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Alexandria Engineering Journal (2013) 52, 187-195

FACULTY OF ENGINEERING ALEXANDRIA UNIVERSITY

Alexandria University Alexandria Engineering Journal

www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Undrained behavior of auger cast-in-place piles in multilayered soil

Fathi M. Abdrabbo, Khaled E. Gaaver *

Structural Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt

Received 18 October 2012; revised 8 December 2012; accepted 16 December 2012 Available online 18 January 2013

KEYWORDS

Undrained; Piles;

Multilayered soil; Load

Abstract Auger cast-in-place piles (ACIP) are often installed through multilayered soil profiles, which make accurate predictions of the performance of the piles more complex than piles constructed in either clay or sand deposits. This study is intended to shed some light on the undrained behavior of ACIP embedded in stratified soil and to explore a methodology to predict the ultimate pile loads. The study is based on practical measurements of load-displacement relationships of 51 static loading tests of full-scale ACIP installed through multilayered soil profiles. The study revealed that the normalized load-displacement relationships of the tested piles have deterministic range with upper and lower bounds. Equations for these bounds and the mean load-displacement relationship are developed in this study. There is a deficiency in the literature concerning the calculations of ultimate loads for piles embedded in multilayered soil. Therefore, this paper presents an attempt to estimate the ultimate pile load in undrained conditions utilizing two approaches. The first approach assumed the failure pattern of the soil beneath the pile base to be punching into the sand followed by general shear failure in clay underneath. The end-bearing resistance at the pile tip was estimated by implementing Meyerhof and Hanna's [24] shallow foundation procedure. The second approach assessed the depth of the influence zone below the pile tip using isobars of pressure around and below the pile tip due to a point load, based on the theory of elasticity and characterization of a semi-infinite soil mass (Martins [3]). Soil layers, within the zone of influence, were considered to be an equivalent geoma-terial with shear strength parameters computed by weighted average of shear strength parameters of the soil sub-layers. For comparison purposes, the ultimate pile load of each test was interpreted experimentally using the method proposed by Chin (1970). Reasonable agreement was obtained between the predicated and the experimental values, with an accuracy of about ±17%.

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* Corresponding author.

E-mail addresses: f.m.abdrabbo@excite.com (F.M. Abdrabbo), khaledgaaver@yahoo.com (K.E. Gaaver).

Peer review under responsibility of Faculty of Engineering, Alexandria

1. Introduction

Although most theories of soil mechanics were developed by considering the behavior of either ideal clays or pure sands, in-field soil profiles do not confirm to either ideal soil type. In practice, auger cast-in-place piles (ACIP), also known as continuous flight auger (CFA) piles, are often installed

University.

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through profiles consisting of multiple layers of soil. The literature concerning the response of axially loaded piles embedded in multilayered soil is sparse. Most of the studies pertaining to piles have dealt with piles embedded in either sand or clay [15]. Kim et al. [19] investigated the behavior of closed-ended pipe piles driven into stratified soil by conducting static and dynamic axial load tests on three piles. Seo et al. [32] presented the results of two static load tests on an H-pile driven into a silt-dominated multilayered soil profile.

Different approaches to analyze vertical piles under axial loads have been developed in recent decades. An approach was conducted assuming soil resistance along the pile shaft and at the pile tip can be represented by a series of independent springs [20,17,16]. The spring stiffness can be determined through theoretical, experimental, or empirical procedures. Another approach considered the soil as a continuum [26,21,22,31]. Furthermore, other approach was based on energy principles [4]. Seo et al. [30] combined the elastic continuum approach with the potential energy principle to predict the displacement of circular and rectangular piles in stratified soil.

The responses of single piles and pile groups under axial loads were studied using laboratory tests, centrifuge models, full-scale tests, and theoretical and numerical studies. The results of laboratory tests are usually affected by scale effects. Centrifuge models produce reliable results, but they require complex instruments and they are cost prohibitive. Full-scale tests are more representing to field conditions, however, they are expensive. Despite significant theoretical advances in the analysis and prediction of pile behavior in recent decades, static pile loading tests remain the most reliable means of assessing the response of single piles and pile groups under design loads [23]. Pile loading test results provide reliable data for reverse engineering that enable the engineer to confirm and refine appropriate soil strength, stiffness, and compressibility characteristics. Refined soil parameters make it possible to better understand and characterize subsurface conditions, justify and refine initial engineering assumptions, and improve final predictions.

Many studies of piled foundations have been based on gathering relevant databases. Dithinde et al. [12] presented four load test databases for driven and bored piles in cohesive and cohesionless soils to identify and also to quantify the uncertainties associated with various geotechnical design approaches. Chen et al. [8] established a database to evaluate the capacity of drilled shaft foundations under axial uplift loading. Based on pile load-settlement test data from case studies obtained from literature, Haldar and Babu [18] proposed a procedure to determine partial factors in a reliability-based design format for pile foundations. Schneider et al. [29] examined the predictive performance of a range of pile design methods using a compiled database of static load tests on driven piles in cohesionless soils.

The undrained behavior of auger piles depends principally on the type of soil through which the pile is installed. When ACIP are installed in stratified soils, they exhibit more complex behavior compared to those installed in uniform soils. The tip resistance, which may be affected by multiple soil layers located within the zone of influence of the pile base, is more difficult to analyze. Moreover, methods developed separately for clean sand and pure clay are also used for soils that contain various proportions of sand and clay. Therefore, both

theoretical and experimental efforts should be made to develop a better understanding of the behavior of piles installed through multilayered soil profiles. This is the motivation for the research reported in this paper. The study sheds some light on this problem by analyzing the results of pile loading tests on 51 individual piles installed in multilayered soil. Each of the pile tips was embedded through a sand layer overlying a clay layer of limited thickness. To avoid the complexity of mathematical models and the uncertainties inherited in theoretical assumptions, the analyses were based on practical measurements of load-displacement relationships of the tested piles. An attempt was made to establish two procedures for the calculation of the ultimate pile load in undrained conditions. The study presents a comparison between the predicted results and the experimental values.

2. Description of soil profile

Pile loading tests were collected from 12 different construction sites at the city of Alexandria and nearby districts in Egypt. The database was limited to sites at which the pile tip was bearing in a sand layer overlying a clay layer of limited thickness, as shown in Fig. 1. In the studied sites, the clay is alluvial type and normally consolidated. Exploration programs were conducted at the construction sites using boreholes and retrieving representative soil samples to determine the subsoil stratification system and the geotechnical properties of each stratum. Soil samples were retrieved using a split-spoon sampler and Shelby tubes whenever possible. Standard penetration tests were performed in accordance with ASTM D 1586 during borehole sampling. The soil samples recovered were classified in accordance with ASTM D 2487. The depth of the stable groundwater table was measured in the boreholes 24 h after of the completion of soil sampling.

To establish the soil profile at each site, the soil classifications available from the boring logs were reevaluated based on the laboratory test results. Undisturbed soil samples obtained from cohesive soil strata were tested in the laboratory to assess the properties of the soil layers. Sieve and hydrometer analyses were conducted on representative samples from all soil layers in the profile. Atterberg limits and natural water content values were determined for the cohesive soil layers. Direct shear tests and unconfined compression tests were conducted to determine the shear strength parameters of the cohesive soils. Consolidation tests were performed on samples collected from cohesive soils. All tests were performed in accordance with relevant ASTM standard test methods. Table 1 summarizes soil stratifications and number of pile loading tests at each site.

3. Procedure for pile loading tests

Loading tests were carried out on working piles in accordance with the Egyptian code of soil mechanics and foundations [13]. The procedure entails a load cycle in which the pile is loaded in increments up to the design test load and then unloaded in a similar manner. For working piles, the test load is recommended to be one and one half times the working load. The test load was applied in six equal increments. The applied load increment was maintained using a calibrated hydraulic jack, and the vertical displacement of the pile head was measured

Load (kN)

Figure 1 Schematic drawing of a pile in multilayered soil.

using four dial gauges attached to two reference beams. The accuracy of the hydraulic jack is ±0.50 kN, and the accuracy of the dial gauges is ±0.01 mm. The displacements obtained from the four dial gauges attached on opposite sides of the pile cap were averaged to determine the corresponding head displacement of the pile. For each load increment, the pile head displacement was recorded at elapsed times of 1, 2, 5, 10, 20, 40, and 60 min. Each load increment was held constant until the rate of pile displacement became less than 0.30 mm/h, as determined from three consecutive readings from the dial gauges. At the same time, each increment of load, up to the working load of the pile, was held constant for at least 1.00 h. At a load greater than or equal to the working load and less than the test load, the same criterion was implemented except that the loading period was increased to 3 h at least. At the test load, the load was maintained for 12 h ensuring that the rate of pile displacement was less than 0.30 mm/h.

—•—T2 —K • T22 -.-T48 -

\ \\ \ \

» \ X \ X \

\ V \ T i \

Figure 2 Typical load-settlement relationships.

Unloading was conducted in six equal decrements. Each load decrement was kept constant for 15 min. During each decrement, the pile head displacement was recorded, along with the elapsed time. When the pile became free from load, the pile displacement was recorded for 4 h. For each loading increment or decrement, a curve showing the relationship of the pile displacement to the elapsed time was drawn. The stabilized displacement was assessed from the displacement-time relationship. From the data obtained, the load-displacement relationship of the tested pile could be determined. Fig. 2 illustrates three typical load-displacement relationships obtained from three static load tests on three piles at three different sites. These relationships will be included in the compiled database.

4. Collected database

A database was compiled containing the results of static com-pressive loading tests on 51 individual auger cast-in-place piles (ACIP) embedded in multilayered soil at 12 different sites, along with associated geotechnical data. The database includes information on soil stratification at the 12 sites, the geotechni-cal properties of each soil layer, and the load-displacement relationships of the tested piles. The database only contains data on ACIP in multilayered soil profiles. The study addresses the undrained behavior of piles, so neither down-drag load nor drained bearing capacity was considered. Furthermore, the effect of the installation process on the responses of the piles was not considered. The pile loading test data collected

Table 1 Soil stratifications and number of tests at each construction site.

Site no. 1 2 3 4 5 6 7 8 9 10 11 12

No. of boreholes 5 20 18 3 5 7 2 2 9 3 24 23

D1 (m) 1.0/2.0 2.0/3.0 2.0/4.0 1.0 1.0/2.0 3.0/4.0 2.0/5.0 2.0 1.0 2.0 3.0 2.0/3.0

D2 (m) 15.0/14.0 10.0/9.0 6.0/7.5 7.5 6.0/5.0 6.0/5.0 6.0/3.0 5.0 10.0 20.0 9.0/20.0 16.0/18.0

D3 (m) 9.0 8.0 5.0/6.0 5.5/6.5 5.0 10.0 9.0 8.0 8.0/9.0 8.0 4.6/10.0 6.50/8.0

X(m) 11.0/12.0 6.0 4.0/8.0 5.0/6.0 8.0 3.0/4.0 3.0 4.5/5.0 10.0 5.0 5.0/6.0 3.0/8.0

D4 (m) 1.25 0.80 0.50 1.50 0.75 2.00 0.60 1.75 0.30 0.60 0.90 1.50

No. of pile loading tests 3 9 8 2 2 3 2 2 3 2 8 7

were carefully studied to assess their suitability for use in this study. The suitability criterion was the completeness of the required information, including pile length, pile diameter, complete records of the load-displacement relationship in accordance with the specified loading procedure, and availability of subsurface soil data for the site. Loading test data with insufficient information were discarded from the compiled database. The geotechnical data included soil profile, results of standard penetration tests (SPT), and results of laboratory tests, including index property tests, direct shear, unconfined compression, and oedometer tests.

Based on the case history descriptions, it appears that the construction and test performance of the studied piles were of high quality. Consequently, these data should reflect real field situations, and therefore should be reliable for application in practice. The database contains information on piles 400, 500, and 600 mm in diameters. The pile lengths vary from 10.00 to 25.40 m below ground surface. Table 2 presents the details of the compiled data. Histograms of pile diameters and pile lengths included in the database are presented in Figs. 3a and 3b.

5. Prediction of ultimate pile loads from load-displacement relationships

Once the pile loading test results and the accompanying geo-technical data were compiled as described in the previous sections, the next step was to determine the ultimate load of each of the piles in the collected database. Different criteria are available in the geotechnical literature to interpret a pile's ultimate load from its load-displacement relationship. The applicability of a method for determining the ultimate pile load depends on the shape of the load-displacement relationship, the level of the test load, and the magnitude of the recorded pile displacement at the test load. Zhang et al. [36] stated two different failure criteria based on settlement limitations. The first criterion suggests that the ultimate pile load is mobilized at a pile displacement that is typically 5% to 10% of the pile diameter. The second criterion suggests that the ultimate pile load is mobilized at a pile displacement of 50 mm. The skin friction capacity of a pile is usually developed at a displacement of the pile head in the range between 0.5% and 2.0% of the pile diameter [14]. Fleming et al. [14] reported that the design end bearing capacity of a pile may be taken at a displacement equal to 10% of the pile diameter, rather than a true ultimate value, which may require a displacement in excess of one pile diameter to mobilize. Czech, Italian, and Norwegian specifications indicate that the ultimate pile load corresponds to a displacement of 10% of the pile diameter [11]. The United States' Federal Highways Administration (FHWA) method [28], for ultimate pile load calculation, was developed using a failure criterion of 5% of the pile diameter in sands and plunging failure in clays. Neely method [25] was based upon a pile head movement of 10% of the pile diameter in sands. It was observed that the recorded pile displacements at the test loads varied from 1% to 3% of the pile diameter. Thus, none of the tests whose results were collected in the database reached settlement values sufficient to determine the ultimate pile load. Therefore, it is not applicable to use the settlement criteria cited above to determine the ultimate pile loads of the tested piles.

Extrapolation methods for predicting ultimate pile loads such as those proposed by Terzaghi [33], Chin [9], Davisson [10], Butler and Holly [7] and Abdrabbo and El-Hansy [1] are documented in literature. Some of these methods require the pile to be loaded nearly to failure, which is not usually permitted for working piles. Because the piles in the compiled database are working piles, they were loaded up to about one and one half times their working loads with limited displacements. Therefore, most of the extrapolation methods are not suitable for predicting the ultimate loads of these piles. In this study, Chin's extrapolation procedure was found to be a suitable way to estimate the ultimate load of a pile load from its load-displacement relationship. According to Chin's procedure, each displacement value (s) is divided by its corresponding load value (P), and the resulting ratio (s/P) is plotted against the pile displacement (s). The plotted s/P-displacement relationship falls on a straight line, and the inverse of the slope of this line is considered to be the ultimate load of the tested pile. Sometimes a broken line occurs in the s/P-displacement relationship. In this case, the inverse of the initial slope represents the ultimate skin friction load of the pile, while the inverse of the second slope denotes the ultimate load of the pile. Chin's hyperbolic relationship is defined as follows:

P = s/(a + b ■ s) (1)

where P is the applied load (kN), s is the pile head displacement and a and b are the hyperbolic curve-fitting parameters for the normalized load-settlement relationship. Note that the curve-fitting parameters are physically meaningful.

Chin's method assumes that the load-displacement relationship of the tested pile has a hyperbolic shape. In most cases, this condition does not prevail. Thus, scatter is anticipated in the predicted values of the ultimate pile loads. Fig. 4 illustrates three typical s/P-displacement relationships used to predict ultimate pile loads using Chin's procedure. Table 2 presents the values of the predicted ultimate pile loads for all of the tests compiled in the study database.

6. Discussion of results

Knowledge of pile behavior under both working and ultimate loads is important in the design of structures supported by pile foundations. In this section, load-displacement relationships are used to represent the serviceability behavior of piles, while the predicted ultimate loads of piles are discussed in relation to the undrained response of piles at failure and the appropriate safety factor for a pile under a working load. This section consists of two parts. The serviceability behavior of piles is addressed in the first part, and the experimentally determined ultimate loads of piles are compared with the calculated pile loads in the second part.

6.1. Load-displacement relationships

The load-displacement relationships for all piles in the collected database are plotted in generalized form. It is important to note that these load-displacement relationships were recorded over short periods of time, so these responses represent undrained behavior of the piles. It is anticipated that the drained, long-term behavior of piles may be different from

Table 2 Details of the compiled database.

Test Site Pile diameter Pile length L (m) h (m) X (m) / for sand in third qu for clay Pu (kN),

(d) (mm) (Lp) (m) layer (degrees) (kN/m2) Chin [9]

T1 1 600 21.00 5.00 4.00 11.00 36 228.50 2870.00

T2 1 600 21.00 5.00 4.00 11.00 36 228.50 2940.00

T3 1 600 21.00 5.00 4.00 12.00 36 228.50 3125.00

T4 2 500 14.50 2.50 5.50 6.00 37.9 200.00 2177.40

T5 2 500 14.50 2.50 5.50 6.00 37.9 200.00 2156.00

T6 2 500 14.50 2.50 5.50 6.00 37.9 200.00 2276.70

T7 2 600 14.50 2.50 5.50 6.00 37.9 200.00 3733.00

T8 2 600 14.50 2.50 5.50 6.00 37.9 200.00 4763.20

T9 2 500 14.50 2.50 5.50 6.00 37.9 200.00 3164.00

T10 2 500 14.50 2.50 5.50 6.00 37.9 200.00 3378.00

T11 2 500 14.50 2.50 5.50 6.00 37.9 200.00 2087.50

T12 2 500 14.50 2.50 5.50 6.00 37.9 200.00 1880.90

T13 3 500 14.00 5.00 1.00 4.00 32 310.00 2612.00

T14 3 500 14.00 5.00 1.00 5.00 32 310.00 2545.00

T15 3 500 13.00 4.00 1.00 6.00 32 310.00 1649.00

T16 3 500 11.00 3.00 2.50 6.00 32 310.00 1489.00

T17 3 500 12.00 2.00 3.00 7.00 32 310.00 1423.10

T18 3 600 14.00 2.50 3.00 8.00 32 310.00 1955.10

T19 3 600 13.00 2.00 4.00 7.00 32 310.00 1591.00

T20 3 600 12.00 2.00 3.50 8.00 32 310.00 1383.00

T21 4 500 11.00 2.50 4.00 5.00 34 280.00 1431.80

T22 4 500 11.00 2.50 3.00 6.00 34 280.00 1191.30

T23 5 500 10.00 3.00 2.00 8.00 39 180.00 834.00

T24 5 500 10.00 3.00 2.00 8.00 39 180.00 957.00

T25 6 600 13.00 4.00 6.00 3.00 35 165.00 4034.30

T26 6 600 13.00 4.00 6.00 3.50 35 165.00 3695.00

T27 6 600 13.00 4.00 6.00 4.00 35 165.00 3268.40

T28 7 400 16.00 8.00 1.00 3.00 35 192.00 1899.00

T29 7 400 16.00 8.00 1.00 3.00 35 192.00 2260.40

T30 8 600 11.00 4.00 4.00 4.50 36 100.00 1410.70

T31 8 600 11.00 4.00 4.00 5.00 36 100.00 1425.30

T32 9 500 15.00 4.00 5.00 10.00 34 260.00 1700.00

T33 9 500 14.00 3.00 5.00 10.00 34 260.00 1190.00

T34 9 500 14.00 3.00 5.00 10.00 34 260.00 1138.00

T35 10 600 25.00 3.00 5.00 5.00 33 130.00 1970.90

T36 10 600 25.00 3.00 5.00 5.00 33 130.00 2010.00

T37 11 500 25.40 2.40 2.60 2.00 33 150.00 2642.00

T38 11 600 25.30 2.30 2.70 2.00 33 150.00 2367.00

T39 11 600 14.50 2.50 3.50 5.00 33 150.00 2282.70

T40 11 600 15.00 3.00 3.00 5.00 33 150.00 1761.60

T41 11 500 14.40 2.40 3.60 5.00 33 150.00 1485.80

T42 11 600 14.50 2.00 4.00 6.00 38 160.00 1977.20

T43 11 600 14.50 2.00 4.00 6.00 38 160.00 1848.90

T44 11 500 14.40 2.00 4.00 6.00 38 160.00 1848.90

T45 12 600 23.00 2.00 5.00 6.00 35 140.00 3354.00

T46 12 600 23.00 4.00 3.00 7.00 35 140.00 3268.00

T47 12 600 22.50 1.50 5.00 3.00 35 140.00 1891.00

T48 12 600 22.50 2.50 5.00 4.00 35 140.00 3026.00

T49 12 600 22.50 4.00 3.00 7.00 35 140.00 2528.00

T50 12 600 22.00 4.00 4.00 8.00 35 140.00 2432.20

T51 12 600 21.00 3.00 4.00 7.00 35 140.00 2288.30

the undrained response. The displacement of the pile head (s) is normalized by divided it by the pile diameter (d) to obtain the term s/d, while the corresponding pile load (P) normalized with respect to (k) is expressed as follows:

d ■ L ■ h ■ qu ■ tan(^)

where X is the thickness of the clay layer (m), d is the pile diameter (m), L is the embedment depth of the pile through the sand

layer (m), h is the thickness of the sand layer below the pile tip (m), qu is the unconfined compressive strength of the clay (kPa), and / is the angle of internal friction of the sand (degrees).

Fig. 5 illustrates the relationships between the values of k and s/d for all of the tested piles. It is clear that there is a certain data range for all of the tested piles. The upper bound, lower bound, and mean values of the data range are illustrated in Fig. 5. Fig. 6 demonstrates that the trend lines representing

For the mean,

d ■ L ■ h ■ qu ■ tan(/)

= 5.02 ln(s/d) + 33.22 (5)

Settlement (

Figure 4 Typical s/p-settlement relationships for three piles.

the upper bound, lower bound, and mean values have log-normal relationships. The equations of these relationships are as follows:

For the lower bound, —-^ X-——

d ■ L ■ h ■ qu ■ tan(/)

= 3.14 ln(s/d) + 20.36

For the upper bound, — , „ ,,

pp ; d ■ L ■ h ■ qu ■ tan(/)

= 6.89 ln(s/d) + 46.08

The above equations demonstrate that the pile load within the serviceability stage is dependent on several parameters such as the pile diameter, the embedment depth of the pile through the sand layer, the thickness of the sand layer below the pile tip, the unconfined compressive strength of the clay, the angle of internal friction of the sand, and the thickness of the clay layer. The pile load increases with increasing pile diameter, embedment depth of the pile through the sand layer, thickness of the sand layer below the pile tip, unconfined compressive strength of the clay, and angle of internal friction of the sand. The pile load decreases with increasing clay layer thickness. Eqs. (3)-(5) can be used by the geotechnical engineers during the preliminary design stage. At the same time, it is essential to conduct pile loading tests on working and nonworking piles to confirm the values obtained in this study.

6.2. Ultimate pile loads

An axial compression load acting on a pile is transferred to the surrounding and underlying soil layers. Therefore, the pile load is carried partly by skin friction along the pile shaft and partly through the end-bearing at the pile base. It should be borne in mind that mobilization of the end-bearing resistance of a pile requires a relatively higher displacement than the skin friction resistance, even though the theoretical ultimate load of a pile is determined by adding the ultimate skin friction and the end-bearing resistance. It is customary to calculate the ultimate pile load in terms of undrained soil conditions, even though the long-term ultimate pile load, for drained soil conditions, is considerably larger than the undrained capacity. This is because the settlement associated with long-term pile capacity is far too large to be tolerated by most structures. In addition, short-term failure should be prevented. Thus, it is essential to compute the ultimate capacity of a pile in a cohesive soil based on the undrained shear strength of the soil. Available international building codes do not contain any

>< m \ . x»c X > \ X ' \ X >0 x\x \

* K x 1 ' 3 K \ Ï < \ X X x\ *V \ X \ X x^ x \

1 \ X \ x \ XX \ X X \ \

1 ¥ I I X X I \ \

Figure 5 Values of k-s/d relationships.

method for calculation of the ultimate load of piles installed through multilayered soil profiles. Thus, it is advisable to address clauses in international building codes to specify the method of calculation of ultimate pile loads for these soil conditions. For short-term conditions, no down-drag load should be considered. The skin friction resistance of a pile shaft f) in clay is computed from the undrained shear strength (cu), using an empirical adhesion factor (a), as follows:

fs = a ■ Cu (6)

The value of the adhesion factor (a) depends mainly on the pile type and the undrained shear strength of soil. Values of a appear to decrease from unity for piles in soft clay to 0.50 or less for piles in clays with shear strengths greater than approximately 100 kPa [34].

The skin friction resistance of a pile in sand is calculated based on the effective vertical stress at the centerline of the sand layer (rmc) as follows:

fs = rVc ■ k ■ tan d (7)

The value of k depends upon the in-situ earth pressure coefficient, the method of pile installation, and the initial relative density of sand. For auger cast-in-place piles, the value of k is considered to be 0.90 for sand and 0.60 for silty sand [34]. The friction angle between the pile and the soil d is dependent on the pile material and the friction angle of the soil. In general, the value of d is between the friction angle of the soil (/) and the constant volume (or critical state) angle of friction (/cv). The critical state angle of friction (/cv) relates to conditions where the soil shears with zero dilation. The values of /cv for different types of sand rang from 25° for mica to 40° for feldspar. The presence of silt particles means that /cv for most deposits will rarely exceed 30° [14]. In our calculations, the value of /cv was considered approximately equal to the residual angle of shearing resistance.

The end-bearing resistance beneath a pile in a uniform deposit of cohesionless soil is directly proportional to the vertical effective stress at the pile tip. Vesic [35] showed that end-bearing resistance appeared to approach a limiting value beyond which there is no further increase with depth. The limiting

value depends on the soil type and the relative density of the soil. A limiting value of 11-12 MPa was proposed by Tomlin-son [34] and the American Petroleum Institute [2]. Modern approaches to pile design have moved away from limiting values of end-bearing capacity, but they accept that there is a gradually decreasing gradient of design end-bearing resistance with depth. This trend is attributed to a decrease in the rigidity index, the ratio of shear stiffness to strength, with increasing stress level [27]. The end-bearing capacity of a pile (qb) resting on a uniform sand bed can be expressed in terms of the effective vertical stress at the pile tip (rm) and the bearing capacity factor (Nq) as follows:

qb = r ■ Nq (8)

The values of Nq quoted in the literature vary considerably. In the current study, values of Nq recommended by Beresant-sev et al. [5] were used. It is important to choose an appropriate value of / consistent with the soil type, relative density, and average stress level at failure. Bolton [6] related the corrected relative density of sand (IR) and critical state angle of friction (/cv) as follows:

/ = + 3Ir (degrees)

The corrected relative density of sand (IR) depends on the uncorrected relative density (ID), the mean effective stress level (p), and the atmospheric pressure (pa = 100 kPa) as follows:

For(p) p 150 kPa, Ir = Id[5.4 - \n(p/pa)\ - 1 (10)

For(p) < 150 kPa, IR = 5ID - 1 (11)

The ultimate skin friction along the pile shaft was calculated as outlined above, using Eqs. (6) and (7). To consider the effect of the clay layer under the pile tip on the end-bearing resistance at the pile base, two approaches are proposed. The following section summarizes the proposed methods and presents a comparison between the calculated values and the experimental results.

6.2.1. Method (A)

With this method, the failure pattern of the soil under the pile base is assumed to be punching into the sand layer followed by general shear failure in the clay layer. In this approach, the clay layer was considered to be of infinite thickness. The end-bearing capacity at the pile tip was computed using the procedure for shallow foundations proposed by Meyerhof

Figure 7 Experimental and theoretical ultimate loads, method (A).

Table 3 Values of Ft for different sub-layers.

Sub-layer no. 1 2 3 4 5 6

Depth of top surface of sub-layer below the pile tip 0.00 0.25LP 0.5LP 0.75LP 1.0 Lp 1.5LP

Thickness of sub-layer 0.25LP 0.25LP 0.25LP 0.25LP 0.5Lp 0.5Lp

Value of Ft at top surface of sub-layer 5.00 5.00 1.00 0.45 0.25 0.15

Value of Ft at bottom surface of sub-layer 5.00 1.00 0.45 0.25 0.15 0.08

Selected value of F 5.00 3.00 0.72 0.35 0.20 0.12

and Hanna [24]. Bearing capacity factors for deep foundations recommended by Beresantsev et al. [5] were implemented in the analysis. The calculated end-bearing resistance at the pile tip should not exceed the ultimate bearing capacity of sand underneath the pile base, assuming the sand is infinite in depth. Fig. 7 illustrates a comparison between the theoretical pile loads obtained and the experimental pile loads. The figure indicates that this method underestimates the experimental ultimate loads of piles by approximately 9%.

6.2.2. Method (B)

The depth of the influence zone below the pile tip is assessed to determine the soil layers affecting the end-bearing resistance of the pile. Isobars around and below a pile due to a point load constructed by Martins [3], based on the theory of elasticity and assuming a semi-infinite soil mass, were used. From these isobars, an influence depth equal to double the pile length (2LP) below the pile tip was considered. At this depth, the average vertical stress induced due to end-bearing pressure is about 8% from the actual value [3]. The soil layers through the influence zone were considered to be an equivalent geoma-terial. The undrained shear strength parameters of the equivalent geomaterial (cavg, and /avg) were computed by averaging the shear strength parameters of soil sub-layers in the influence zone as follows:

g F ■h- ■ c-

Fi • h

v-^F ■ hi ■

/avg = —FT.

Ft ■ hj ■ tan/

Fi ■ h

where Ft is the weight of sub-layer (i), corresponding to the average stress imposed within the sub-layer under consider-

y = 1.17x ♦ / ✓ / /

♦ * s t.

Jf / y

Experimental ultimate loads (MN)

Figure 8 Experimental and theoretical ultimate loads, method (B).

ation [3], as shown in Table 3, and hi is the thickness of the sub-layer.

The values obtained for cavg, and /avg were used to compute the end-bearing resistance at the pile tip. Based on the value of /avg, bearing capacity factors for deep foundations recommended by Beresantsev et al. [5] were evaluated. The theoretical pile loads were then calculated and plotted against the experimental pile loads, as shown in Fig. 8. The figure indicates that the proposed method overestimates the experimental ultimate loads of piles by about 17%.

7. Conclusions

This paper is intended to shed some light on the undrained behavior of auger cast-in-place piles (ACIP) installed in multi-layered soil by analyzing a database of 51 static loading tests performed on full-scale piles. The test program was complemented by an in-situ and laboratory testing program to evaluate soil profiles and properties at the test sites. The following lessons were learned from this study:

1. The pile load within the serviceability range depends upon several parameters such as the pile diameter, the embedment depth of the pile through the sand layer, the thickness of the sand layer below the pile tip, the unconfined com-pressive strength of clay, the angle of internal friction of the sand, and the thickness of the clay layer.

2. There is a certain data range for the normalized load-settlement relationships for the tested piles considered in the compiled database. Equations were developed in this study for the upper bound, the lower bound, and the mean value of normalized load-settlement relationships for undrained conditions. These equations can be used by the geotechnical engineers in the preliminary design stage.

3. Two approaches for the calculation of the ultimate load of piles embedded in multilayered soil in undrained conditions are tested. The first approach assumed the failure pattern of the soil beneath the pile base to be punching into the sand followed by general shear failure in the clay layer. The second approach considered the soil layers within the influence zone to be an equivalent geomaterial, with shear strength parameters computed by weighted averaging of the shear strength parameters of soil sub-layers within the zone of influence. The study reveals that the first approach underestimates the experimental ultimate loads of piles by about 9%, while the second approach overestimates the experimental values by about 17%.

4. It is advisable to address clauses in international building codes to specify the method of calculation of the ultimate loads of piles installed through multilayered soil profiles.

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