Permeable piles: An alternative to improve the performance of driven piles

Computers and Geotechnics 84 (2017) 78–87

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

Research Paper

Permeable piles: An alternative to improve the performance of driven piles Pengpeng Ni a, Sujith Mangalathu b, Guoxiong Mei c,⇑, Yanlin Zhao c a

GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, Queen’s University, Kingston, Ontario K7L 3N6, Canada School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA c Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China b

a r t i c l e

i n f o

Article history: Received 2 September 2016 Received in revised form 1 November 2016 Accepted 24 November 2016

Keywords: Finite elements Infinite elements Permeable piles Driven piles Pore water pressure Consolidation

a b s t r a c t This paper investigates the soil displacements and excess pore pressures induced by driven piles using a combined 3D finite and infinite element approach. The analyses are compared with analytical evaluations and field measurements. Consolidation analysis is conducted to illustrate the variation in pore pressure with time. A technique of drilling drainage holes on the pipe pile is proposed in this paper to accelerate the dissipation of pore pressure to improve the performance of displacement piles. It has been noticed that optimal performance of piles can be obtained by assigning openings in piles within the bottom 50% of the pile length. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Piles can be installed by driving (displacement piles) or inserting (non-displacement piles), and the stress state and the developed pore water pressure in the surrounding soil differ significantly based on the installation method. In the case of non-displacement piles, a relatively uniform stress condition is formed due to the presence of casing and drilling mud. Design of such piles relies on empirical correlations [1]. On the other hand, a great amount of uncertainty exists in the design of displacement piles, since the driving mechanism is project-specific, where the soil-pile interaction (i.e., displacements, strains and stresses) is altered by geological conditions, pile properties and installation procedures. For displacement piles, a foundation pit is often excavated prior to pile driving to minimize the radial displacement and ground heave at shallow depth, especially in soft soil layers. Pore water pressure must also be carefully controlled during the installation of displacement piles to reduce the settlement at greater depth. Empirical evaluation of displacement piles is generally carried out based on experimental evidence, either from field

⇑ Corresponding author. E-mail addresses: [email protected] (P. Ni), [email protected] (S. Mangalathu), [email protected] (G. Mei). http://dx.doi.org/10.1016/j.compgeo.2016.11.021 0266-352X/Ó 2016 Elsevier Ltd. All rights reserved.

measurements or controlled laboratory conditions. Bozozuk et al. [2] measured the soil disturbance of sensitive marine clay in an in situ pile driving project. They found that vertical heave could be at a distance as far as approximately 39 times the pile diameter (d), and the developed pore water pressure was 35–40% higher than the overburden stress during the installation, which was dissipated 8 months after completion of the project. In addition to these conservative estimations, pore pressure cells [3] and piezocones [4] had been used in full scale field tests. An influencing zone of 3d was reported, where undrained shear strength of sensitive clay changed due to excess pore pressure, but a full dissipation was observed after 25 days [3]. Field observations of Cooke et al. [5] demonstrated that ground heave occurred up to a depth of about 10d, below which the soil behaviour was governed by settlement and radial displacement. A recent field testing program provided evidence that the excess pore water pressure could be generated in a range of 15d from the pile and the radial displacement occurred within a distance of 3d [6]. Laboratory tests have been conducted to evaluate the displacement pattern around driven piles. For example, image-based geomechanics facilitated understanding of the penetration mechanism in plane-strain calibration chamber tests [7]. Centrifuge techniques were used for the analysis of heave/settlement of energy piles due to thermal loading [8]. The complexity of analysis of displacement piles lies in the unpredictability of soil deformation (i.e., ground heave at shallow

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depth and settlement at greater depth) and the pore water pressure development. The Cavity expansion method (CEM) [9] is a typical closed-form solution for the analysis of the soil-pile interaction problem. Vesic [10] proposed the CEM and Randolph and Wroth [11] initially used this method for evaluating the consolidation behaviour around a driven pile. Different derivations have been developed based on the CEM, such as stress rotation analysis [12]. An alternative approach using the strain path method has been developed by Baligh [13] for floating piles, which was further improved to predict ground movement induced by pile driving [14,15]. Load transfer function was also derived for axially loaded piles [16]. However, this type of analysis depends heavily on the choice of spring stiffness. The limitation of the spring-based approach has been identified for similar buried structures, where the use of springs calibrated for high stiffness pipelines could result in very conservative estimate of bending behaviour [17], and over- and under-estimated axial force on flexible pipes in loose [18] and dense sand [19], respectively. Numerical techniques have been used greatly to facilitate the analysis of driven piles including geometric nonlinearity, material nonlinearity, and soil-pile interaction. The source-sink technique was developed to predict ground heave [20,21]. Boundary element analysis enabled 3D coupled evaluation of vertical piles subjected to passive loading [22]. Koumoto and Kaku [23] performed 3D finite element analysis for static cone penetration into clay. Advanced modelling techniques have been proposed to tackle complex interaction behaviour between pile and soil, such as introducing 1D wave equation analysis in piles (WEAP model) for wave propagation analysis during pile driving [24], using the MEPI-2D model (a Mohr Coulomb oriented failure criterion accounts for strain softening) to evaluate installation effects for driven piles [25], formulating analysis in an updated Lagrangian framework for calculating large deformations associated with pile driving [26,27], developing a Coupled Eulerian Lagrangian (CEL) approach for simulation of pile jacking [28] and implementing Convected Particle Domain Interpolation (CPDI) based on the Material Point Method (MPM) to trace material displacement during pile driving [29]. In this paper, a 3D finite element model with infinite element boundary conditions has been developed in the Dynamic/Explicit analysis mode of ABAQUS to address large mesh distortions in the vicinity of the pile. Numerical simulation is calibrated against soil displacement responses and pore water pressures during pile driving obtained from analytical solutions and experimental measurements. The consolidation behaviour with time is also evaluated. Excess pore water pressure dissipates with time after pile installation, so that the bearing capacity of the pile can be further mobilized based on the principle of effective stress. Measures that can accelerate soil consolidation could potentially help the driven pile to reach its maximum resistance in a shorter time span. Therefore, an alternative is proposed to improve the performance of pipe piles by drilling drainage holes around the pile circumference. An extra drainage path is allowed in the lateral direction at the pile. Numerical calculations are used to evaluate the efficacy of the proposed strategy. Further parametric study has been conducted to investigate the most efficient location and ratio of permeable area on the pile.

vertical direction (major principal stress, r1), which induces the increase in the minor principal stress (r3). Additionally, pile driving causes the increase in r3 due to cavity expansion [9,11] around the pile and the variation in r1 needs to be determined. During the pile driving process, the increase in vertical stress (Dr1) due to lateral expansion (increase in horizontal stress, Dr3) may exceed the overburden stress, which causes the occurrence of ground heave. At greater depths, the induced vertical stress is less than the overburden stress, so that the soil will settle and move laterally (see Fig. 1). By drawing an analogy to an expanded cylindrical cavity, Randolph [1] suggested that the pile driving process occurs under undrained conditions. The radial displacement, dr, at final installation can be estimated as:

dr ¼ r 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2  r 20

ð1Þ

in which, the value r0 represents the pile radius and r corresponds to the distance from the pile centreline. 2.2. Pore water pressure For saturated elastic-perfectly plastic materials, pore water pressure increment can be evaluated from the Henkel equation based on cavity expansion theory [9]. The Henkel pore water parameter a can be substituted by the Skempton pore pressure coefficient A as follows:

a ¼ 0:707  ð3A  1Þ

ð2Þ

The excess pore water pressure around the pile circumference in the plastic zone (i.e., the radius of the plastic zone is pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rp ¼ r 0 E=½2ð1 þ lÞcu  as a function of pile radius r0 and soil parameters including the modulus of elasticity E, the Poisson’s ratio l, and the undrained shear strength cu) is subsequently estimated as:

  Du Rp ¼ 2 ln þ 1:73A  0:58 cu r

ð3Þ

The maximum pore pressure occurs at the soil-pile interface, where the distance from the pile r is then reduced to r0.

  Dumax E þ 1:73A  0:58 ¼ ln 2ð1 þ lÞcu cu

ð4Þ

3. Numerical method Different modelling techniques have been developed to solve the convergence problems to simulate pile driving, where excessive distortions of element mesh in the close vicinity of the pile often occur. Advanced numerical tools, such as the updated Lagrangian framework [26,27], Coupled Eulerian Lagrangian (CEL) approach [28] and Convected Particle Domain Interpolation (CPDI) method [29], are effective to provide solutions for 2D plane strain

Soil

Pile tip 2. Pile driving analysis

Driving Radial

2.1. Soil displacement A pile foundation provides resistance to support the vertical load transmitted by the superstructure. Therefore, it is a general practice to calculate the soil displacement due to loading in the

Vertical Cavity expansion Fig. 1. Displacement of the surrounding soil due to cavity expansion.

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driving problem in a subsequent section, where the pile was replaced by a UDL in this investigation. The free boundary condition was applied at the ground surface (i.e., surface 1). Elements at surfaces 2 and 3 were C3D8R and symmetric boundary condition was used. At a distance from the UDL, infinite elements (CIN3D8) were used (i.e., surfaces 4, 5 and 6). Different numerical techniques were considered, such as finite element modelling using increased model size and infinite element modelling. When the model size was 15 m, almost identical results compared to theoretical evaluations were obtained. For the model size of 5 m, although there was a small difference in the results, the computational efforts were reduced significantly. The comparison of stresses and settlements below the UDL calculated from infinite element analyses and evaluated by the closed-form solution is illustrated in Fig. 3. It can be seen from that the results from the numerical model are in perfect agreement with the theoretical solutions. For example, at a depth of 1 m, the stress and settlement evaluated by the infinite element modelling with 5 m model size lie within 2.3% and 0.5% of values calculated from the analytical solution. This demonstrated the effectiveness of the choice of model size, mesh discretization and boundary conditions for subsequent pile driving analysis.

analysis. However, the increased computational efforts in terms of time and hardware requirements hinder their application in full 3D analysis. In this paper, a powerful Dynamic/Explicit analysis in the finite element program ABAQUS has been generated to perform large displacement simulations. Its ability to model quasi-static processes has been demonstrated for pipelines subjected to differential ground motion, as long as the kinetic energy is controlled to be a small portion of internal energy [30]. 3.1. Stresses in the elastic soil mass due to surface pressure In order to analyze the pile driving problem, an adequate large soil domain and suitable boundary conditions need to be modelled. This section presents calculations for stresses and settlements within a semi-infinite, homogeneous, isotropic, weightless, elastic half-space subjected to a Uniformly Distributed Load (UDL) on the ground surface. This problem is chosen, because the closedform solution is available, against which calculations from finite element analysis can be compared. Interested readers are directed to Bowles [31] and Das [32] for further details about the soil responses using Newmark integration of the Boussinesq solution for a half-space under a point load. The width and length of rectangular surface load (a UDL of 100 kPa) were considered as 0.25 m and 0.5 m respectively. The soil had a Young’s modulus of 60 MPa and a Poisson’s ratio of 0.3. The behaviour below the UDL at depth up to 3 m was considered, because the theoretical derivations are only effective up to 5 times the UDL size [31] (i.e., 5  0.5 m = 2.5 m). Due to the symmetry of the investigated problem, only one quarter of the elastic soil and the surface load were modelled. A short parametric study has been conducted to determine the model size, where soil blocks of 5 m  5 m  5 m, of 10 m  10 m  10 m and of 15 m  15 m  15 m were simulated. The model size had a minimal influence on the results of the analyses once the ratio between the model size and the UDL size was greater than 5, being consistent with the observations for the soil-pipe interaction problem [30]. The choice of a 5 m block was used thereafter to evaluate the effects of boundary conditions. Surface load spreads within the soil to a certain distance from the UDL. Therefore, a fine mesh can be used in the vicinity of the UDL, and coarser one at a distance. The soil was characterized using 8-node linear hexahedral elements (C3D8R), while it was switched to 8-node linear infinite elements (CIN3D8) for elements at boundaries. Fig. 2 illustrates the mesh discretization for the pile

(a)

3.2. Displacements of driven piles This section presents the calibration of the pile driving model, where a discrete rigid part was employed to characterize the pile. The influence of driving on pile strength was neglected. The selected pile had a diameter of 0.6 m and an embedment length of 18 m. A smoothened treatment of the pile tip was conducted and an offset of 0.001 m was assigned between the pile centreline and the symmetric boundary of the soil, in order to facilitate the convergence of the calculation (see Fig. 4). Note that the current study used the 3D finite element mesh as given in Figs. 2 and 4 is just a schematic illustration of the modelling strategy. A porous elastic and clay plasticity model was used to represent the soil following the Modified Cam Clay constitutive relationship. The properties of the soil were determined from triaxial tests [33] and can be seen in Table 1. A model size of 24 m was used, corresponding to 40 times the pile diameter. This choice was to consider the approximate influencing range for a driven pile, which could be as far as approximately 39d [2]. Infinite elements at a far distance can also help to eliminate boundary effects. The combined finite and

(b) Pile

(c) Pile

Pile

1 1 3 2

4

3 Z

X

4

5

Z

Z

Y

Y

X

Fig. 2. Mesh discretization for the pile driving analyses.

Y

6X

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Stress below the corner of UDL

Stress below the center of UDL

(b) 0

Depth (m)

Depth (m)

(a) 0

−1

−2

−1

−2

Theoretical solution Numerical results −3

0

5

10

15

20

−3

25

0

20

Stress (kPa) Settlement below the corner of UDL

(d)

0

Depth (m)

Depth (m)

(c)

−1

−2

−3

0

0.1

40

60

80

100

Stress (kPa)

0.2

0.3

Settlement below the center of UDL 0

−1

−2

−3

0

Settlement (mm)

0.2

0.4

0.6

Settlement (mm)

Fig. 3. Comparison between calculated responses of a semi-infinite elastic half-space and numerical analyses.

Axis of symmetry

Reference point Pile element r0 = 0.25 m

Smoothened pile tip

Drainage boundaries

Depth

Radius of 0.3 m

Radius of 0.08 m Offset of 0.001 m Width Fig. 4. A schematic illustration to show the modelling strategy of pile tip and drainage conditions.

infinite element mesh developed for the analysis is illustrated in Fig. 2. The soil-pile interaction was characterized by contact elements with zero thickness. The interface friction coefficient was calculated as tan / ¼ 0:36, which fell within the range 0.2–0.4 for buried pipelines that had negligible effects on the interaction behaviour [30]. The separation between the soil and the pile was allowed in the model. A symmetric boundary condition was also applied to the pile. A displacement-controlled scheme was used to push the pile into the soil. The obtained vertical and radial displacement profiles at a distance of r = 0.5 m from the pile are presented in Fig. 5. Excessive mesh distortions occurred in the close vicinity of the pile and the choice of r = 0.5 m was to avoid the influence of relative soil-pile slippage. The positive and negative values of vertical displacement in Fig. 5a indicate ground heave and settlement respectively. The depth of ground heave reached to approximately 5 m from the ground surface, below which settlement occurred due to the vertical component of pile movement (see Fig. 1). It is interesting that the radial displacement was smaller above the depth of 5 m (see Fig. 5b), where heave governed the soil behaviour. At greater depths, soil response was dominated by the combination of settlement and radial displacement due to cavity expansion. It is consistent with the observations of a multi-column composite foundation by Abusharar et al. [34], where the upper soil experienced heave and the lower part settled.

Table 1 Modified Cam Clay model parameters of soil [33]. Effective unit weight, c0 (kN/m3)

Young’s modulus, E (MPa)

Poisson’s ratio,

Cohesion, c (kPa)

Friction angle, / (°)

Undrained shear strength, cu (kPa)

10 Logarithmic bulk modulus, j

2 Logarithmic plastic bulk modulus, k

0.35 Tensile limit

1.8 Stress ratio at critical state, M

20 Void ratio at NCL, e1

25 Hydraulic conductivity, k (m/s)

0.002

0.045

0

1.04

1.06

109

l

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(a) 0

(b) 0

2

2

4

4

Settlement Heave

6

6 8

Depth (m)

Depth (m)

8 10 12 14

10 12 14

16

16

18

18

20

20

22

22

24

−0.02

0

0.02

0.04

0.06

24

0.08

0

0.02

Vertical displacement (m)

0.04

0.06

0.08

0.1

0.12

Radial displacement (m)

Fig. 5. Displacement of the surrounding soil (r = 0.5 m): (a) vertical and (b) radial.

(b) 0.3

0

Radial displacement (m)

Depth of ground heave (m)

(a)

1 2 3 4 5 Numerical results 6

0

2

4

6

8

10

Numerical results Theoretical solution

0.25 0.2 0.15 0.1 0.05 0

12

0

2

Distance from the pile, r (m)

4

6

8

10

12

Distance from the pile, r (m)

Fig. 6. Calculated soil responses: (a) depth of ground heave and (b) radial displacement.

3.3. Pore pressure changes of driven piles The ability of the developed numerical tool to evaluate pore pressure changes during pile diving is assessed using the experimental measurements of Roy et al. [4]. Their field tests were conducted on the St. Alban site, 80 km west of Quebec City. The test pile was 7.6 m long with an outer and inner diameter of 219 mm and 203 mm, respectively. In the field test, soft soil of silty clay mixed with organics had an average water content of 80%, an undrained shear strength of 18 kPa and a coefficient of consolida-

tion of 6  103 cm2/s. Numerical analysis was carried out using a model size of 5 m (i.e., more than 20d). The measured changes in pore water pressure at 6.1 m depth [4] are compared to numerical calculations at 6 m depth in Fig. 7.

100

Pore pressure changes (%)

The numerical analyses showed a larger depth of ground heave as the distance from the pile decreased (Fig. 6a). At r = 0.5 m, the depth of ground heave was about 5.5 m. This is consistent with the suggestion of Cooke et al. [5] that heave could occur up to a depth of 10d (i.e., 6 m). At approximately r = 12 m, there was no heave at the ground surface. Fig. 6b compares the radial displacements as a function of the distance from the pile at greater depths (i.e., 15 m) obtained from numerical and analytical calculations. It can be seen that larger radial deformations occurred within a distance of 2 m from the pile, and became negligible at 12 m (i.e., 20d). Therefore, a model size of 20d is regarded to be sufficient for the influencing range during pile driving.

80 60 40 20 0 3 10

Measurements Calculations 10

4

10

5

10

6

10

7

Time (s) Fig. 7. Comparison between measured pore water pressure changes and numerical calculations.

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For short-term consolidation (less than 105 s or 1 day), the undrained behaviour was captured well as the difference between calculations and measurements was less than 6.0%. The developed numerical model slightly overestimated the field testing data for long-term consolidation (e.g., the calculated and the measured values differ by about 16.8% at 3.5  105 s or 4 days). In general, the modelling of pore pressure dissipation by the developed numerical method is satisfactory. 4. Improvement of the performance of driven piles A typical pipe pile of 10 m long with a diameter of 0.5 m is considered as a case study in the following analyses. The dissipation of pore water pressure has a significant impact on soil response and will be investigated in detail. In general, the zone of excess pore water pressure could range from 10 to 20 times the pile diameter, being consistent with the experimental evidence of about 15d [6]. A model size of 10 m was therefore selected, which corresponded to a distance of 20d from the pile. To eliminate boundary effects, a 20 m depth was modelled, which was 2 times the pile length. 4.1. Responses of driven piles Soil displacement profiles at a distance of r = 3r0 during pile driving are plotted in Fig. 8, where the influence of installation can be seen clearly. The general trend of soil deformation is similar when the pile is driven to different depths. It is interesting that the depth of ground heave did not change during the installation process. The maximum settlement occurred right above the pile tip, as well as the maximum radial displacement. Soil responses reduced to zero rapidly at greater depths below the pile tip (at approximately 15 m), which demonstrated that the model depth was sufficient. After completion of pile driving, both the vertical and radial displacements were derived at different distances from the pile. Fig. 9a illustrates that the soil near the ground surface was heaving whereas the lower part was settling. The magnitude of vertical deformation was larger at smaller distance from the pile (e.g., the maximum heave at the ground surface at r = 3r0 was about two times the value at r = 6r0). The maximum settlement was observed at the pile tip, which was also a decreasing function of the distance from the pile. Fig. 9b presents that although the radial

(a) 0

4.2. Comparing the consolidation behaviour between driven and permeable piles Due to pile driving, excess pore water pressure is developed within the surrounding soil as illustrated in Fig. 13a. The consolidation behaviour is critical, since pore pressure dissipates with

(b) 0

Settlement

2

2

Heave

4

4

6

6

Depth (m)

Depth (m)

displacements varied near the ground surface, there were no dramatic changes from 4 m to 10 m depth. Both the vertical and radial deformations reduced with depth below the pile tip and the influencing zone reached approximately at depth of 15 m (5 m or 10d below the pile). Variations of radial displacement with the distance from the pile are reported in Fig. 10. The general trend of numerical calculations is consistent with theoretical solution, where a nonlinear degradation of radial deformation can be seen. Beyond a distance of r = 1.5 m, the radial displacement was minimal and the soil could be considered to behave in the elastic range [9]. This coincides with the observation of Hwang et al. [6] that the influencing zone of radial displacement was within a distance of 3d. At the pile tip, the radial displacement was zero, which was increased initially with the distance and decreased afterwards. Note that, this mechanism cannot be captured by cavity expansion theory. Pore water pressure changes were evaluated in Fig. 11 for the installation effect during the pile driving process and the influence of the distance from the pile after completion of pile driving. The developed excess pore pressure increased with depth, and peaked near the pile tip. Due to the short time span of installation, undrained response was dominant. Suction (i.e., negative pore pressure) occurred at the ground surface and it dissipated with time. After installation, it is anticipated that larger pore pressure occurs at a smaller distance from the pile. Below the pile tip, the pore water pressure was not reduced to zero, since there was not enough time for consolidation. Comparison of pore water pressure changes estimated from analytical and numerical approaches is given in Fig. 12. The two methods provide reasonable agreement, where a nonlinear reduction of pore pressure with the distance from the pile can be observed. At approximately 7.5 m, pore pressure was reduced to a very small value, which corresponded to an influencing zone of excess pore pressure at a distance of about 15d from the pile as reported by Hwang et al. [6].

8 10 12 14 16 18 20 −0.06

8 10 12 14 16

Driving to 2.5 m Driving to 5 m Driving to 10 m −0.04

−0.02

Driving to 2.5 m Driving to 5 m Driving to 10 m

18 0

0.02

Vertical displacement (m)

0.04

20

0

0.01

0.02

0.03

Radial displacement (m)

Fig. 8. Soil displacement profile at a distance of r = 3r0 during pile driving: (a) vertical and (b) radial.

0.04

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P. Ni et al. / Computers and Geotechnics 84 (2017) 78–87

(a) 0

(b) 0 Settlement

2

2

4

4 Heave 6

Depth (m)

Depth (m)

6 8 10

8 10

12

12

14

14 r = 3r0 r = 4r0 r = 6r0

16 18 20 −0.06

−0.04

r = 3r0 r = 4r0 r = 6r0

16 18

−0.02

0

0.02

20

0.04

0

0.01

Vertical displacement (m)

0.02

0.03

0.04

Radial displacement (m)

Fig. 9. Soil displacement profile at different distance from the pile (driving to 10 m): (a) vertical and (b) radial.

time, which influences the bearing capacity of piles significantly. The average degree of consolidation, Uavg, is therefore calculated [32] using

Theoretical solution Numerical, z = 0 m Numerical, z = 3 m Numerical, z = 8 m Numerical, z = 10 m

0.25 0.2 0.15

R zh U av g ¼ 1  R 0zh 0

0.05 0 0

1

2

3

4

Distance from the pile, r (m) Fig. 10. Variation of radial displacement with distance from the pile.

(b) 0

2

2

4

4

6

6

Depth (m)

(a) 0

8 10

10 12

14

14

20 −50

0

50

100

Pore water pressure (kPa)

r = 3r 0 r = 4r0 r = 6r

16

Driving to 2.5 m Driving to 5 m Driving to 10 m

18

ð5Þ

u0 dz

8

12

16

ut dz

where u0 and ut are the initial pore water pressure and the value at any time t, respectively; and the parameter zh represents the thickness of soil layer. The integration means that the responses at all nodes in finite element analysis need to be considered. Variations of the average degree of consolidation with time are then calculated as presented in Fig. 14. The surrounding soil is compacted to a denser state (i.e., void ratio decreases) due to the vibration induced by pile driving, which may improve the performance of the pile. Based on the principle of effective stress, dissipation of excess pore pressure with time after installation will enhance the bearing capacity of the pile. Therefore, measures that

0.1

Depth (m)

Radial displacement (m)

0.3

18

0

150

20 −50

0

50

100

150

Pore water pressure (kPa)

Fig. 11. Pore water pressure profile: (a) at a distance of r = 3r0 during pile driving and (b) at different distance from the pile.

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P. Ni et al. / Computers and Geotechnics 84 (2017) 78–87

Pore water pressure (kPa)

200

(a) Drainage boundaries

Theoretical solution Numerical, z = 9 m Numerical, z = 10 m

150

(b) Drainage boundaries

Segment a Pile

100

Segment b

Pile

Segment c Segment d

50

0

0

2

4

6

8

Soil

10

Permeable area

Soil

Distance from the pile, r (m) Fig. 12. Variation of pore water pressure with distance from the pile.

Fig. 15. Drainage conditions for permeable piles.

(a)

(b) Drained water

Driving

Drainage path

Accumulation of excess pore water pressure

Drainage hole Fig. 13. Schematics of (a) normal pile and (b) permeable pile.

U imp ¼ 1 

0

Uavg (%)

20 40 60

Normal pile Permeable pile

80 100 1 10

by using an equivalent permeability near the shaft to stimulate the effect of holes that do not form a continuous drainage boundary. However, such a study is beyond the scope of current paper and further studies are needed to address this. Fig. 14 compares the computed average degree of consolidation with time from analyses of normal and permeable piles. In this investigation, the permeable area is along the full length of the pile. The effectiveness of extra drainage boundary can be seen clearly. For a specific average degree of consolation, it requires less time for the permeable pile than that for the normal pile. After completion of pile driving, the average degree of consolidation around the normal pile is lower. The consolidation curve of the permeable pile is always on the left, which indicates that this technique could potentially improve the bearing capacity of the pile. In order to better interpret the efficacy of the proposed strategy of a permeable pile, an improved average degree of consolidation, Uimp, is calculated as

10

2

10

3

10

4

10

5

10

6

10

7

Time (s) Fig. 14. Comparison of the average degree of consolidation.

can accelerate consolidation are sought to improve the ability of a normal pile to provide maximum resistance in a shorter time span. Similar to vertical drains [35], the concept of a permeable pile is proposed in this paper as an alternative to a normal pile to provide an extra drainage path. As schematically shown in Fig. 13b, drainage holes (i.e., permeable area) can be drilled around the pile circumference, so pore water pressure can dissipate through these openings. It is assumed in the current study that the pile shaft is completely permeable. The modelling can be improved further

tperm t norm

ð6Þ

where tperm and tnorm indicate the consolidation time for permeable and normal piles respectively. At different average degree of consolidation, the improved efficiencies are estimated as given in Fig. 16. The advantage of a permeable pile to accelerate pore pressure dissipation is obvious, especially at the early stage of consolidation (e.g., at Uavg = 20%, Uimp = 68%). This reduces the time required for consolidation significantly, such that the permeable pile can have a higher bearing capacity in a short time span. With the increase of the average degree of consolidation, the effect of improvement by the proposed scheme becomes less remarkable. 4.3. Parametric study of permeable piles The permeability of drainage boundaries is actually finite, but not a constant. It depends on soil properties and real-time pore water pressure. In general, with the decrease in pore pressure, the permeability reduces [11]. This explains why the beneficial effect of permeable piles is degraded with time. Further numerical analyses were conducted to evaluate the influence of various parameters on the efficacy of permeable piles, such as hydraulic conductivity, and location and ratio of permeable area. The driving process of permeable piles is the same as normal piles, where undrained behaviour is dominant. The variation of pore water pressure is dependent on pile diameter and installation

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80

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Fig. 16. The improved average degree of consolidation. Fig. 18. The influence of location of preamble area on the average degree of consolidation.

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method, which is not affected by drainage conditions too much. Therefore, it is not necessary to design piles based on the initial pore water pressure. However, piles could behave differently when they are embedded in soils with different permeability. Three groups of analyses were performed to investigate the influence of hydraulic conductivity on the average degree of consolidation. Fig. 17 shows that permeable piles can always accelerate soil consolidation compared to normal piles. For the soil around permeable piles, less time was required to reach a certain average degree of consolidation. The consolidation curve moved to the left when the hydraulic conductivity increased, which corresponded to an enhanced dissipation of pore water pressure. The influence of location of permeable area is investigated to optimize design. Fig. 15a illustrates the analyses with different segment of pile length modified as a drainage boundary (e.g., if drainage is allowed at segment a, segments b, c and d are impermeable). The results of average degree of consolidation with time are presented in Fig. 18. The consolidation curves of all four models were similar. However, the most notable effect was obtained when the drainage condition was altered at segment d, where less time was required for the surrounding soil to reach a certain level of consolidation. This is consistent with the observations from both the numerical simulations and the calibration chamber tests of Song and Voyiadjis [27], where pore pressure changed drastically at greater depths along a penetrating object. The permeable area is therefore suggested to be placed near the pile tip to improve the dissipation of pore water pressure, so that the maximum bearing capacity of the pile can be mobilized at early stages of construction.

Uavg = 40% Uavg = 60%

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The ratio of permeable area is then studied to provide an optimal solution. Fig. 15b depicts the location of openings within the bottom of the pile length, which varies from 20%, 30%, 50%, 60% to 80% of the pile length in this investigation. The improved average degree of consolidation of permeable piles compared to normal piles was calculated as a function of permeable area ratio as shown in Fig. 19. At different average degree of consolidation, the observed consolidation was increased with openings. The increase rate was dramatic when the permeable area ratio was raised from 20% to 50%, beyond which a steady state was obtained. At the early stage of consolidation, the improvement in consolidation was more apparent. For example, at Uavg = 20%, an opening of 20% provided an improved value of Uimp = 52%; an opening of 50% had a Uimp of 64%; and an opening of 80% resulted in a Uimp of 66%. The corresponding values were Uimp = 35%, 52% and 55% for an opening of 20%, 50% and 80% at Uavg = 60%, respectively. Overall, the permeable area is suggested to be placed within the bottom 50% of the pile length. 5. Conclusions

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Time (s) Fig. 17. The influence of hydraulic conductivity on the average degree of consolidation.

In this paper, the installation process of displacement piles has been studied numerically using a 3D finite element model. The soil is characterized as a Modified Cam Clay material using 8-node linear hexahedral elements (C3D8R). Theoretical derivations of stress and settlement in the elastic soil mass due to surface pressure are used to calibrate the numerical tool. A model scale of 20d is found

P. Ni et al. / Computers and Geotechnics 84 (2017) 78–87

to be adequate to minimize boundary effects. The far field boundaries are then modified using 8-node linear infinite elements (CIN3D8) to further eliminate errors associated with the modelling strategy. Considering the symmetry of the problem, a quarter pile is modelled as a discrete rigid part. The developed simulation method can address large mesh distortions during pile driving, and provide reasonable estimates of soil responses compared to analytical solutions and field measurements. The consolidation behaviour is subsequently evaluated using the calibrated numerical tool. An alternative measure that could accelerate dissipation of excess pore pressure is proposed in this paper. Drilling drainage holes (i.e., permeable openings) on the pipe pile could potentially provide an extra drainage path. Comparisons between normal and permeable piles demonstrate that soil consolidation is improved significantly when permeable piles are used, especially at the early stage of installation. A parametric study is performed to investigate the influence of parameters. A higher hydraulic conductivity within the soil is found to be beneficial to the reduction in pore pressure. The permeable area is suggested to be placed within the bottom 50% of the pile length to optimize the efficacy of the proposed scheme. Acknowledgements This work had been supported by the National Science Fund for Excellent Young Scholars (Grant No. 51322807) and the National Natural Science Foundation of China (Grant No. 51578164), and by the Ministry of Education of China through the Changjiang Scholars Program to Dr. Guoxiong Mei. References [1] Randolph M. Science and empiricism in pile foundation design. Geotechnique 2003;53(10):847–76. [2] Bozozuk M, Fellenius BH, Samson L. Soil disturbance from pile driving in sensitive clay. Can Geotech J 1978;15(3):346–61. [3] Roy M, Blanchet R, Tavenas F, Rochelle PL. Behaviour of a sensitive clay during pile driving. Can Geotech J 1981;18(1):67–85. [4] Roy M, Tremblay M, Tavenas F, Rochelle PL. Development of pore pressures in quasi-static penetration tests in sensitive clay. Can Geotech J 1982;19 (2):124–38. [5] Cooke R, Price G, Tarr K. Jacked piles in London Clay: a study of load transfer and settlement under working conditions. Geotechnique 1979;29(2):113–47. [6] Hwang J-H, Liang N, Chen C-H. Ground response during pile driving. J Geotech Geoenviron Eng 2001;127(11):939–49. [7] White D, Bolton M. Displacement and strain paths during plane-strain model pile installation in sand. Géotechnique 2004;54(6):375–97. [8] Ng C, Shi C, Gunawan A, Laloui L, Liu H. Centrifuge modelling of heating effects on energy pile performance in saturated sand. Can Geotech J 2015;52 (8):1045–57.

87

[9] Yu HS. Cavity expansion methods in geomechanics. Springer Science & Business Media; 2013. [10] Vesic AS. Expansion of cavities in infinite soil mass. J Soil Mech Found Div 1972;98(sm3). [11] Randolph MF, Wroth C. An analytical solution for the consolidation around a driven pile. Int J Numer Anal Meth Geomech 1979;3(3):217–29. [12] Salgado R, Mitchell J, Jamiolkowski M. Cavity expansion and penetration resistance in sand. J Geotech Geoenviron Eng 1997;123(4):344–54. [13] Baligh MM. Strain path method. J Geotech Eng 1985;111(9):1108–36. [14] Poulos H. Effect of pile driving on adjacent piles in clay. Can Geotech J 1994;31 (6):856–67. [15] Sagaseta C, Whittle AJ. Prediction of ground movements due to pile driving in clay. J Geotech Geoenviron Eng 2001;127(1):55–66. [16] Ni P, Song L, Mei G, Zhao Y. A generalized nonlinear softening load transfer model for axially loaded piles. Int J Geomech; 2016 [in press]. [17] Saiyar M, Ni P, Take WA, Moore ID. Response of pipelines of differing flexural stiffness to normal faulting. Géotechnique 2016;66(4):275–86. [18] Weerasekara L, Wijewickreme D. Mobilization of soil loads on buried, polyethylene natural gas pipelines subject to relative axial displacements. Can Geotech J 2008;45(9):1237–49. [19] Wijewickreme D, Karimian H, Honegger D. Response of buried steel pipelines subjected to relative axial soil movement. Can Geotech J 2009;46(7):735–52. [20] Chow Y, Teh C. A theoretical study of pile heave. Geotechnique 1990;40 (1):1–14. [21] Sagaseta C. Analysis of undrained soil deformation due to ground loss. Geotechnique 1987;37(3):301–20. [22] Xu K, Poulos H. 3-D elastic analysis of vertical piles subjected to ‘‘passive” loadings. Comput Geotech 2001;28(5):349–75. [23] Koumoto T, Kaku K. Three-dimensional analysis of static cone penetration into clay. In: Proc 2nd European symp on penetration testing; 1982. p. 635–40. [24] Masouleh SF, Fakharian K. Application of a continuum numerical model for pile driving analysis and comparison with a real case. Comput Geotech 2008;35(3):406–18. [25] Said Id, De Gennaro V, Frank R. Axisymmetric finite element analysis of pile loading tests. Comput Geotech 2009;36(1):6–19. [26] Sheng D, Eigenbrod KD, Wriggers P. Finite element analysis of pile installation using large-slip frictional contact. Comput Geotech 2005;32(1):17–26. [27] Song CR, Voyiadjis GZ. Pore pressure response of saturated soils around a penetrating object. Comput Geotech 2005;32(1):37–46. [28] Qiu G, Henke S, Grabe J. Application of a coupled Eulerian-Lagrangian approach on geomechanical problems involving large deformations. Comput Geotech 2011;38(1):30–9. [29] Hamad F. Formulation of the axisymmetric CPDI with application to pile driving in sand. Comput Geotech 2016;74:141–50. [30] Ni P, Moore ID, Take WA. Numerical modeling of normal fault-pipeline interaction and comparison with centrifuge tests. Soil Dynam Earthq Eng; 2016 [in press]. [31] Bowles J. Foundation analysis and design. New York: McGraw-Hill; 1996. [32] Das BM. Principles of foundation engineering. Pacific Grove, California: PWS PUBLISHING, Brooks/Cole Publishing Company; 1999. [33] Li T. Analysis of finite element about compacting effect of piles by considering dynamic penetration process. Yangzhou, China: Yangzhou University; 2012 [MASc thesis]. [34] Abusharar SW, Zheng J-J, Chen B-G. Finite element modeling of the consolidation behavior of multi-column supported road embankment. Comput Geotech 2009;36(4):676–85. [35] Hird C, Moseley V. Model study of seepage in smear zones around vertical drains in layered soil. Geotechnique 2000;50(1):89–97.