rourke TD. Construction-induced movements of in-situ walls. In: Proceedings, design and performance of earth retaining structures, ASCE special conference, Ithaca, New York; 1990. p. 439–70. [71] Mašín D. Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotech 2013;8(5):481–96. [72] Benz T. Small-strain stiffness of soil and its numerical consequences. Ph D thesis. Stuttgart: University of Stuttgart, 2007. [73] Atkinson J. Non-linear soil stiffness in routine design. Géotechnique 2000;50(5):487–508. [74] Jaky J. The coefficient of earth pressure at rest. J Soc Hung Archit Eng 1944;7:355–8. [75] Al-Tabbaa A. Permeability and stress-strain response of speswhite kaolin. PhD Thesis. Cambridge (UK): University of Cambridge; 1988. [76] Hossain M, Hu Y, Randolph M, White D. Limiting cavity depth for spudcan foundations penetrating clay. Géotechnique 2005;55(9):679–90.

[38] Abaqus. Abaqus 2017 Documentation, SIMULA, Dassault Systemès; 2017. [39] Zheng J, Hossain MS, Wang D. Estimating Spudcan penetration resistance in stiffsoft-stiff clay. J Geotech Geoenviron Eng. 2018;144(3):04018001. [40] Atkinson J, Richardson D, Stallebrass S. Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 1990;40(4):531–40. [41] Gasparre A. Advanced laboratory characterization of London clay Ph D thesis. London, UK: University of London, Imperial College of Science, Technology and Medicine; 2005. [42] Mašín D, Herle I. State boundary surface of a hypoplastic model for clays. Comput Geotech 2005;32(6):400–10. [43] Mašín D. A hypoplastic constitutive model for clays. Int J Numer Anal Methods Geomech 2005;29(4):311–36. [44] Niemunis A, Herle I. Hypoplastic model for cohesionless soils with elastic strain range. Mech Cohesive-frictional Mater: Int J Exp Mech Cohesive-Frict Mater 1997;2(4):279–99. [45] Najser J, Mašín D, Boháč J. Numerical modelling of lumpy clay landfill. Int J Numer Anal Methods Geomech 2012;36(1):17–35. [46] Wang L, Chen K, Hong Y, Ng C. Effect of consolidation on responses of a single pile subjected to lateral soil movement. Can Geotech J 2014;52(6):769–82. [47] Rott J, Mašín D, Boháč J, Krupička M, Mohyla T. Evaluation of K0 in stiff clay by back-analysis of convergence measurements from unsupported cylindrical cavity. Aata Geotech 2015;10(6):719–33. [48] Soomro M, Ng C, Liu K, Memon N. Pile responses to side-by-side twin tunnelling in stiff clay: effects of different tunnel depths relative to pile. Comput Geotech 2017;84:101–16. [49] Von Wolffersdorff PA. A hypoplastic relation for granular materials with a predefined limit state surface. Mech Cohesive-frictional Mater: Int J Exp Mech Cohesive-Frict Mater 1996;1(3):251–71. [50] Mašín D. Hypoplastic cam-clay model. Géotechnique 2012;62(6):549–53. [51] Mašín D. Clay hypoplasticity model including stiffness anisotropy. Géotechnique 2014;64(3):232–8. [52] Gudehus G, Amorosi A, Gens A, Herle I, Kolymbas D, Mašín D, et al. The soilmodels. info project. Int J Numer Anal Methods Geomech 2008;32(12):1571–2. [53] Tho KK, Leung CF, Chow YK, Swaddiwudhipong S. Eulerian finite element simulation of spudcan–pile interaction. Can Geotech J 2013;50(6):595–608. [54] Chen W, Randolph M. External radial stress changes and axial capacity for suction caissons in soft clay. Géotechnique 2007;57(6):499–511. [55] Ministry of Housing and Urban and Rural Development of the People's Republic of China (MOHURD). Code for construction of open caisson and pneumatic caisson. Beijing: China Planning Press, 2016 [in Chinese]. [56] Lade PV, Jessberger HL, Makowski E, Jordan P. Modeling of Deep Shafts in Centrifuge Tests. In: Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering. Rotterdam: Balkema, 1981. [57] New B, Bowers K. Ground movement model validation at the Heathrow Express

18