Design equations of uplift capacity of circular piles in sands
Introduction
Many high-rise structures such as transmission towers, tall chimneys, mooring systems, jetty structures, superstructures for offshore works, etc., are generally supported by pile foundations under uplift forces. Thus, the uplift capacity of a single pile is one important design parameter for these types of foundations. Structural requirements of piles in tension induced from superstructures can be satisfied by effectively reinforcing them with steel bars or steel pipes while geotechnical considerations are required to ensure a sufficient safety factor over the uplift capacity of pile generated from soil resistance. In general, a calculation of the uplift capacity of pile is obtained by integrating a skin friction of pile shaft over the contact area between pile and soil. However, a prediction of the skin friction is difficult and complex as it is involved with finding the unknown horizontal effective stress along pile at the limit state, which depends on an unknown failure curved surface propagating at pile tip. In this paper, the study is scoped with the uplift capacity of circular piles in sands. Some experimental studies [[1], [2], [3]] reported that the skin friction of piles in sands under compressive loads was significantly larger than that under pullout loads. Extensive experimental model tests (e.g. [[4], [5], [6], [7], [8], [9], [10]]) were carried out to investigate the uplift capacity of piles in sands while some results of field tests (e.g. [1,11,12]) were also reported. The study of the pullout capacity of suction anchors or caissons has received much attention in research as well (e.g. [[13], [14], [15], [16], [17], [18], [19]]).
Numerical and analytical studies on the uplift capacity of piles in sands were also conducted previously in the literature. Matsuo [20] studied the uplift capacity of a footing in which a logarithmic spiral failure surface around a footing corner was assumed. Chattopadhyay and Pise [21] employed the limit equilibrium method with a failure mechanism of a curve failure surface propagating at pile tip in order to predict the uplift capacity of piles in which the length, diameter, and surface characteristics of piles and soil properties were considered in design charts for a calculation of an average skin friction of piles. Later, Shanker et al. [22] proposed an analytical method for a calculation of uplift capacity of piles in sands by assuming an inverted and truncated conical slip surface making an angle of one quarter of the sand friction angle to the vertical and propagating at the critical length of pile. A semi-analytical method for the uplift capacity of piles was developed by Deshmukh et al. [23] using the limit equilibrium method with Kötter’s equation and an assumed failure surface of a frustum cone. Based on soil deformation images captured in physical models of pullout pile tests, Hong and Chim [24] developed an analytical approach of pile uplift capacity by deducing a similar failure surface making an angle of half of the soil friction angle to the vertical. In addition, experimental studies on the assumed failure surface for the pile uplift capacity considering the critical pile length were performed by Meyerhof [25], Das [7,26], and Su et al. [27]. Faizi et al. [28] presented the results of a series of small-scale physical modelling tests in which a photogrammetric technique and particle image velocimetry were employed to investigate the observed failure surface during pullout tests, which were validated by a finite element analysis. Table 1 summarizes the existing methods for the prediction of the ultimate uplift capacity of piles in sands.
It can be observed that the aforementioned researches on the predictions of the uplift capacity of circular piles in sands are based on the limit equilibrium method (LEM) or semi-empirical techniques. Thus, there is a major limitation of the methods in obtaining the accurate predictions. In other words, the accuracy of the existing predictions is related to the assumed failure surfaces that are neither theoretically correct nor applicable to all properties of piles and sands. Thus, an accurate prediction of the uplift capacity of circular piles in sands is still desirable in practice, which is the main objective of the present study.
Limit analysis is one of the best suitable methods for analyzing the uplift capacity of piles in sands as the proposed study is involved with a calculation of the limit load of a stability problem in soils, which can be bracketed from above and below by the upper and lower bound limit analysis based on the plastic bound theorems [29]. In recent years, the computational limit analysis using finite element concept and mathematical optimization, known as finite element limit analysis (FELA) [30], has been advocated for stability analyses in geotechnical problems [18,19,[31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45]]. The computational limit analysis has a significant advantage over the limit equilibrium method in that there is no need to assume any failure surface while the optimal accurate UB and LB solutions as well as the actual failure mechanism can be obtained by the numerical optimization employed in the analysis. Therefore, the computational limit analysis using FELA is chosen as the method of analysis in the present study. So far, there are very few numerical solutions of the uplift capacity of circular piles in sands based on the computational limit analysis.
The objectives of this paper are: 1) to investigate the uplift capacity of circular piles in sands by employing the computational limit analysis; and 2) to develop and propose the approximate design equations of the uplift capacity of piles in sands based on a nonlinear regression analysis to the computed limit analysis solutions for a practice use. The performance of the proposed design equations is verified by laboratory 1 g physical models and a full-scale pile test available in the literature.
Section snippets
Method of analysis
Fig. 1 shows the problem definition of the uplift capacity of a circular pile in sand. The circular pile with an embedded length (L) and a diameter (D) is pulled out by the ultimate uplift force (F). Because of the circular geometry of the pile, the axisymmetric condition is applicable. It is also assumed that the pile behaves as a rigid structure with weightless material, and the effect of pile installation on the surrounding soil is not considered (i.e., “wished-in-place” assumption). The
Results and discussions
The relationship between the uplift capacity factor of pile (N) and pile embedded length ratio (L/D) at different soil friction angles (φ = 20–45°) is shown in Fig. 3. Note that each subplot of the figure corresponds to a different interface roughness factor (α). In all cases, the N factors can be accurately bracketed by the computed upper bound (UB) and lower bound (LB) solutions within 1%. A closer investigation indicates that a nonlinear relationship of both N versus L/D and N versus φ is
Approximate statistical equations
A curve-fitting exercise is performed to develop a mathematical equation that provides an accurate prediction of the computed solutions of the computational limit analysis presented in the previous section. The lower bound (LB) solutions (commonly known as safe solutions) are chosen in the curve fitting method to represent the best estimate of the uplift capacity factor (N) of piles in sands since the differences of bound solutions are very small for all cases.
The concept of the curve-fitting
Comparisons with experimental results
The new design equation of the ultimate uplift force of piles in sands in Eq. (13) is verified against the experimental data of 1 g physical model tests (Das [7]; Dash and Pise [9], Chattopadhyay and Pise [21]; Shanker et al. [22]) as summarized in Table 5. Note that the data of soil and pile properties (i.e., γ, D, L, δ, φ) and the measured uplift forces reported in Table 5 are compiled in the existing two studies [22,23] of uplift capacity of piles in sands, and hence they are adopted in this
Final remarks
Readers are advised to be aware of the following limitations when applying the results in the present study to full-scale field conditions:
- 1)
The proposed approximate lower bound expressions for the uplift capacity of piles in sands were developed based on the limit analysis approach that assumes the associated flow rule of a material whose the dilation angle of sand is equal to its friction angle. Note that the associated flow rule assumption is not applicable for real sands with high friction
Conclusions
In the paper, the computational limit analysis is employed to investigate the ultimate uplift capacity of circular piles in sands. The parametric study of the problem is performed to examine three important parameters including the pile embedded length ratio, the soil friction angle, and the soil-pile interface roughness factor while the new plasticity solutions are numerically derived as a function of these. In all cases, the true limit loads of the problem can be accurately bracketed by the
Acknowledgements
The authors would like to thank all anonymous reviewers for valuable and constructive comments and suggestions, which greatly contributed to improving the quality of the final version of the paper.
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