Solution to critical suction pressure of penetrating suction caissons into clay using limit analysis

Abstract

The critical suction pressure will lead to the difference in equivalent overburdens at the skirt-tip level between outside and inside the caisson exceeds N_c^rs_u (N_c^r is the local reverse bearing capacity factor, and s_u is the undrained shear strength of clay at the skirt-tip), which may induce the local reverse bearing capacity failure of soil near the skirt-tip. As a result, soil flows into the caisson cavity, making soil plug heave higher that prevents the caisson from penetrating to its desired depth. This paper is the first to apply the limit analysis to obtain a theoretical study on determining the critical suction pressure based on the local reverse failure mechanism near the skirt-tip. This study is also the first to consider the effects of adhesion factors along the inside (α_i) and outside (α_o) of the skirt wall on the local reverse bearing capacity failure mechanism reflecting that N_c^r includes α_i and α_o. It is shown that N_c^r ranges from 5.14 (α_i=α_o=0) to 8.28 (α_i=α_o=1), and the values of α_o and α_i are all between 0 and 1. In addition, the critical penetration depth can be determined under the condition that the critical suction pressure equals the required suction pressure. And, the proposed method of calculating the critical penetration depth is testified to be in good agreement with the experimental results.

Introduction

Suction caissons have become the preferred foundation for offshore platforms or wind turbines due to their competitive technical and economic advantages over other foundations like driven piles [1], [2], [3], [4], [5], [6], [7]. A suction caisson initially penetrates the seabed under its self-weight, and then the encased water is gradually pumped out, producing downward suction pressure to drive it to the desired depth. During suction-assisted penetration, the suction pressure inside the caisson must be higher than the required suction pressure (p_re) to overcome the total penetration resistance consisting of skin frictions along the inside (F_i) and outside (F_o) of the skirt wall and the bearing capacity at the skirt-tip (F_t) [8], [9], [10], [11]. According to Fig. 1(a), by using limit equilibrium theory in the vertical direction, the required suction pressure for caisson installation can be expressed by

$$p_{\text{re}}=\frac{F_{\mathrm{i}}+F_{\mathrm{o}}+F_{\mathrm{t}}-W_{\mathrm{c}}}{A_{\mathrm{i}}}=\frac{\pi D_{\mathrm{i}}h{\alpha }_{\mathrm{i}}{s}_{u1}+\pi D_{\mathrm{o}}h{\alpha }_{\mathrm{o}}{s}_{u1}+\pi D_{\mathrm{m}}t{\sigma }_{\text{tip}}-W_{\mathrm{c}}}{\pi {D_{\mathrm{i}}}^2/4}$$

Meanwhile, the suction pressure should be lower than the critical suction pressure (p_cr) in order to avoid the reverse bearing capacity failure at the skirt-tip level. Otherwise, soil flows into the caisson cavity, leading to higher soil plug heave that prevents the caisson from penetrating to the desired depth [[8], [9], [10], [12], [13], [14], [15], [16]]. Consequently, to minimize the soil plug heave, the reverse bearing capacity failure should be avoided near the skirt-tip. As recommended by Andersen et al. [8], House et al. [12], Li et al. [15], and Randolph et al. [17], the critical suction pressure can be calculated in terms of the free body of soil plug. From Fig. 1(b), it has

$$p_{\text{cr}}=N_{\mathrm{c}}^{\mathrm{r}}{s}_{\mathrm{u}}+\frac{\pi D_{\mathrm{i}}h{\alpha }_{\mathrm{i}}{s}_{u1}}{\pi D_{\mathrm{i}}^2/4}=N_{\mathrm{c}}^{\mathrm{r}}{s}_{\mathrm{u}}+\frac{4h{\alpha }_{\mathrm{i}}{s}_{u1}}{D_{\mathrm{i}}}$$

By considering a general reverse bearing capacity failure of soil at the skirt-tip level, N_c^r was recommended to vary from 6.2 to 9.0 [8, 18], 7.0 to 9.0 [9], and 5.14 to 7.5 [15]. However, these researchers did not consider the effect of the local reverse bearing capacity failure near the skirt-tip on the soil plug heave. House et al. [12] pointed out that the experimental data indicated the critical penetration depth before soil plug failure is somewhat lower than that obtained from Eq. (2). Guo et al. [18] concluded that all the soil displaced by the skirt wall flows inwards during suction-assisted penetration, and even more volume of soil would enter the caisson cavity before the general reverse bearing capacity failure occurs at the skirt-tip level. They also indicated that the reverse bearing capacity failure may be progressive due to the water pumping continuously. Houlsby et al. [10] presented a simplified design procedure to determine the critical suction pressure based on the local reverse bearing capacity failure mechanism at the skirt-tip level. However, they did not take the effects of adhesion factors (α_i) and (α_o) on the local reverse bearing capacity failure mechanism into consideration. They assumed that the downward skin friction inside the caisson results in a uniform increase of vertical stress and the downward skin friction outside the caisson is carried by constant stress over an annulus with inner (D_o) and outer diameters (mD_o). Since the downward skin friction enhances the vertical stress in the vicinity of the skirt wall, the equivalent overburden at the skirt-tip level outside the caisson may vary from γ'h at an infinite position to a maximum at the skirt wall surface (D_o), as shown in Fig. 1(d). Additionally, due to the reverse effect of the suction pressure, the vertical stress within the soil plug is reduced, and the equivalent overburden at the skirt-tip level inside the caisson is lower than that outside the caisson. The difference in equivalent overburdens between outside and inside the caisson in excess of N_c^rs_u causes the local reverse bearing capacity failure near the skirt-tip, as shown in Fig. 1(d), which is affirmed by House et al. [12] and Guo et al. [18].

This paper presents a theoretical study on the critical suction pressure that motivates the local reverse bearing capacity failure near the skirt-tip when the difference in equivalent overburdens between outside and inside the caisson exceeds N_c^rs_u. The equivalent overburdens at the skirt-tip level inside and outside the caisson necessitate predicting the critical suction pressure, which will be calculated in Section 2. In Section 3, N_c^r of the local reverse bearing capacity failure near the skirt-tip will be derived using the limit analysis involving α_i and α_o. It should be noted that the critical penetration depth can be achieved when the critical suction pressure equals the required suction pressure by Eq. (1), which will be validated in Section 4.