Earth Pressure Distribution and Sand Deformation Around Modified Suction Caissons (MSCs) Under Monotonic Lateral Loading

The modified suction caisson (MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson (RSC). The MSC can provide larger lateral bearing capacity and limit the deflection compared with the RSC. Therefore, the MSC can be much more appropriate to use as an offshore wind turbine foundation. Model tests on the MSC in saturated sand subjected to monotonic lateral loading were carried out to investigate the effects of external structure sizes on the sand surface deformation and the earth pressure distribution along the embedded depth. Test results show that the deformation range of the sand surface increases with the increasing width and length of the external structure. The magnitude of sand upheaval around the MSC is smaller than that of the RSC and the sand upheaval value around the MSC in the loading direction decreases with the increasing external structure dimensions. The net earth pressure in the loading direction acting on the internal compartment of the MSC is smaller than that of the RSC at the same embedded depth. The maximum net earth pressure acting on the external structure outer wall in the loading direction is larger than that of the internal compartment, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure.


Introduction
A suction caisson is widely used in offshore engineering, such as petroleum exploration and productions in deep waters, floating platforms and jacket structures, which is extended to the offshore wind turbines (Bagheri et al., 2017;Chen et al., 2016;Zhang et al., 2018). Compared with the gravity-based foundation and the large diameter mono-pile, the suction caisson is very suitable to use in deep water because they can readily penetrate into seabed under the combination of the self weight and suction resulting from the encased water being gradually pumped out of the caissons (Li et al., 2015;Bienen et al., 2018).
Suction caissons acting as foundations of offshore wind turbines will be subjected to large horizontal loads from wind, waves and currents, while the vertical loads are relatively small. Therefore, the horizontal bearing capacity is an important consideration in suction caissons design (Zhang et al., 2017;Jalbi et al., 2018). In order to increase the lateral bearing capacity and reduce the lateral deflection, Li et al. (2010) proposed a modified suction caisson (MSC). The MSC consists of an internal compartment (the regular suction caisson) and an external structure (Fig. 1). Besides, Fig. 2 shows photos of the regular suction caisson (RSC) and the MSC models. There are four holes on the external skirt lid of the MSC to reduce the water resistance during the suction-assisted installation. Li et al. (2014) conducted a series of small-scale model tests to investigate the lateral bearing capacity of the MSC embedded in saturated marine fine sand. The results indicate that, under the load eccentricity of e/D=2.0, the ultimate lateral bearing capacities of MSCs enhanced by approximately 26.5% compared with the RSC. Besides, the lateral bearing capacity of the MSC increases with the increase of the external structure size and the internal compartment as-pect ratio. Furthermore, Li et al. (2014) found that the MSC rotates around a rotation center during the lateral loading, and the rotation center moves downward with the increasing load and lateral deflection, then it tends to stable when the limit load approaches. The rotation center of the RSC lies in about 0.8 times the length of the RSC, while it is approximately 0.55-0.7 times the length of the internal compartment for the MSC (Fig. 3).
The horizontal bearing capacity of suction caissons can be obtained based on the failure mechanism, the earth pressure distribution along the embedded depth, and the deformation range of the soil around the suction caisson (Byrne et al., 2002;Sun et al., 2010;Li et al., 2018). Although the MSC is a new type of foundation, we can borrow some ideas from the RSC to explore its bearing behavior. Sharma (2005) investigated the failure mechanism of the RSC under various load eccentricities by FEM. The results show that, during loading, the failure mechanism of the RSC and the deformation range of the soil around the RSC can be used to calculate bearing capacity of the RSC. Zhu et al. (2013) and Zhu (2011) conducted large-scale model tests on RSCs in saturated silt to investigate the interaction between soil and suction caisson wall and the deformation behavior of silt clay. Test results indicate that the incremental earth pressure along the outer caisson wall follows a binomial relationship with the embedded depth. In addition, Kumar and Rao (2010) performed laboratory tests on the earth pressure mobilization along the RSC embedded depth in soft clay. They found that the magnitude of the earth pressure at a certain depth increases with the increasing aspect ratio of the suction caisson; however, the loading eccentricity has little effect on the earth pressure distribution. Li et al. (2014) conducted an experimental study on the lateral bearing capacity of MSCs and RSC in saturated sand. Test results show that the deformation range increases with the load eccentricity increase. Furthermore, Zhang et al. (2016a) developed a three-dimensional continuum finite element model to investigate the soil deformation and earth pressure on the MSC during lateral loading. The results reveal that the lateral load and the overturning moment are mainly resisted by the soil in the upper passive earth pressure zone along the inner and outer shafts of the internal compartment and the external structure both in the loading and opposite the loading directions.
The objective of this study is to investigate the sand deformation behavior around MSCs and the earth pressure distribution along the internal compartment and the external structure of MSCs by conducting a series of model tests in saturated marine fine sand. It reveals the relationship between the incremental passive earth pressures and the deflection of MSCs. This study extends our previous research on the lateral bearing capacity of the MSC embedded in sand (Li et al., 2014(Li et al., , 2015Zhang et al., 2016aZhang et al., , 2016b.  Table 1 shows the size and self-weight of MSCs. In this study, the diameter of the internal compartment, D 1 ,   LI Da-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 198-206 199 equals 120 mm. The length of the internal compartment, L 1 , equals 240 mm; Thus, the value of the aspect ratio of the internal compartment, L 1 /D 1 , is equal to 2.0.

Tank and sand
The tank used has the dimensions of 1.0 m×1.0 m×0.8 m in length, width and height, whose dimensions were proved to be large enough to eliminate the boundary effects (Li et al., 2014;Zhang et al., 2016b). Besides, there is a ball valve placed at the bottom of the tank to control the water level in the tank, as shown in Fig. 4a.
The sand used was collected from the Gold Beach of Qingdao of East China. Physical properties of the sand are: specific gravity G s =2.69, mean grain size D 50 =0.097 mm, maximum void ratio e max =0.903, minimum void ratio e min =0.610, specific gravity G s =2.69 and buoyant unit weight γ'=10.2 kN/m 3 . For sand preparation, please refer to Li et al. (2014). The sand relative density can reach a value of 0.997. To make the test results reproducible, it is vital to keep each testing condition unchanged and keep the relative density of sand ground in the same state.

Transducers
As shown in Fig. 4a, lateral loads were applied through a steel wire over a pulley connected to weights. An LVDT (Linear Variable Differential Transformer) numbered LVDT1 was set horizontally to measure the lateral displacement of the loading point. LVDT1 was kept in line with the lateral loading wire. Besides, in order to establish the variation in the incremental earth pressures developed under the lateral loading, eight earth pressure cells with the range from 0 to 50 kPa were embedded along the internal compartment wall. In addition, as shown in Fig. 4b, there are seventeen transducers placed at the loading direction and opposite the loading direction to measure the deformation range for the sand surface and the vertical displacement of sand.
The lateral load was gradually applied by increasing the standard weights with a load incremental step of 2.1 N. It should be noted that when the deflection rate measured by LVDT1 is smaller than 0.0125 mm/10 min, and then the next load step was applied, indicating an evolving drainage (Zhang et al., 2017). To make the test results reproducible, it is vital to keep each testing condition unchanged, and each testing case will be carried out at least three times to insure the maximum error of maximum horizontal load within 5%. In this study, the ultimate lateral bearing capacity is defined as the load at which there is a continual increase in deflection without further increase in the load.

Lateral loaddeflection relationships
In this study, the lateral load is normalized as F/(2πR 3 γ'), where F is the force applied by the weights; R and γ' are the radius of the internal compartment of MSCs and the buoyant unit weight of sand, respectively. Fig. 5 gives the relationships between the lateral load and the deflection for the MSCs and the RSC under the loading eccentricity of e/D=1.0. Results indicate that the MSCs can significantly increase the lateral bearing capacity and reduce the lateral deflection, compared with the RSC.

Sand deformation
As shown in Fig. 6a, during the lateral loading, the sand being in the loading direction moves upwards, whereas that opposite the loading direction subsides. The subsidence range of the sand around MSCs is about (1.6-2.0)R. Besides, there is an upheaval region beyond the subsidence area. The reason is that the MSC rotates around a point during the lateral loading; thus, the sand at the bank of the MSC and in some depth below the ground surface are squeezed, resulting in the mobilization of passive earth pressure. It also can be found that the sand deformation was symmetric along the loading axis.
The deformation range of sand can be used to calculate  the lateral bearing capacity based on the strain wedge theory of limit equilibrium method (Li et al., 2014). As shown in Fig. 6b, L b and L f are the maximum upheaval ranges of sand opposite and in the loading directions (Section A), respectively. Besides, W f and W b are the maximum upheaval range of sand in Section B and Section C, respectively. The vertical displacement of the sand surface (V) around MSCs and the deflection of the loading point (H) for MSCs are normalized as V/D 1 and H/D 1 , respectively. Fig. 7 shows the measured vertical displacement of the sand surface around the MSC No. II-1D and the RSC. The magnitude of sand upheaval in the loading direction decreases with the increasing distance from the RSC edge, and it reaches zero at a distance of 300 mm, which is similar to the results shown in Fig. 7b for the MSC No. II-1D. In addition, Fig. 7c gives the sand surface upheaval in the loading direction around the MSCs and RSC in the limit state. The upheaval value of the sand surface increases with the increasing suction caisson deflection. The maximum upheaval value of the sand surface around the RSC is 6.35 mm, while the maximum upheaval values of the sand surface around MSCs Nos. II-1A, II-1C, II-1D, II-2C and II-2D are 6.15, 5.87, 5.60, 5.28 and 5.02 mm, respectively, indicating that the MSC can effectively control the sand deformation. In addition, the deflection of the MSC decreases with the increasing external structure dimensions, leading to the decrease of the sand upheaval value around the MSC in the loading direction (Fig. 5).   LI Da-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 198-206 201 Fig. 8 and Fig. 9 give the upheaval ranges of sand around MSCs in the loading direction and opposite the loading direction in the limit state. In the loading direction, the values of L f /D 1 and W f /D 1 increased with the increasing external structure length L 2 . The relationship between L f /D 1 and L 2 can be fitted by a linear function. Besides, the values of L b /D 1 and W b /D 2 of sand opposite the loading direction increase with the increase of the length of the external structure. However, the effect of the length of the external structure on the upheaval range of the sand surface is larger than that of the external structure width.

Earth pressure distribution along MSCs
It has been proved that the maximum excess pore pressure along the outer caisson wall was extremely small (approximately equals 0.3-0.4 kPa) (Zhang et al., 2017). Therefore, the influence of excess pore pressure on the earth pressure was neglected.
In this study, the earth pressure acting on the suction caissons is normalized as P/(γ'D 1 ), where P is the earth pressure acting on the suction caissons; D 1 and γ' are the diameter of the internal compartment of the MSC and the buoyant unit weight of sand, respectively. Figs. 10 and 11 give the distributions of the incremental earth pressure along the RSC and the MSC No. II-1D embedded depths, respect-ively. As shown in Fig. 10a, the induced incremental earth pressures acting on the outer caisson wall of RSC in the loading direction with the depths of 40, 90, and 140 mm below the RSC top lid are positive, indicating that these earth pressure cells are in the passive zone. Moreover, the incremental earth pressure along the RSC outer wall follows a binomial relationship with the embedded depth under various lateral deflections of RSC. However, at the depth of 190 mm below the top lid of RSC, the value of incremental earth pressure is negative, indicating that the earth pressure cell is in the active earth pressure zone. However, the earth pressure cell being located at the depth of 190 mm opposite the loading direction is in the passive earth pressure zone (Fig. 10b). Fig. 11 presents the incremental earth pressures distributions along the outer wall of the internal compartment of MSC No. II-1D. The maximum passive earth pressure acting on the outer wall of the RSC in the loading direction is 9.6 kPa, while the maximum passive earth pressure acting on the internal compartment of MSC No. II-1D is 7.7 kPa. The reason is that the external structure can resist a portion of the lateral load, causing the reduction of the earth pressure acting on the internal compartment of the MSC.
In this study, the positive sign of the values of the incremental earth pressures indicates that the earth pressure cell is in the passive earth zone. On the contrary, the earth pres-  sure cell is in the active earth pressure zone when the value of the incremental earth pressure is negative. The position where the incremental earth pressure equals zero can be regarded as the rotation center. As shown in Fig. 12a, the incremental passive earth pressure acting on the external structure in the loading direction increases with the increasing embedded depth. The incremental earth pressures are positive, indicating that these earth pressure cells are in the passive earth pressure zone. However, the incremental earth pressures acting on external structure opposite the loading direction are negative, which means that the earth pressure cells are located in the active earth pressure zone (Fig. 12b). Fig. 13 gives the net earth pressure distributions along the internal compartment and the external structure of MSCs in the limit state. The net earth pressures along the suction caisson embedded depths were calculated by using the method proposed by Prasad and Chari (1999). It can be observed that, in the loading direction, with the increase of the external structure length the net earth pressure acting on the internal compartment of MSCs gradually decreases under a given external structure width D 2 . Moreover, the magnitudes of the net passive earth pressures acting on the in-   LI Da-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 198-206 203 ternal compartment of MSCs are smaller than those of the RSC at the same embedded depth. However, the values of net earth pressure significantly increase as L 2 increases opposite the loading direction, and these values are larger than that of the RSC. This is because the MSC can considerably increase the lateral bearing capacity, which results in the large soil resistance and the large passive earth pressure.
Results also show that, in the loading direction, the maximum net earth pressure acting on the external structure outer wall is larger than that of the internal compartment and that of RSC, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure. Fig. 14 demonstrates the curves of the incremental passive earth pressure along the embedded depth and the deflection of suction caissons. The incremental passive earth pressures acting on the internal compartment of MSC No. II-1D and RSC first increase up to the maximum value with the increase of the embedded depth. Subsequently, a reduction in the incremental passive earth pressure was observed with the further increasing embedded depth. The maximum increment passive earth pressure was obtained when the embedded depth equals 0.37L 1 for RSC, while it is 0.58L 1 for MSC No. II-1D.

Effects of the lateral deflections of the MSCs on the earth pressure values
The RSC and the MSCs rotate around a rotation center during the lateral loading (Li et al., 2014;Zhang et al., 2017). Therefore, the failure mechanism of suction caissons in the upper zone of the rotation center can be investigated by borrowing some ideas from a retaining wall and laterally loaded piles (Keshavarz and Ebrahimi, 2017;Ni et al., 2018). Mei et al. (2009) proposed an expression to obtain the earth pressure acting on a retaining wall with various lateral deflections. The following assumptions were made: the lateral deflections range from s a to s p (s a and s p are the corresponding later deflections when the active earth pressure and the passive earth pressure are mobilized); and the earth pressure at a certain depth increases with the increasing lateral deflection. Thus, the expression can be given as:

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LI Da-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 198-206 where P 0 is one half of the value of the earth pressure at rest, k 0 is the coefficient of the earth pressure at rest, k a and k p are referred to as the active and passive earth pressure coefficients, respectively. In addition, s is the lateral deflection of a retaining wall at a certain depth. Therefore, the values of K, b, and P 0 can be obtained from the corresponding earth pressures for three different lateral deflections of raining wall at a certain embedded depth. If s 2 =2s 1 and s 3 =3s 1 (s 1 , s 2 , and s 3 are the corresponding lateral deflections of suction caissons at three different tilting states), expressions for K, b, and p 0 can be given as: where (the plus sign is taken for the active state and the minus sign is taken for the passive state) and Table 2 and Table 3 illustrate the comparison between the test results on the incremental passive earth pressure acting on the RSC and MSC No. II-1D and the calculated results obtained by using Eq. (1), respectively. It can be seen that the maximum error range between the experimented and the calculated results is 32.2%. However, under the deflection of suction caissons smaller than 1 mm, the error between the experimented and the calculated passive earth pressure is relatively large. Furthermore, Fig. 15 gives the errors between the measured and calculated increment passive earth pressure for MSCs under various external structure dimensions. Results indicate that the error ranges from 3% to 20% and the average error is approximately 8.5%, indicating that the calculated results agree well with the experimental results. However, it should be noted that when the embedded depth of the earth pressure cell is smaller than 0.37L, the corresponding maximum lateral deflections are approximately 0.18D 1 and 0.3D 1 for the MSC and the RSC, respectively. Moreover, when the embedded depth of the earth pressure cell equals 0.58L, the corresponding maximum lateral deflection is about 0.06D 1 . When the lateral deflections of the suction caissons at different embedded depths are beyond the above-mentioned ranges, the error will up to more than 20%.

Conclusions
The modified suction caissons (MSCs) have the advantages of higher bearing capacity, and lower lateral deflection compared with regular suction caisson. In this study, the model tests on MSCs subjected to monotonic lateral loading in saturated sand were conducted to investigate the ef- LI Da-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 198-206 205 fects of the external structures on the sand deformation around MSCs and the earth pressure distribution along the outer wall of MSCs embedded depth. The following conclusions are drawn: (1) The sand surface in the loading direction moves upwards, whereas that opposite the loading direction subsides. Moreover, there is an upheaval region beyond the sand subsidence area opposite the loading direction. The upheaval ranges of sand around MSCs both in the loading and opposite the loading directions increase linearly as the length of the external structure increases.
(2) The external structure considerably reduces the net earth pressure acting on the internal compartment of MSCs in the loading direction, compared with that of RSC at the same embedded depth. However, the net earth pressure acting on the MSC opposite the loading direction is larger than that of RSC at the same embedded depth. In addition, the magnitude of the net earth pressure acting on the external structure of MSCs increases with the increase of the external structure lengths.
(3) Comparisons between the experimented and calculated results show that the model proposed by Mei is applicable to predict the incremental passive earth pressure acting on the internal compartment in the loading direction for RSC and MSCs embedded in the saturated fine sand under lateral loading. The results indicate that the average error between the experimented and calculated incremental passive earth pressure is about 6.5%. Fig. 15. Errors between the measured and calculated results of the passive earth pressure.