Keywords

1 Introduction

Various conditions of a pile foundations can lead into various load (Q) – displacement (ρ) curve types that is gathered from axial load tests on such foundations. These varieties may exhibit any one of three shapes, A, B, or C, as shown in Fig. 1. But due to the requirements of structures that can only withstand a range of displacements, most of the load-displacement curves that are gathered from load test results resemble that of curve C. This may pose a dilemma as the capacity of the pile is not clearly visible on such condition of the load-displacement curve. Therefore, the capacity almost always needs to be interpreted from the load test results. Interpretation criteria (e.g., [1,2,3,4,5,6,7,8,9,10]) have been proposed over the years for interpreting such failure load. Table 1 defines nine representative criteria for the interpreted failure load based on a variety of assumptions, individual judgments, extrapolations, and others from the measured load–displacement curve. As found in practice, these interpretation criteria will give different results that can vary substantially.

Fig. 1.
figure 1

Typical load–displacement curves for pile foundations

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With these uncertainties in the interpretation of the capacity of a foundation, it is of utmost importance to analyze the application of these interpretation on various conditions and pile types. These load test data may provide vital information in determining the effects of different loading conditions to various soil and pile properties. Various researchers have also compiled relational databases of axial load test on different types of piles [11,12,13,14,15,16]. And since the 1980s, Kulhawy and co-workers have examined this issue in detail for drilled foundations. Their research [9, 10] and [17,18,19,20] mainly focused on the L1 (elastic limit) – L2 (failure threshold) method. Later, Chen and co-authors ([13, 16] and [21,22,23,24]) performed a more extensive evaluation to cover the existing representative uplift and compression interpretation criteria for various soil and pile types. What lacked in these analyses is a detailed comparison of various interpretation criteria when they are applied to barrette piles under uplift loading conditions.

Therefore, in this paper, nine representative uplift interpretation methods are examined in detail to assess their relative merits and their interrelationships. A database consisting of axial uplift load tests for barrette piles under drained and undrained soil conditions is used for this purpose. The results are compared statistically and graphically, and conclusions are reached for consistent use in practice.

Table 1. Definitions of representative uplift interpretation criteria for pile foundations
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2 Database

The database that was utilized in this study consisted of eight (8) load test results of barrette piles under uplift loading conditions. These load tests were done both in drained and undrained soil conditions, thus, the database was further divided into the said soil conditions, respectively. Division of the database into drained and undrained groups is governed by the prominent soil type along the pile length of each load test. Table 2 shows the soil and pile parameters that have been utilized in the study for its analysis. It can also be calculated in the table that the average equivalent diameter of the database is at 1.98 m while average pile length is at 41.7 m ranging from 3.5 to 57.5 m.

3 Interpreted Axial Uplift Capacity

As discussed, nine different criteria were used to analyze the interpreted capacity, as given in Table 1. These criteria were selected because they represent various displacement ranges and may represent the distribution of the interpreted results from the lower, middle and higher ranges as seen in past researches. Table 3 shows the results of each of the interpreted capacities (Q) based on each of the methods and represents different ranges of the capacities. However, during extrapolation, some load tests were terminated before achieving the available interpolated values. Following the conclusions of Phoon and Tang [25], bias is deemed inside a reasonable range for extrapolation from a load test terminated at 75% or higher of the actual Davisson capacity which is around 133% or lower of the final terminated load from any load test. Thus, these interpreted results were denoted as greater than (>) the value of 133% of the terminated load.

Table 2. Soil and pile information for barrette piles
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Table 3. Interpreted uplift capacities utilizing various interpretation criteria
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In addition to the results of the interpreted capacities, the relative displacements (ρ) are also determined in order to assess the location of each of the interpreted capacities and their distribution along the load-displacement curve as seen in Table 4. Furthermore, comparison between each of the interpreted capacities was done in order to assess where each of the interpretation methods are distributed along the normalized load displacement curve. In order to assess this, a normalizing interpretation method must be determined in order to check each of the other methods’ location in the curve in relation to the normalizing method. the L2 method was used as the normalizing criterion. This graphical method interprets the capacity as the start of the load–displacement curve’s final linear region. This method is effective for load–displacement curves resembling that of curves B and C with the application of a hyperbolic extension.

After normalizing the interpreted capacities and calculating the mean values for both drained and undrained soil conditions, it can be found that the interpreted load of the L1 provided the initial linear elastic stage of the developed normalized load–displacement curve. It may be used to predict the serviceability load that can be resisted by barrette piles or designs that require displacements that do not exceed mean displacements of 4.1 mm and 7.3 mm, respectively for drained and undrained soil conditions.

Table 4. Relative displacements utilizing various interpretation criteria
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Most of the interpretation criteria fell on the transition region of the normalized load–displacement curve with the methods of L2, Davisson, slope-tangent, Terzaghi and Peck, van der Veen, and DeBeer. These interpretation criteria provided good estimates of the capacity of barrette piles and are effective for designs that require mean displacements that do not exceed a range from 15 to 25 mm for drained and from 21 to 34 mm for undrained soil conditions. Lastly, the methods of Fuller and Hoy, DIN4026, and Chin had overestimated capacities and thus were un-conservative in interpreting the capacity of barrette piles for both drained and undrained soil conditions with mean displacements exceeding 40 mm for drained and 53 mm for undrained soil conditions. Graphical representation of the location for these methods on the normalized load-displacement curve can be seen in Figs. 2 and 3 for drained and undrained soil conditions, respectively.

Fig. 2.
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Normalized load displacement curve for barrette piles in drained soils

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Fig. 3.
figure 3

Normalized load displacement curve for barrette piles in undrained soils

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It can also be seen in the calculated results that the drained soils mobilize capacity at a lower displacement values in comparison to the undrained soil conditions. This means that lower capacities can be expected from sandy soils at lower displacements in comparison to clayey soils at slightly higher displacements.

Normalized load-displacement curve equations are also computed based on the data that were interpreted for both drained and undrained soil conditions. These equations may help in simplifying the analysis of each interpreted capacities in relation to that of the normalizing method that is L2. The equations are listed below for drained and undrained soil conditions, respectively.

$$\frac{Q}{{Q_{L2} }} = \frac{\rho }{3.21 + 0.82\rho }\quad \quad {\text{for}}\,{\text{drained}}\,{\text{soils}}\,\left( {{\text{r}}^{2} = { }0.99} \right)$$
(1)
$$\frac{Q}{{Q_{L2} }} = \frac{\rho }{7.09 + 0.78\rho }\quad \quad {\text{for}}\,{\text{undrained}}\,{\text{soils}}\,\left( {{\text{r}}^{2} = { }0.99} \right)$$
(2)

Furthermore, the results of this preliminary analysis may be able to shed light on the behaviour of each of the interpretation criteria when applied to barrette piles under uplift loading conditions. In order to increase the reliability and decrease the uncertainty of the results of the analysis, additional load tests should be employed to the database. It is therefore recommended for future expansion of the study the addition of load test data, in order to increase the range of pile and soil properties included in the analysis. Also, analysis of the behaviour of the interpretation criteria to the side and tip resistances is advised in order to present a more robust comparison between the interpretation methods that are being studied.

4 Summary and Conclusions

Axial uplift load test data were used to evaluate the capacity of barrette piles in various soil conditions. The database included 8 field uplift load tests, including 5 drained and 3 undrained soil conditions. Nine representative interpretation criteria were utilized to evaluate the available data. From these analyses, the following results were drawn:

  1. 1.

    L1 method provided the initial linear elastic stage or the serviceability region of the developed normalized load–displacement curve with mean displacements that do not exceed 4.1 mm and 7.3 mm, respectively, for drained and undrained soil conditions.

  2. 2.

    The methods of L2, Davisson, slope-tangent, Terzaghi and Peck, van der Veen, and DeBeer are located at the transition region to the initial stage of the final linear region of the curve. These interpretations yielded at mean displacements that do not exceed a range from 15 to 25 mm for drained soil conditions.

  3. 3.

    For undrained soil conditions, the methods of L2, Davisson, slope-tangent, Terzaghi and Peck, van der Veen, and DeBeer yielded at mean displacements ranging from 21 to 34 mm.

  4. 4.

    The methods of Fuller and Hoy, DIN4026, and Chin have overestimated capacities and thus were un-conservative in interpreting the capacity of barrette piles for both drained and undrained soil conditions. These methods have mean displacements exceeding 40 mm and 53 mm for drained and undrained soil conditions, respectively.

  5. 5.

    Normalized load-displacement curves and their respective equations have been presented to be utilized for future designs of barrette piles in different soil conditions. Drained soil conditions yielded an equation of \(\frac{Q}{{Q_{L2} }} = \frac{\rho }{3.21 + 0.82\rho }\) with an \(r^{2} = 0.99\); while undrained soil conditions yielded an equation of \(\frac{Q}{{Q_{L2} }} = \frac{\rho }{7.09 + 0.78\rho }\) with an \(r^{2} = 0.99\).

  6. 6.

    In order to increase the reliability of the analysis, additional load test data is necessary for the analysis.