Design and analyses of open-ended pipe piles in cohesionless soils

Abstract

Large open-ended pipe pile has been found to be advantageous for use in transportation projects. The current design method, however, is not adequately developed. To close this practice gap, this paper first summarized different design methods for open-ended pipe piles in sandy soils. A major factor for all the design codes is to properly account for the formation and effects of soil plug. The comparison indicates that there is a large variation in the base capacity evaluation among different methods due to the complex behaviors of soil plug. To close the knowledge gap, discrete element method (DEM) was used to simulate the soil plugging process and provide insight on the plugging mechanism. The simulation results show that the arching effect significantly increases the internal unit shear resistance along pipe piles. The porosity distribution and particle contact force distribution from DEM model indicate a large stress concentration occurs at the bottom of the soil plug. Besides, nearly 90% of the plug resistance is provided by the bottom half portion of the soil column. The soil-pile friction coefficient has a significant effect on the magnitude of plug resistance, with the major transition occurred for friction coefficient between 0.3 and 0.4.

Keywords

open-ended pipe pile / soil plug / DEM / base capacity

Introduction

Large open-ended pipe pile has been found to be advantageous for use in transportation projects. These piles, when properly constructed, offer superior load carrying capability to traditional ones. As they can be driven into the ground, there is no need to construct a cofferdam as required for the construction of drilled shafts. The saving in the construction cost and schedule can be substantial. The use of large open-ended pipe piles in the existing state DOT projects produces satisfactory results. With the use of large open ended pipe piles, the number of pile used for the project is significantly reduced. This, however, also means there is less amount of redundancy in the foundation design. Therefore, reliable design and quality assurance of large open ended pipe piles is crucial for the safety of bridges.

The large diameter open-ended pipe piles are widely used in the offshore engineering as well as the transportation engineering. Most of such piles are installed through driven operations. When the steel pipes are driving into the ground, soil beneath will be squeezed inside, forming the soil plug. Due to the lateral friction and squeeze effect, arch will be formed usually at the bottom of the soil plug, which will largely increase the plug resistance [ 1– 3]. Typically the compressive bearing capacity of open-ended pipe piles consist of two parts: lateral friction and lesser one of tip resistance and annulus resistance plus plug resistance [ 4].

(1) Q_c=Q_{f,c}+\min \left(Q_{tip,}\text{}\text{}{Q}_{ann}+Q_p\right).

This indicates that the plug resistance plays an important role in bearing capacity estimation. The soil plug can be classified into fully-plugged and partially-plugged using the incremental filling ratio (IFR) [ 5], which is defined as the ratio of plug length increment and pile driving increment.

(2) IFR=\frac{\Delta L_p}{\Delta L}.

Ideally we hope the pile can be fully-plugged after installation, making it as a closed-ended pile. When IFR= 0, as the pipe pile is fully-plugged, the base capacity of open-ended pile is regarded as equivalent to closed-ended pile. When IFR>0, the pipe pile is regarded as partially-plugged. The value of IFR is determined by many factors, including the soil property, relative density of sand, OCR of clay, friction coefficient of pile-soil interface, driving depth, pile diameter, etc [ 6, 7]. These factors make IFR difficult to be determined before pile installation.

Due to relatively short history in applying such type of foundation in transportation projects, experience with this type of piling in the transportation community is still limited. Most designs refer to the experience accumulated in the offshore industry [ 4, 8]. It was also found that open-ended pipe piles demonstrate unconventional static and dynamic behaviors. Experience also shows that this type of piles can’t be treated merely as a scale-up version of standard driven piles.

Extensive efforts have been made to understand the behaviors of large open-ended pipe piles. Both the in situ and laboratory measurements have been made to study the plugging mechanism [ 6, 9, 10]. Photoelastic model has been used to simulate the stress distribution in the plug [ 11]. These researches indicate that the bottom 3~4D of the soil plug provides the majority plug resistance. Randolph [ 1] introduced a one-dimensional analytical model to describe the plug resistance in sand and clay. The bottom part of soil plug is used to calculate the plug resistance while the upper part is regarded as extra loading. Numerical models are also used to understand the plugging mechanism [ 12, 13].

In this paper, different design methods for open-ended pipe piles are reviewed in both industry and academia. The design principles of different methods are compared. A discrete element method (DEM) is used to simulate the plug formation in granular materials. The DEM model can easily simulate the sand particle movements during driving and will provide an insightful understanding of soil plugging mechanism.

Summary of typical design methods for open-ended pipe piles

API design practice

American Petroleum Institute (API) Recommended Practice is a widely accepted design criterion in petroleum industry and civil engineering. It gives a basic design principle of pipe piles in offshore engineering. The unit shaft friction f (z) is determined as following:

\mathrm{for clay:}\mathrm{ }f\left(z\right)=\alpha ·S_u,

(3) \mathrm{for sand:}\mathrm{ }f\left(z\right)=\beta ·{p^{\prime }}_{\mathrm{0}}^{ }\left(z\right),

where \alpha =\mathrm{0.5}{\left({\displaystyle \frac{S_u}{{p^{\prime }}_{\mathrm{0}}^{ }\left(z\right)}}\right)}^{-\mathrm{0.5}}, for {\displaystyle \frac{S_u}{{p^{\prime }}_{\mathrm{0}}^{ }\left(z\right)}}\le \mathrm{1.0}, \alpha =\mathrm{0.5}{\left({\displaystyle \frac{S_u}{{p^{\prime }}_{\mathrm{0}}^{ }\left(z\right)}}\right)}^{-\mathrm{0.25}}, for {\displaystyle \frac{S_u}{{p^{\prime }}_{\mathrm{0}}^{ }\left(z\right)}}>\mathrm{1.0} with the constraint that \alpha \le \mathrm{1.0} ; S_u is the undrained shear strength; \beta is the dimensionless shaft friction factor ranging from 0.29 to 0.56, mainly determined by relative density and soil description; {p^{\prime }}_{\mathrm{0}}^{ }\left(z\right) is the effective stress at depth z.

The unit tip resistance is given below:

\mathrm{for clay:}\mathrm{ }q=\mathrm{9}{S}_u,

(4) \mathrm{for sand:}\mathrm{ }q=N_q·{p^{\prime }}_{\mathrm{0},tip}^{ },

where, N_q is a dimensionless factor ranging from 12 to 50, mainly determined by relative density and soil description; {p^{\prime }}_{\mathrm{0},tip}^{ } is the effective stress at pile tip.

In the design process, an inner unit shaft friction, which equals to the outer unit shaft friction, is used to determine the plug condition. If the plug resistance is larger than the tip resistance of the equivalent area, then the pile is regarded as fully plugged and the end bearing capacity is controlled by soil at the pile tip. Otherwise the sum of annulus resistance and plug resistance should be used to calculate the end bearing capacity.

FHWA method

The plug formation is greatly influenced by pile installation, like the hammer blow size, and is quite different under static and dynamic loadings. Federal Highway Administration (FHWA) provides a relatively conservative method for the bearing capacity evaluation for open-ended pipe piles. The ultimate static capacity in cohesionless soils is the lesser of plugged and unplugged values [ 14].

Q_u=f_{so}{A}_s+q_t{A}_t, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{p}\mathrm{l}\mathrm{u}\mathrm{g}\mathrm{g}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s},

(5) Q_u=f_{so}{A}_s+f_{si}{A}_{si}+q_t{A}_{ann}, \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{u}\mathrm{n}\mathrm{p}\mathrm{l}\mathrm{u}\mathrm{g}\mathrm{g}\mathrm{e}\mathrm{d} \mathrm{p}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s},

where Q_u is the ultimate capacity; f_{so} is the external unit shaft friction; q_t is the unit tip resistance; f_{si} is the internal unit shaft resistance; A_s,A_t,A_{ann} are the shaft, tip and annulus areas of the pile.

A smaller unit tip resistance q_t is used here compared with the displacement piles. For example the unit tip resistance of a fully plugged pile in clay is 4.5·S_u , 50% smaller than the API recommendation. The value of interior unit shaft resistance in the open-ended pipe pile is typically on the order of 1/3 to 1/2 the exterior unit shaft resistance, and is influenced by soil type, pile diameter, and pile shoe configuration.

For pipe piles driven into stiff clays, the static pile capacity for fully-plugged conditions is given below [ 15]:

Q_u=\mathrm{0.8}{c}_a{A}_s+\mathrm{4.5}{c}_u{A}_t,

where, Q_u is the ultimate capacity; c_a is pile adhesion; A_s is pile-soil surface area; c_u is the average undrain shear strength at the pile toe; A_t is the toe area of a plugged pile.

FinnRA method

Finnish National Road Administration (FinnRA) document Steel Pipe Piles [ 7] introduces the design considerations for open-ended pipe piles. The unit shaft and tip resistances are determined by laboratory or in situ tests. The total bearing capacity of open-ended piles is as following:

(6) Q_u={\displaystyle {\int }_{\mathrm{0}}^z\mathrm{\pi }d·f_s\text{d}z}+\eta ·A_t·q_t,

where d is external diameter of the pile; z is the pile length inside the ground; f_s is shaft friction on the external shaft; \eta is the plugging coefficient; A_t is cross section area of pile toe corresponding to equivalent closed-ended pile; q_t is tip resistance.

The plugging coefficient \eta is used to describe the soil plugging level. It is determined by the penetration ratio, i.e., driving depth divided by pile diameter, z/d.

In moraine condition: \eta =\mathrm{0.8}, if z/d = 10; In sand or gravel: \eta =\mathrm{0.8}, if z/d = 15. As z/d decreases, the plugging coefficient reduces linearly.

Chinese code

The Technical Code for Building Pile Foundations [ 16] is the most widely used pile design criterion in China. In the design of steel pipe piles, a toe plugging coefficient {\lambda }_p is introduced similar as FinnRA Method.

Q_u=\mathrm{\pi }d{\displaystyle \sum f_{so,i}·l_i+{\lambda }_p·q_t·A_t},

{\lambda }_p=\mathrm{0.16}{h}_b/d,

when

{\lambda }_p=\mathrm{0.8},

when

(7) h_b/d\ge \mathrm{5},

where {{\displaystyle l}}_i is the thickness of soil layers; {\lambda }_p is the toe plugging coefficient, for closed-ended pipe piles, {\lambda }_p=\mathrm{1.0}\mathrm{;} h_b is the penetration depth of the pile; d is the outer diameter of pipe pile.

If h_b/d\ge \mathrm{5}, the pipe pile is considered as fully plugged, and a plugging coefficient of 0.8 is used for the total bearing capacity calculation. This method gives a larger plug resistance compared with the FinnRA Method. The selection of plugging coefficient is summarized in Fig. 1.

ICP method

Imperial College Pile (ICP) method was developed based on the database including pile tests and CPT tests. This method classifies the pipe piles into plugged or unplugged mode. For driven piles in sand, if either of the following two conditions is satisfied, the pile will be regarded as fully-plugged:

or

(8)

For clay, the criterion is:

(9)

where D_{inner} is the inner diameter of pipe pile; D_r is the relative density of sand; D_{CPT} is the cone diameter; q_c is the tip resistance of CPT; P_a is the standard atmospheric pressure, 100 kPa.

The ultimate unit tip resistance in sand, corresponding to a pile head displacement of 0.1D, is determined by inner diameter of the pile d, and outer diameter of the pile D.

Plugged:

q_b=[\mathrm{1}-{(d/D)}^{\mathrm{2}}]·q_c,

Unplugged:

(10) q_b=\max [\mathrm{0.14}-\mathrm{0.25}\log D,\text{}\mathrm{0.15},\mathrm{1}-{(d/D)}^{\mathrm{2}}]·q_c.

UWA method

In University of Western Australia (UWA) method, incremental filling ratio is introduced in the estimation of tip resistance of open-ended pipe piles. IFR can directly describe the plugging mode during pile driving. The tip resistance can be calculated without the predetermination of plugged or unplugged conditions. The unit tip resistance in sand is determined as:

(11) q_b/q_c=\mathrm{0.6}-\mathrm{0.45}{(d/D)}^{\mathrm{2}}IFR,

where q_b is the unit tip resistance; q_c is the tip resistance of CPT; d is the inner diameter of the pile; D is the outer diameter of the pile.

The UWA Method provides the end bearing capacity as a whole instead of divided into annulus resistance and plug resistance like the API Method. IFR describes the plugging mode explicitly, but measurement of IFR during pile installation is a challenge.

NGI method

Norwegian Geotechnical Institute (NGI) method is based on the CPT database established by NGI. In this method, the tip resistance of the open-ended piles is taken as the smallest of the plug resistance and the tip resistance. When driven in sand, the plug resistance is calculated assuming the internal unit friction is three times larger than that of external, due to the soil arching effect. The value by NGI method is much larger than that in API and FHWA methods. The unit tip resistance in sand is calculated as:

(12) {{\displaystyle q}}_{tip}=\mathrm{0.7}·{{\displaystyle q}}_c/\left(\mathrm{1}+\mathrm{3}{{\displaystyle D}}_r^{\mathrm{2}}\right),

where {{\displaystyle q}}_{tip} is the cone tip resistance; D_r is the relative density.

Comparison of different design criteria

The discussion above covers most of current design approaches for open-ended pipe piles. These can be classified into two groups according to the consideration of soil plug: 1) annulus+ plug resistance methods, like API practice, FHWA method, and NGI method; 2) equivalent toe resistance methods, such as FinnRA method, Chinese Code, ICP method, and UWA method. Most of these methods are based on in situ pile tests, while ICP and UWA methods also depend on CPT data. Although the model test and numerical simulation have developed a lot, the current design mainly depends on empirical practice.

For API, FHWA, and NGI methods, the plug resistance and annulus resistance are calculated first, and then compared with the toe resistance at the bottom level. The smaller value is used as the total tip resistance. The process is explicit and straightforward. The major difference is how to calculate the plug resistance: in NGI method, the internal unit friction is treated three times larger than the external friction along the pile; the API method assumes the internal and external unit shaft frictions are equal; in FHWA method, the internal unit friction is 1/2~1/3 to the external unit friction, and the annulus unit resistance is also reduced.

For FinnRA and Chinese methods, the soil plug is simplified as a reduction of total tip resistance by using the plugging coefficient. This coefficient is determined by penetration-diameter ratio, z/D. Chinese code provides a larger plug resistance compared with the FinnRA method. Both of these two methods have not considered the complex of soil properties, and the assumption of linear relationship between plugging coefficient and penetration-diameter ratio, which makes it easy to utilize, may not fully describe the plug mechanism.

Both the ICP and UWA provide the bearing capacity evaluation based on CPT result. In ICP method, piles are divided into plugged or unplugged modes according to the inner diameter and soil properties. The tip resistance is proportional to cone resistance of CPT tests. In UWA method, incremental filling ratio (IFR) is introduced to describe the soil plug behavior to simply the calculating process.

A brief comparison of different pipe pile design approaches are provided in Table 1.

Analysis of soil plug using DEM method

Discrete Element Method (DEM) provides holistic simulations of inter-particle and particle structure interactions. Therefore, they are a near idea tool to understand the soil plug mechanism. In this study, the discrete element method was used to explore the plugging mechanism of soil plug for open-ended pipe piles in sand. The illustration of the DEM pile pile model is shown in Fig. 2. In DEM model, particles can have large displacements and the constitutive relationship is automatically determined based on different parameters describing the interactions among particles. In this paper, soil column of 4 m in height, 0.6 m in diameter is built to represent the soil plug in open-ended pipe piles. 20250 particles are generated with the particle diameters ranging from 3.2 to 4.8 cm, and the particle parameters were calibrated by triaxial test that achieves a modulus of 19.63MPa, Poisson Ratio of 0.252, friction angle of 31°. The parameters used in this simulation are listed in Table 2.

The bottom wall is fixed while the cylinder wall moves downwards with a velocity of 0.02m/s to simulate the pile installation process. The maximum resistance is assumed to be equal to the plug resistance. The model is shown below.

Figure 3 plots the simulated plug resistance versus pile displacement. The plug friction resistance increases linearly with the pile displacement until the peak value of 1131 kN at the displacement of 0.4 m, and then decreases to a smaller residual value around 960 kN. This relatively large friction can be explained by arching effect during driven: particles are squeezed together at the bottom of pile, leading to a large horizontal stress and consequently larger friction resistance along the inner wall of the pipe pile.

The arching effect can be explicitly verified through the monitoring of change of porosity. The initial porosity distribution is near uniform, while after the fully mobilization of arching, porosity distribution has changed significantly. As shown in Fig. 4, in the vertical direction, porosity decreases especially at the bottom due to squeezing between particles. Similarly, as shown in Fig. 5, in the horizontal direction, porosity is much larger near the pile-soil interface due to sliding along the pile wall.

Figure 6 shows the vertical displacement and vertical contact force distribution among particles in the soil plug during driven. From Fig. 6(a), it can be seen that soil particles contacting with pipe pile have a relatively high vertical displacement due to sliding. From Fig. 6(b), it can be seen that the vertical force concentrates among soil particles at the bottom of the soil plug, and sliding between particles and pile wall leads to particle rearrangement and a decrease of vertical contact forces.

To understand the shear resistance distribution along the pile, particles contacting with pipe wall are collected and the cumulative percentage curves of the plug shear resistance are plotted in Fig. 7. Three models were built with the same particle size distribution and density but different initial plug lengths of 2, 4, and 6 m. It needs to be pointed out that the lengths of soil column decreases after driven due to compaction. For plug length L = 2 m, the final length is 1.96 m. For plug length L= 6 m, the final length is only 4.75 m. This indicates the significant influence of driven length to the soil plug formation.

From Fig. 7, it can be seen that for plug length of 4 m, more than 90% of the plug resistance is provided by the bottom 2.0 m soil column. This phenomenon is similar for plug length of 2 or 6 m. The upper part of the soil column can be simplified as surcharge and has little contribution to the plug resistance.

Another influencing factor to the arching effect is the pile-soil friction coefficient, which is determined by soil properties and manufacture of piles. A sensitivity study was conducted and the result is shown in Fig. 8. The friction coefficient of pile-soil interface has a significant influence on the peak plug resistance. For plug length of 4 m, a friction coefficient of 0.5 leads to a very high plug resistance. When friction coefficient is smaller than 0.4, the peak resistance of soil plug starts to drop dramatically. The major transition happened when friction coefficient varies from 0.3 to 0.4.

Conclusion

The first part of this paper synthesized the current design approaches for open-ended pipe piles in sand. The major difference of these methods in bearing capacity estimation is how to account for the formation and contributions of soil plug. The current design methods for plug resistance can be classified into two major groups, i.e., annulus plus plug resistance methods and equivalent toe resistance methods. The behavior of soil plug needs to be further understood.

DEM was developed to analyze the soil plugging mechanism. Soil column inside pipe pile with diameter of 0.6 m and length of 4 m are built to simulate the plug formation during driven process. The following conclusions are drawn from the model simulations. 1) The arching effect greatly increases the plug resistance in sand. This can lead to the internal unit friction resistance much larger than that of external. A reduction of internal friction by 1/2–1/3 of external friction may be conservative. 2) Non-uniform soil deformation occurs inside the pipe, as demonstrated by the porosity distribution along the vertical and horizontal directions. Large soil compaction occurs at the bottom of soil plug. 3) After the soil plug is fully mobilized, 90% of the plug resistance is provided by the bottom half of soil column. 4) The pile-soil friction coefficient has a significant influence on the plug resistance. Particularly, there is a major transition in this case when friction coefficient varies from 0.3 to 0.4.

References

[1] Randolph M F, Leong E C, Houlsby G T. One-dimensional analysis of soil plugs in pipe piles. Geotechnique, 1991, 41(4): 587–598

[2] O'Neill M W, Raines R D. Load transfer for pipe piles in highly pressured dense sand. Journal of Geotechnical Engineering, 1991, 117(8): 1208–1226

[3] Lehane B M, Jardine R J. Shaft capacity of driven piles in sand: A new design approach. In: Proceedings of the 7th International conference on Behaviour of Offshore Structure. MIT, Cambridge, MA, 1994, 23–36

[4] American Petroleum Institute. ANSI/API Recommended Practice 2GEO. Geotechnical and Foundation Design Considerations, 2011, ISO 19901–4:2003

[5] Lehane B M and Gavin K G. Base resistance of jacked piles in sand.  Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(6): 0473–0480

[6] Miller G A, Lutenegger A J. Influence of pile plugging on skin friction in over-consolidated clay. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123(6): 525–533

[7] Finnish National Road Administration. Steel Pipe Piles, Helsinki, 2000, 951–726–617–0

[8] Semple S, Gemeinhardt J P. Stress history approach to analysis of soil resistance to pile driving. In: Proceedings of the Offshore Technology Conference. Houston, Texas, volume OTC 3869,  1981

[9] Paik K, Salgado R, Lee J, Kim B. Behavior of open- and closed-ended piles driven into sands. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(4): 296–306

[10] Gudavalli S R, Safaqah O, Seo H. Effect of soil plugging on axial capacity of open-ended pipe piles in sands. In: Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering. 2013, 1487–1490

[11] Dijkstra J, Broere W. Experimental investigation into plugging of open ended piles. In: Proceedings of the ASME 2009 28th International Conference on Ocean. Offshore and Arctic Engineering, 2009

[12] Randolph M F, May M, Leong E C, Hyden M, Murff J D. Soil plug response in open-ended pipe piles. Journal of Geotechnical Engineering, 1992, 118(5): 743–759

[13] Liyanapathirana D S, Deeks A J, Randolph M F. Numerical analysis of soil plug behavior inside open-ended piles during driving. International Journal for Numerical and Analytical Methods in Geomechanics, 1998, 22(4): 303–322

[14] Paikowsky S G, Whitman R V. The effects of plugging on pile performance and design. Canadian Geotechnical Journal, 1990, 27(4): 429–440

[15] Tomlinson M J. Pile Design and Construction Practice. Fourth Edition, London: E & FN Spon, 1994, 411

[16] China’s Ministry of Construction. Technical Code for Building Pile Foundations. Beijing, JG J94–2008 (in Chinese)

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