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Prediction of Bearing Capacity of Large Drilled Piles in Nonhomogeneous Soil by Using 3D Finite Element Method
Associate Professor, Civil & Environmental Department and Lecturer, Rajamongala Institute of Technology
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ABSTRACT
A 3D finite element analysis method for drilled piles using ABAQUS is presented. Nonlinear analysis of the model is achieved through incorporation of interface elements failure criteria, geotechnical material properties of the elements, and Newton’s method. The analysis method correlates well field load tests, empirical methods, and earlier 2D analyses. The number of expensive pile load tests required in some construction projects will be reduced due to the increased accuracy achieved with this analysis method. Interface elements are used to connect the pile and soil for skin friction and a contact pair at pile tip is used for bearing capacity.
Keywords: drilled piles, finite element analysis method, Nonhomogenous
INTRODUCTION
The study of non-linear behavior of drilled piles in non-homogeneous soil is crucial. A better understanding of the load transfer mechanism of large drilled piles is critically important for drilled pile construction. This research utilizes finite element modeling techniques to simulate an isolated large drilled pile in non-homogeneous soil. This finite element model incorporates the following simulation techniques: initial loading, ultimate bearing capacity by displacement loading, interface elements for pile-soil skin friction interaction behavior, a pile tip contact pair for both patterned stress distribution and pile tip reaction behavior. A complete understanding of the non-linear behavior of drilled piles will allow design engineers to construct efficient and substantial designs with both adequate structure strength and capacity and will result in significant cost savings.
MATERIALS AND METHODS
Historical development of caissons is found in Baker and Khan (1971)[4], Osterberg (1968)[29], and Greer (1969)[13]. According to O'Neill and Reese (1999)[28], the early development of the drilled pile in the San Antonio area was motivated by generally strong but highly expansive surface soils. Drilled piles were used to extend the load below the expanse of surface soil. According to McCleland (1996)[20], in 1950 the first drilled pile was used on a Texas State Department of Transportation (Bridge project). By the early 1970's drilled piles had become the foundation of choice in Texas.
According to O'Neill and Reese (1999)[27], in the late 1950's and early 1960's computers, analytical methods, and full scale testing programs had begun to produce a better understanding of drilled pile behavior. Extensive research began in the1960's and continued into the 1980's: see Whitaker and Cooke;(1966)[48], Reese;(1978)[33], and Kulhawy; (1989)[17]. This research resulted in improved design methods and construction procedures such that drilled shafts became regarded as a reliable foundation system for highway structures by the Texas State Department of Transportation (DOT), Federal Highway Administration (FHWA) and the Electric Power Research Institute. In 1977 the first set of design manuals for the drilled pile was produced by the FHWA. An updated design manual was published by the FHWA in 1999[27]. This dealt heavily with construction procedures and proposed simple, conservative design methods.
Construction of drilled piles in unstable soil is difficult because soil can contaminate the pile. To counteract this the excavation is filled with a drilling slurry. O'Neill and Reese (1999)[27] described that during the 1950's and 1960's it was a common practice for drilled pile contractors to make slurry on-site by mixing water with clay materials. Cross and Harth (1929)[8] obtained patents on the use of Bentonite as an slurry agent capable of gelling and suspending cuttings by the petroleum industry. Veder (1953)[42] was the first engineer to use Bentonite in construction. O'Neill and Reese (1999)[27] indicate that Bentonite, Attapulgite and Sepiolite have been used commonly in domestic drilled pile construction since the 1960's. Using a slurry mixture can cause loss of friction due to the settlement of the slurry residual and may cause the development of thick membrane of weak material at both the sides and bottom of the borehole. Nash (1974)[22] determined that the desired thickness of the residual mud cake is less than 2.5 mm. Wates and Knight (1975)[47] found that the membrane thickness varied with both time and the hydrostatic head of the slurry. Holden (1984)[15] indicats that when the slurry remained in place for a month a thick filter cake had built up and that side resistance was significantly reduced. O'Neill and Hassan (1994)[24] indicate that maintaining the slurry too long potentially reduces the ultimate side resistance by a factor of up to ten. Majano et al. (1994)[19] indicate that a polymer slurry increases the side resistance slightly, compared to mineral slurry. Without proper cleaning sediments may be trapped at the bottom of a drilled hole, and may cause the concrete in the area to be contaminated.
General load capacity prediction procedures have been investigated for several years. O'Neill and Reese (1999)[27] indicate that general approaches to the design of drilled piles have been, historically, developed in three stages. Reese and Coyle [34] in 1966 developed a method capable of predicting the load carrying-capacity and obtaining load settlement data for axially loaded piles. They correlated the ratio of oad transfer to soil shear strength and pile movement for friction piles in clay. Whitaker and Cooke (1966)[48] state that, for belled shafts, the full value of the bearing capacity factor (Nc*) equal to 9, is realized with a base movement between 10% -15% of the bell diameter, compared with 20% base movement for the straight shaft diameter.
Vesic (1967)[43] compared the theoretical results relating the variation of bearing capacity of sand (Nq*) to the soil friction angle. Vesic (1970)[44] states, "Beyond a depth of approximately twenty pile diameters both point (base) and skin (side) resistance reach nearly constant final values. These findings depart from the established concepts of linear increase of bearing capacity of deep foundations with depth". Vesic (1972)[45] proposed that the ultimate bearing capacity (qmax) of cohesive soil is equal to Nc* multiplied by the undrained shear strength (su). Vesic also detailed the meaning of the "Reduced Rigidity Index" (Irr), used for predicting the load bearing capacity of cohesionless soil. Touma and Reese (1974)[39] suggested a procedure for calculating allowable load capacity of drilled pile in sand. For pile length (L) greater than ten times the pile diameter (D) with a base moment of 25.4 mm. Klosinski (1977)[16] observed the settlement to be proportional to the shaft diameter. He recommended that pile settlement should control allowable load, stating, “{that there is a} limit{ed} state of tested pile". Meyerhof (1976)[21] suggested that the ultimate base resistance (qb) in homogeneous granular soil or cohesionless soil could be obtained from standard penetration number (N). The American Petroleum Institute, API, (1984)[1] indicates that the side resistance factor is a function of undrained shear strength (cu). The author of this paper uses this coefficient (cu) as the coefficient of pile-soil friction. Hirany and Kulhawy (1988)[14] proposed one of the most theoretically sound methods, applicable specifically to drilled piles in compression. Kulhaway and Jackson (1989)[18] reported the field test results of 105 straight-drilled shafts, 64 in tension and 41 in compression. The magnitude of the reported side resistance factor a was approximately 0.4.
Reese and O'Neill (1989)[35] proposed an alternative method to calculate the load bearing capacity of drilled piles based on their settlement. This method is currently used today. In 1990 Oonchittikul [28] studied drilled pile capacity predictions and performance in the Bangkok area. The author compiled data from more than 100 pile load tests and performed conventional analysis to determine pile capacity predictions. Four differing calculations have been performed based on the following methods: Butler & Hoy, Mazurkiewicz, Chin, and the pile load test method. The results indicate a wide range of capacity predictions, with the standard deviation ranging from 0.1% to 117%, see Fig. 1. The average relative standard deviation of calculated load capacity is 31.68% based on the data from Oonchittikul [28]. Fig. 1 details the wide range of pile capacity calculated values, obtained by conventional analysis methods.
Figure 1. Relative Standard Deviation of Pile Capacity between Test and Prediction
O'Neill and Hassan, (1994)[24] indicate that local geology and construction processes have a major influence on the performance of drilled pile shafts under load. Chen and Kulhawy (1994)[6] propose that the angle of friction can be estimated from standard penetration tests, cone penetration tests, or similar procedures, where the typical angle of internal friction of cohesionless soil ranges from 25 to 40 degrees and the typical angle of internal friction of cohesive soil ranges from 10 to 25 degrees. The American Society of Civil Engineers (1993)[2] published, "Design of Pile Foundation" as a manual for planning design and construction for the U.S. Army Corps of Engineers based on the current understanding of pile-soil-structure interaction. The author has adopted "The Corp of Engineers Method" to determine failure load of drilled piles based on slope-modulation of the load-settlement curve. International Association of Foundation Drilling (ADSC) recently published "Drilled Shaft: Construction Procedures and Design Methods" by O'Neill and Reese (1999)[27]. This manual has been used domestically by 30 states, The U.S. Department of Transportation (DOT) and The Federal Highway Administration (FHWA).
Zelada (2000)[50] has complied several modern theories and methods, these have been practiced to predict augered pile capacity in sand. The prediction of pile capacity can be classified into two methods: Theoretical and Empirical. Theoretical methods include Wright & Reese's method (1978)[49], Reese & O'Neill's method (1988)[26], Meyerhof's method (1976)[21], and Coyle & Castello's method (1981)[7]. Design engineers occasionally use more than one method to predict pile bearing capacity. The empirical method predicts the ultimate load bearing capacity of a pile through correlation of load and settlement, generation of a load-settlement curve. Methods that accomplish this are: Neely's (1991)[23], Bustamante and Gianeselli's (1981)[5], Viggiani's (1993)[46], Douglas's (1983)[12], Coyle and Castello's (1981)[7], Corp of Engineers Method, ASCE (1993)[3], and Davisson's method (1970)[10].
Three failure criteria were utilized to determine the failure load. They are as follows: the load capacity at 25 mm of pile settlement, the load capacity at 5% of pile diameter settlement and The Corps of Engineers Method [2], which considers a slope of 1T/0.01 inch (9.09 kN/0.25 mm) as a failure capacity to determine failure load for validations. The failure criteria chosen for each model was based on the same criteria as the original source of the pile load test. In general the Corps of Engineers Method was utilized.
Desai and Holloway (1972)[11] developed a unique finite element approach for an axially loaded single pile. Valliappan(1974)[39] analyzed the settlement of pile in layered soils, based on a two-dimensional axisymmetric approach, using quadrilateral isoparametric elements. The results, obtained through finite element analysis, were compared with conventionally obtained solutions and the accuracy of the finite element analysis assessed. The results obtained indicate that fininte element analysis is useful for situations of greater complexity than generally encountered in practice. Ray and Mahapatra (1976)[32] studied displacements and stress at selected points on the pile axis through utilization of a finite element model in a non-homogeneous medium. The precision of the results was limited due to a very coarse finite element pattern. Ray and Mahapatra (1976)[32] also carried out an experimental investigation, which successfully incorporated the formulation of data for finite element analysis. The results of the investigation indicate that theoretical solutions agreed reasonably with solutions obtained from experimental observations.
Ottaviani and Marchetti (1979)[30] compared distribution of vertical stress results obtained from a loading test on a bored cast-in-site pile, with those obtained from a nonlinear finite element analysis based on the geotechnical properties of the cohesive soils in which the pile was placed. They found a general agreement of results at loads below failure. Differences, however, were found at loads closer to failure. In 1991 Trochanis (39) studied the effect of non-linear soil behavior on the axial and lateral response of piles by means of a three-dimensional finite element elastic-plastic model. The model included interface elements representing slippage and pile-soil separation. The numerical results indicate that material non-linearity could significantly affect pile and soil response.
The size of the finite element model width and depth were calibrated to provide correct correlation to the pile load test data. Replicating, the previous research of Trochanis (37) a model size of 200% of pile length in depth and 100% of pile length in width were used. General soil properties were classified into five layers in the following example. The soil elements were divided into five layers by specifying different material properties for each. Axi-symmetric eight node elements (CAX8) were used to construct the pile and soil geometry with, pile elements constructed completely separate from the soil elements. Quadratic six node interface elements were used (INTER3A) at contact points between the first column of soil elements and the pile elements. See Figure 2.
Figure 2. Finite Element Model Loading Conditions
The interface element is a specialized element that bridges two separated element types and transfers only shear stress by friction. The interface element is simulated as an elasto-plastic material that behaves elastically before the yield point and behaves plastically after the yield point. The coefficient of friction and the shear strength are required to correctly simulate the interface element. The coefficient of friction can be obtained from the American Petroleum Institute (API,1984)[3], for this study the value of 0.75 is used. The shear strength of the interface element is an equivalent shear strength this was obtained based on Mohr-Coulomb's Failure Criteria (9, pp.50). The shear stress of the interface element remains constant after reaching the yield point. The equivalent shear strength of interface elements is determined according to Das (1995)[23] (pp. 498).
Three boundaries were utilized in this finite element model: the model border, model base and model center. The boundary conditions of the model center can be simulated as a free moving vertical roller. The boundary conditions of the model border are simulated in two stages with several load steps within each stage. The first stage accounts for existing soil conditions. This stage is necessary to ensure that the soil maintains the initial pressure of its own weight. The soil at the exterior of the model must be simulated with a roller, since it does not support its own weight. After initial loading the unaffected soil outside the model must hold up the soil within the model. Throughout initial loading there are no interactions between the soil and pile because the pile remains separate. See Figure 3.
Figure 3. Finite Element Model Initial Conditions
The pile tip surface and the contacted soil beneath the pile tip must be controlled. A contact pair is defined at the pile tip, for bearing capacity, which simulates pile-soil interaction between two surfaces. The pile tip surface is defined as the master surface and the soil surface is defined as the slave surface. The master surface has property that can penetrate the slave surface. This property allows for contaminated soil at pile tip to be easily compressed.
As indicated previously, the concrete pile does not exist in the initial loading stage therefore interaction between pile elements and soil elements is not modeled. Thus, the contact pair and interface elements are absent in initial loading. In the structural loading stage all interface elements and contact pairs must be redefined as described above. The models solution is displacement controlled. A predetermined displacement increment is applied using Newton’s Method. The program iterates to find the corresponding load. This is repeated for each subsequent load step.
RESULTS
Eleven piles representing soil conditions in both Thailand and the United States were modeled and compared to published data [28], technical report data (73)[74] and Reese (1988)[70]. This sample model has been validated based on published pile load test data in Texas, USA. Reese (1988)[35] provides pile load test data and a boring log profile. The boring log presents the standard penetration test number (N) value and the soil cohesion value (TSF). The value of N can be converted to angle of friction (f) by using this chart, based on the previous work of Peck, Hanson and Thornburn (1974)[33]. Other typical soil properties such as modulus of elasticity (Es), Poisson's ratio (m), unit weight (g) were chosen. See Table 1. The pile had a diameter of 0.91 m and length of 30.49 m (3.0 ft x 100 ft). The sample results are shown in Figure 4. The Load-Settlement curve predicted by the finite element analysis is very close along to the actual load test.
Table 1. Soil Properties
Figure 4. Actual/Theoretical Settlement vs Load
DISCUSSION & CONCLUSIONS
The finite element method has definite advantages over conventional empirical and theoretical analysis methods. There are, however, certain limitations to the finite element method, this is especially demonstrated in correct model calibrations. Simulating a finite element model must be based on at least one pile load test result. This result can be obtained from current or related projects. A thorough soil investigation of each project must be to be accomplished for the pile capacity analysis and results to be considered viable. Please contact the authors for a more detailed report regarding the prediction of load capacity of large drilled piles in non-homogenous soil through utilization of 3D finite element methods.
REFERENCES
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