Effects of inner sleeves on the inner frictional resistance of open-ended piles driven into sand

Abstract

In open-ended piles, inner friction is developed between inner pile shaft and the inner soil. Inner frictional resistance depends largely on the degree of soil plugging, which is influenced by many factors including pile diameter, relative density and end conditions of piles. In this paper, effects of inner sleeves on inner frictional resistance are discussed. The experiments were conducted on a medium-dense sandy ground using laboratory-scale piles. It was observed that the piles penetrated under partially-plugged or unplugged state. The results suggest that inner frictional resistance, Q_in increases with sleeve height, l linearly and requires 2D (D is pile outer diameter) of l to produce a large as 50% of Q_t by Q_in (Q_t is total resistance). The results also indicate that bearing capacity increases with wall thickness at the pile tip, which can be attributed to the increase in annular area. The results also indicate that soil plug height is independent of sleeve height. The results also reveal that the penetration of straight piles is closer to unplugged state than the sleeved piles. The results of incremental filling ratio and plug length ratio also indicate that the degree of soil plugging is affected by the sleeve height.

Keywords

bearing capacity / inner frictional resistance / inner sleeve / open-ended piles / soil plugging

Introduction

Previous studies have shown that the behavior of open-ended piles is different from closed-ended piles [1–3]. Open-ended driven piles are widely used as deep foundations, particularly in offshore constructions due to the long length of the piles. Generally, it is accepted that a short open-ended pile produces a smaller bearing capacity than a similar closed-ended pile [4]. However, a long open-ended pile can produce a similar bearing capacity as a closed-ended pile due to large inner frictional resistance mobilised between the inner pile shaft and inner soil [5]. Ultimate bearing capacity of an open-ended pile, Q_u consists of three components as given in Eq. (1a) (see Fig. 1 also).

(1a)Q_u=Q_{\mathrm{an}}+Q_{\mathrm{out}}+Q_{\mathrm{plug}},

(1b)Q_{\mathrm{plug}}=\min (Q_{\mathrm{in}},Q_b),

where Q_an is annulus resistance, Q_plug is soil plug resistance (see Eq. (1b)), Q_out and Q_in are outer and inner frictional resistance respectively, and Q_b is base resistance.

When an open-ended pile is driven into a soil, underneath soil penetrates into the pile and generates a soil plug. As penetration continues, inner frictional resistance may develop and prevent further soil intrusion. Depending on the degree of soil plugging, an open-ended pile can produce a similar bearing capacity as a closed-ended pile. In practice, most piles are driven under partial plugged mode [6,7]. Figure 2 shows the modes of penetration of open- and closed-ended piles. When an open-ended pile penetrates under fully-plugged mode, the soil plug and the pile settle as an intact body. As shown in Figs. 2c and 2d, a fully-plugged open-ended pile behaves similar to a closed-ended pile. Although a large soil plug is produced by an unplugged pile (see Fig. 2(a)), it does not produce any internal frictional resistance due to upward movement of the soil plug during the pile installation (or loading). Therefore, an unplugged pile produces the smallest bearing capacity due to lack of plug capacity (see Eq. (1a)).

Many factors of pile installation and ground conditions can affect the formation of soil plug length [8]. It is understood that dynamic pile installation methods are less likely to encourage soil plugging compared to static installation methods. It has also been reported that loose ground conditions lead to higher plugging conditions [9,10]. The uncertainty of the knowledge of soil plug length has led different design methods adopting different design parameters for open-ended piles. In Japan, most of the pile foundations are designed based on the JRA specifications for highway bridges [11], which specifies the ratio of embedment length to pile outer diameter as the main factor governing inner frictional resistance regardless of the ground conditions. However, the ICP method considers inner diameter and relative density as the main factors governing soil plugging and base capacity [12]. The main problem with the ICP and the API [13] methods are that they classify the piles into either fully-plugged or unplugged mode whereas most piles in practice are driven under partially-plugged mode. As partially-plugged piles can be classified into the unplugged mode, the ICP and API methods may underestimate the bearing capacity of open-ended piles. Reviews of widely used current design methods can be found in [14,15]. As reported in many design methods, it can be seen that that the evaluation of inner frictional resistance has not been universally established due to uncertainty of formation of soil plug length.

The effects of ground conditions on soil plug formation have been sufficiently investigated [9,10,16]. While the effects of pile diameter on the inner frictional resistance have been studied adequately, effects of outer or inner sleeves (i.e., the attachments at the pile base) on the formation of soil plug length have been scarcely studied. In this research, the behavior of open-ended piles attached with inner sleeves was studied.

Ground preparation and testing method

The model ground was prepared in a soil tank with the dimension of 300 mm inner diameter and 250 mm height as shown in Fig. 3(a). The bearing house fitted on the top cover was designed to maintain the verticality of the piles. The loading apparatus is shown in Fig. 3(b). Silica sand was used to prepare the model ground. The physical properties and particle size distribution of silica sand are shown in Table 1 and Fig. 4 respectively. The model ground was prepared with 60% of relative density. The sand was poured from a tube of 30 mm diameter from a constant height to produce the required relative density (i.e., air pluviation method). A similar procedure of ground preparation has been used in Kikuchi (2011) [7]. Static penetration with a penetration rate of 3 mm/min was applied during pile penetration. The penetration resistance and penetration depth were measured during the loading. Soil plug height was measured using a scaled-mark string connected to a small weight at the bottom by stopping loading at 10 mm intervals as shown in Fig. 5.

Stainless steel piles were used in the experimental work. Five open-ended piles and one closed-ended pile with different conditions were used in the tests as given in Table 2 and Fig. 6. In pile notations of P₅₀-4.0-10 (see Table 2), 50 is pile outer diameter, 4.0 is wall thickness at the pile tip and 10 is sleeve height. The open-ended piles have 50 mm of outer diameter (D), 380 mm of pile length (L) and 2 mm of top thickness (t_top). The non-sleeved pile of P₅₀-2.0-380 has 2 mm of wall thickness throughout the pile whereas the sleeved piles have different wall thicknesses at the sleeve and above it as given in Table 2 and Fig. 6. The closed-ended pile too has 50 mm diameter and 380 mm pile length. As inner friction resistance can be limited to lower part of the pile, height of the sleeve, l were designed such that l = 10 mm and 0.5D, 1.0D and 2.0D as given in Table 2. Kikuchi [7] has reported that the inner frictional resistance is mobilised within 2D (D is pile outer diameter) from the pile base. Therefore, we selected the maximum length of sleeve height as 100 mm (i.e., 2D).

Results

Two indexes widely used to discuss inner frictional resistance of open-ended piles, namely, plug length ratio (PLR) and incremental filling ratio (IFR) are defined in Eqs. (2) and (3) respectively [17,18]. The PLR indicates an average behavior of plugging state for a long penetration depth. In contrast, the IFR indicates the instantaneous plugging state at small penetration depth. As soil plugging condition may change discontinuously with pile penetration, the IFR gives a better indication of plugging condition than the PLR.

(2)PLR={\displaystyle \frac{h}{H}},

(3)IFR={\displaystyle \frac{\Delta h}{\Delta H}}\times \mathrm{100}(\%),

where Dh is the change of soil plug length for penetration depth of DH (see Fig. 5).

Effects of wall thickness at the pile base

Figure 7 shows the results of penetration resistance versus penetration depth for the piles. As shown in Fig. 7, the closed-ended pile (i.e., P₅₀-0.0-380) produces a larger penetration resistance than the open-ended piles. Theoretically, only a fully-plugged open-ended pile (i.e., IFR = 0%) can produce a penetration resistance similar to a closed-ended pile. The results of t = 2.0 and 4.0 mm piles indicate that the thicker-walled piles (i.e., those of 4.0 mm) produce larger penetration resistance than thinner-walled pile (i.e., that of 2.0 mm), which can be attributed to larger annular area (see Table 2). However, it should be noted that the effects of the wall thickness on the bearing capacity of the piles used in practice might not be significant as the tests conducted in this study due to a relatively smaller annular area compared to the total area by the pile outer diameter (i.e., smaller A_an/A_t values in the field).

Effects of sleeve height

As shown in Fig. 7, in the four piles of t = 4.0 mm (i.e., P₅₀-4.0-10, P₅₀-4.0-25, P₅₀-4.0-50 and P₅₀-4.0-100) with different sleeve heights (i.e., l = 10, 25, 50 and 100 mm), penetration resistance increases with sleeve height. Figure 7 clearly shows that piles with higher sleeve height produce larger penetration resistance. Therefore, we can conclude that height of the sleeve influences the bearing capacity. As annular area, A_an is equal in t = 4.0 mm piles (i.e., 578.1 mm²), annulus resistance, Q_an can be assumed to be equal in these piles. Therefore, the difference in penetration resistance can be attributed to the difference in inner frictional resistance, Q_in given that outer frictional resistance too should be approximately same for all the piles.

Inner frictional resistance

As outer frictional resistance, Q_out (see Eq. (4)) was found to be 19 N at 150 mm depth (assuming 35° of soil frictional angle, f; 0.6f of interface frictional angle between the pile shaft and soil, d; 0.45 of coefficient of lateral earth pressure, k according to Tomlinson [6], it was ignored in the analysis. Annulus resistance, Q_an was calculated using the area ratio (i.e., A_an/A_t) given in Table 2 and Q_t (Q_t is total resistance and equal to the penetration resistance, P) of the respective closed-ended pile as given in Eq. (6). In Eq. (6), it is assumed that the base resistance of a closed-ended pile distributed uniformly throughout the bottom surface area. Therefore, annulus resistance, Q_an of an open-ended pile can be calculated from a closed-ended pile using the area covered by the walls of the open-ended pile. Then, Q_in was calculated by subtracting Q_an from Q_t.

(4)Q_{\mathrm{out}}=Aq,

(4)where A is effective surface area of pile shaft and q is unit outer frictional resistance as given in Eq. (5).

(5)q=k\sigma \tan \delta ,

where k is coefficient of lateral earth pressure, s is effective overburden pressure and d is frictional angle between the pile shaft and soils.

(6)Q_{\mathrm{an,}\mathrm{t}=4\mathrm{.0}}={\displaystyle \frac{A_{\mathrm{an}}}{A_t}}{Q}_{\mathrm{t,}D=\mathrm{50}},

where Q_{an,t= 4.0} is annulus resistance of t = 4.0 mm piles, A_an is annular area (see Eq. (7)), A_t is total area covered by pile outer diameter, D and Q_{t,D= 50} is total resistance of D = 50 mm closed-ended pile.

(7)A_{\mathrm{an}}={\displaystyle \frac{\pi }{\mathrm{4}}}(D^{\mathrm{2}}-d^{\mathrm{2}}),

where d is pile inner diameter.

Figure 8(a) shows the results of inner frictional resistance, Q_in versus penetration depth of the sleeved piles. Figure 8b shows Q_in versus sleeve height. As shown in Figs. 8(a) and (b), Q_in is dependent of sleeve height, l and also a linear function of l. Figure 9 shows the contributions of Q_in and Q_an as a percentage of the total resistance, Q_t. Figure 9 indicates that only the pile with 2D of l produces as large as 50% of Q_t by Q_in. Figure 9 also shows that the pile with 10 mm of l produces only 10% of Q_t by Q_in. Therefore, we can suggest that higher sleeve height is necessary to produce a large inner frictional resistance. It should be noted that there should be an effective sleeve height and beyond it, inner frictional resistance does not increase with sleeve height. The effective sleeve height should be either less than or equal to the soil plug length. Kikuchi [7] has suggested that the inner frictional resistance is mobilised within 2D (D is pile outer diameter) from the pile base.

Figure 10 shows soil plug height versus penetration depth. The straight piles (i.e., the piles with no sleeve) penetrate closer to unplugged state than the sleeved piles. However, there is no significant difference in soil plug height among the sleeved piles. Figure 11 shows the results of incremental filling ratio versus penetration depth. As shown in Fig. 11, the results suggest that the piles with smaller inner diameter, d (see Table 2) produce higher degree of soil plugging (by comparing d = 42 and 46 mm piles). The results from Fig. 11 also suggest that sleeve height affects degree of plugging here. Figure 11 reveals that higher sleeve height, l results in higher degree of soil plugging (by comparing l = 10, 25, 50 and 100 mm piles) although the differences are slightly small. Figure 12 shows the results of plug length ratio, PLR versus penetration depth. As mentioned earlier, the PLR indicates the average behavior of soil plugging over a large penetration depth. Figure 12 also suggests the sleeve height, l influences the PLR although the variations are slightly small. We assume that the variations of PLR of relatively larger diameter piles (e.g., the piles used in practice) may produce significant differences in the PLR (and also IFR) when the sleeve height is varied. In the next stage of this research, we plan to conduct model tests using relatively larger diameter piles, such that, any scale-effects can be discussed.

Conclusions

In this paper, effects of wall thickness at the pile base and inner sleeve height of open-ended piles on the bearing capacity, particularly inner frictional resistance were discussed using laboratory-scale piles. The results showed that bearing capacity increases with the wall thickness, which can be attributed to the increase in annular area. The results also suggest that the inner frictional resistance, Q_in is dependent of sleeve height, l and increases linearly with l. The results of Q_in further suggest that an open-ended pile needs 2D (D is pile outer diameter) of a sleeve height to produce as large as 50% of Q_t by Q_in (Q_t is total resistance). They also indicate that soil plug height is independent of sleeve height. The results also reveal that penetration of straight piles (i.e., the piles with no sleeve) is closer to unplugged state than the sleeved piles. The results of incremental filling ratio and plug length ratio also reveal that the degree of soil plugging is affected by the sleeve height, although the variations among the sleeve heights were relatively small.

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