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The initial wave induced failure of silty seabed: Liquefaction or shear failure
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The initial wave induced failure of silty seabed: Liquefaction or shear failure Yupeng Ren a, b, Guohui Xu a, b, *, Xingbei Xu a, b, Tianlin Zhao a, b, Xinzhi Wang a, b a b
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, China Laboratory for Marine Geology, Qingdao National Laboratory for Marine Science and Technology, Qingdao, 266061, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Silty soil Pore-water pressure Consolidation time Initial failure Liquefaction development patterns
A silty seabed can be destabilized in two ways under wave loading: by liquefaction or shear failure. In this paper, the wave-induced initial failure mode of a silty seabed under different consolidation conditions is studied using flume experiments. Through a comparison of the pore water pressure, initial failure, and liquefaction develop ment patterns in a relatively soft and dense seabed, it is found that liquefaction is responsible for the initial failure of the soft seabed, while shear failure is responsible for the initial failure of the dense seabed. Liquefaction progresses from the surface and gradually downward in the soft seabed, but it propagates from the interface where the shear failure occurs in the dense seabed.
1. Introduction Silty seabed liquefaction caused by the cyclical loading of a hurri cane or storm on the seafloor is considered to be one cause of the damage to the subaqueous delta slopes of the Mississippi River and Yellow River. However, the exact mechanism of this damage has not been studied in depth (Coleman et al., 1998; Prior et al., 1986). The effect of wave action on the seabed can cause the liquefaction or sliding of the seabed, which will cause significant damage to marine structures. In 1969, channel 70 and platform 3 in the southern part of the Mississippi submarine delta were damaged by seabed sliding caused by Hurricane Camille (Prior and Suhayda, 1979). Research on the lique faction of seabed soils caused by waves is mainly based on the variation in the pore water pressure in the soil, and the identification of lique faction is based on the effective stress principle. The law of the variation in the pore water pressure in the soil can be obtained through the analysis of the dynamic response of the seabed soil under the effects of wave loading, which is based on the consolidation theory equation. Additionally, applications of the effective stress principle are used for liquefaction identification (Luan et al., 2004; Wang et al., 2001). In addition, many field measurements of the pore pressure were used to study wave-induced soil liquefaction problems (Groot et al., 2006; Jotisankasa et al., 2015; Miyamoto et al., 1989; Tang et al., 2015; Zen and Yamazaki, 1991). Sassa (Sassa and Sekiguchi, 1999; Sassa et al., 2001) used a centrifuge test and a calculation, which was based on the
effective stress principle, to propose that the liquefaction of the seabed under wave action propagates downward from the surface. Moreover, wave flume experiments have also indicated the validity of the devel opment model (Ren et al., 2017; Sumer et al., 2012). In addition, a numerical method was used to describe the downward progression of liquefaction in the loose sand of the seabed under wave action (Wang et al., 2015). With the development of marine resources and the con struction of marine structures, to increase the protection of these structures, recent research on liquefaction has mainly focused on the soils surrounding marine structures, such as submarine pipes and marine pile foundations. Previous studies have shown that, previous studies have shown that when pipelines are buried in the seabed, the soil around the pipelines is more prone to liquefaction (Lin et al., 2016, 2017; Sui et al., 2019; Sumer et al., 2006; Sun et al., 2019; Dunn et al., 2006; Zhao et al., 2016). When the bed liquefies, the pipelines buried in the bed will be exposed to the liquefied fluidized soil and face a greater threat of being damaged. The newly deposited soil has a high moisture content and a low strength. Under a long duration of wave action, the soil is consolidated. With the progress of consolidation, the moisture content of the soil de creases and the strength increases. This consolidation may lead to complex stress distributions in the bottom bed (Jian et al., 2017; Sui et al., 2017; Ye, 2012). The form of seabed failure that occurs under wave action depends on the type of soil, the state of soil consolidation, and the intensity of the wave action. In addition, the damage zones
* Corresponding author. Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, China. E-mail address: [email protected] (G. Xu). https://doi.org/10.1016/j.oceaneng.2020.106990 Received 22 August 2019; Received in revised form 15 January 2020; Accepted 17 January 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.
Please cite this article as: Yupeng Ren, Ocean Engineering, https://doi.org/10.1016/j.oceaneng.2020.106990
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Fig. 1. Schematic diagram of the flume test device.
caused by different failure modes and the methods of evaluating the failure also differ based on these factors (Taiba et al., 2016; Wang et al., 2016; Zen et al., 1998). The limit equilibrium method can be used to analyze the variation in the seabed wave pressure. The results of this method show that the seabed can be sheared, causing damage from submarine sliding (Henkel, 1970; Zhang et al., 2016). Many methods have been used to judge the shear slip of the seabed, in which the effect of excess pore water pressure in the soil cannot be ignored (Gu, 1989). Especially when the pile foundation and other structures are buried in the bed, the change of pore water pressure around the pile foundation is different from that of the soil in other places, and the shear failure is more likely to occur around the pile foundation, rather than at the lower part of the pile foundation (Sui et al., 2017). Experimental and computational studies have shown that even for a flat seabed, arc shear failure may occur under the conditions of a pres sure difference between the wave crest and trough. Some scholars have also described the process and morphology of the circular arc shear failure of the seabed (Chang and Jia, 2010; Xu et al., 2009b). Especially when there are structures such as piles in the seabed after consolidation, shear failure is more likely (Chang and Jeng, 2014; Sui et al., 2017). In summary, the present study shows that a flat silty soil seabed can not only undergo liquefaction damage but also shear damage. However, the reasons for this difference are not clear. Whether or not it is due to the initial consolidation state of the seabed soil is worth considering. For silty soil, if it has undergone consolidation, it is well constructed due to the interaction of fine particles and clay, and its internal structure will
produce cohesion. Damage to a consolidated silty seabed under wave cyclic loading is the result of the constant undermining of its structure. In the case where the volume of the soil is not compressed, the process of soil structural failure does not necessarily produce an increase in the pore water pressure. However, if the silty seabed is not consolidated, the soil particles cannot form a structural connection, so the pore water pressure accumulates, and the response of the soil under wave loading should be similar to that of sand. Thus, for a silty seabed, the initial failure pattern may be different under wave loading due to the difference in the degree of consolidation. When the degree of consolidation is high, shear failure may occur first. However, if the seabed is not consolidated, the loose seabed material may accumulate pore water pressure, and liquefaction failure may occur first. Therefore, in this paper, flume experiments were carried out on a silty seabed with different degrees of consolidation to study the initial failure mode. The results of these experiments provide an explanation for the initial failure mechanism of the subaqueous deltas of the Mis sissippi River and the Yellow River. 2. Flume experiments The experiments were carried out in a wave flume that was 0.5 m in width, 1.2 m in depth, and 14 m in length. Uniform regular waves were produced using a piston-type wave generator. The water depth was maintained at 40 cm, and the soil was placed in a 0.6 m deep and 2.6 m long box (Fig. 1). Two tests were carried out. In test 1, the seabed
Fig. 2. Schematic diagram of the probe placements. 2
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Table 1 The order in which the waves were applied in the tests. Test 1
Test 2
H ¼ 6 cm (low wave height) for 90 min H ¼ 10 cm (medium wave high) for 240 min H ¼ 18 cm (high wave height) to the end of the test
H ¼ 6 cm (low wave height) for 11 min H ¼ 9 cm (medium wave high) for 60 min H ¼ 14 cm (high wave height) to the end of the test
Table 2 Liquefaction process in the seabed. Test 1
Test 2
No liquefaction was observed at the initial wave height H ¼ 6 cm No liquefaction was observed at the wave height H ¼ 10 cm
Liquefaction was observed at the initial wave height H ¼ 6 cm liquefaction displayed downward development at the wave height H ¼ 9 cm liquefaction displayed downward development at the wave height H ¼ 14 cm
Liquefaction was observed at the wave height H ¼ 18 cm and liquefaction developed downward
Fig. 3. Particle size grading curve of the test soil.
with d50 ¼ 0.052 mm and a clay content of 10% (Fig. 3). The silty soil retrieved from the Yellow River Delta is screened for impurities and then, in the form of a remolded soil, a certain percentage of the silty soil and water are mixed into a slurry, ensuring a water content of approximately 32% (as close to 32% as possible to produce an even test bed). Then, we transferred the slurry into the flume in batches to create a seabed measuring 2 m � 0.5 m � 0.6 m. After laying the seabed, we added water to a depth of 40 cm. Test 1 was left standing for 7 days, and the consolidation time was long. In test 2, the seabed was left to stand for only 4 h, and it did not undergo consolidation. Before the wave was initiated, the content and penetration resistance were measured at different depths in the two experiments (Fig. 4a). In addi tion, the cohesion c and internal friction angle φ of the soils in the two test beds were determined by a direct shear test (Fig. 4b). The results show that the consolidation, strength, and compactness of the seabed in test 1 were higher than those in test 2 (the bottom bed of test 1 was “dense” and the bottom bed of test 2 was “soft”). In addition, in the early stage of test 1, the application of small waves resulted in the dynamic consolidation of the test bed bedrock soil, which made the soil more compact than that at the beginning of the test. The waves imposed by the two tests mainly simulate three wave conditions: low wave height, medium wave height and high wave height. The wave height was gradually increased according to the observed state of the soil and pore pressure changes (in test 1, the wave height was increased after the point at which the seabed was unbroken and the pore pressure of the soil stabilized). The sequence applied in the two experiments is shown in Table 1.
(a) Comparison of the soil moisture and penetration resistance of the two tests
3. Test results In the two experiments, the differences in the initial failure range and the variation of the pore water pressure in the seabed were due to the different consolidation degrees of the test seabed. 3.1. Initial failure of the seabed and the development of liquefaction
(b) Cohesion of soil in two tests
The initial failures of the tests of seabed 1 and 2 were significantly different (Table 2). In test 1, in which the degree of consolidation of the seabed was relatively high, the bottom bed did not liquefy under the action of the smaller waves, and the soil at a depth of 16 cm was observed to fluctuate from the sidewall of the flume when the wave height was 18 cm. In test 2, in which the seabed consolidation was relatively low, we observed that the soil at a depth of 8.5 cm fluctuated under the action of the waves with a wave height of 6 cm. After the
Fig. 4. Soil parameters of the bottom bed in two tests.
underwent consolidation, but for test 2, it did not. The pore pressure probe is fixed in the vertical direction at different depths of the seabed (Fig. 2). To ensure the authenticity of the test results, the soil used for the experiments was an original sample of silt from the Yellow River Delta 3
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Fig. 5. Liquefaction progress of the seabed in the two tests.
The beginning of the initial failure of the seabed was taken at time 0, and the liquefaction depths of tests 1 and 2 were plotted versus time to display the evolution of the liquefaction depth (Fig. 6). In test 1, after the initial failure of the seabed, the liquefaction depth gradually increased and finally reached the maximum liquefaction depth for a wave height of 18 cm. For test 2, the depth of liquefaction increased rapidly since the initial failure of the seabed occurred at H ¼ 6 cm, reached a stable depth, and then for the larger wave heights of 9 cm and 14 cm, the liquefaction depth continued to increase until the maximum liquefaction depth was reached. 3.2. Pore water pressure variation in the test seabed For test 1, at wave heights of 6 cm and 10 cm, the pore water pressure value was stable at different depths of the seabed. When the wave height increased to 18 cm, the soil structure was destroyed, and the pore water pressure increased rapidly at a depth of the 21 cm of the seabed. After the initial failure of the seabed, the pore water pressure of the under lying non-liquefied soil accumulated for a long duration of time. In test 2, when the wave action was applied at a height of H ¼ 6 cm, the pore water pressure at all depths increased rapidly. The accumulated soil pore water pressure in the upper layer (25 cm deep) was larger than that in the lower layer (35 cm and 45 cm deep). When the wave height was 9 cm, the pore water pressure in the soil continued to accumulate, and the growth rate of the upper soil layer was smaller due to its ten dency to liquefy, while the growth of the lower soil mass was larger. When the wave height was 14 cm, the upper soil had already liquefied, so the pore water pressure remained stable, while the pore water pres sure of the lower soil (because it had not liquefied) continued to
Fig. 6. Variation in the liquefaction depth with time in the two tests.
initial failure of the two soils in the test seabed, the liquefaction process exhibited a gradual downward development. In the experiments, the liquefaction depth was determined by observing the fluctuation through the wall of the flume. The depth of the soil liquefaction development is represented by the position of the soil fluctuation as observed through the wall of the flume. The initial liquefaction depth and the depth of the downward evolution of the liquefaction observed in the test are indicated on the sidewalls of the flume depicted in Fig. 5. 4
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During test 1, the initial failure of the soil was accompanied by a rapid increase in the pore water pressure. However, in test 2, when the wave was applied, the pore water pressure increased. When the wave became stable, the pore water pressure continued to accumulate. Thus, before the initial failure of the bed, the pore water pressure will increase. Then, the internal pore water pressure will continue to accumulate after the wave height increases, and the accumulation will be slower and will last longer. After the initial failure of the seabed soil in the two tests, the lique faction of the bottom of the seabed develops under the cyclic loading of the waves, and the pore water pressure in the undrained soil increases. After the initial failure of the seabed in the two tests, the change in the pore water pressure with time under the continuous load of the wave is shown in Fig. 8. It can be seen from Fig. 8 that with the continuous loading of the waves, after the initial failure, the increase in the pore water pressure of the undrained soils of the two tests are stable and accumulate slowly and continuously.
Table 3 Changes in the pore water pressure of the seabed during the tests. Test 1
Test 2
When H ¼ 6 cm the pore water pressure of the soil remained stable, and no obvious increase was observed. When H ¼ 10 cm the soil pore water pressure still remained stable.
When H ¼ 6 cm the pore water pressure began to obviously increase in all layers of the seabed. When H ¼ 9 cm the pore water pressure of the soil continued to increase, and the accumulative velocity accelerated. When H ¼ 14 cm the pore water pressure of the upper soil layer was stable, while that of the lower soil layer continued to increase.
When H ¼ 18 cm, the pore water pressure began to increase in all layers of the seabed.
accumulate(See. Table 3). When the soil liquefied, the pore pressure was characterized by a rapid increase and a large fluctuation amplitude. According to these characteristics, the time of liquefaction recorded by the probe inside the soil is earlier than that observed through the wall of the flume. In view of the constraining effect of the fixed wall on the soil, the fluctuation of the liquefaction of the soil observed through the wall should lag behind the fluctuation of the interior soil. The initial failure observed in the two tests and the variations in the pore water pressure of the seabed were significantly different. The change in the pore water pressure with time as recorded by the upper most probe for the two tests is shown in Fig. 7.
4. Discussion The mechanism of the initial failure of the seabed is shear failure or liquefaction, and the failure mechanism is different depending on the consolidation of the soil. There should be differences in the failure morphology and pore water pressure in the soil (Zen et al., 1998).
Fig. 7. The change in the pore water pressure with time as recorded in the uppermost layer of the seabed.
Fig. 8. Changes in the pore water pressure with time at different depths. 5
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Excess pore water pressure
Fig. 10. Schematic diagram of the Arc shear failure mode (Note: This figure was first seen in Xu (2006), and this article has been revised on this basis).
Fig. 9. Schematic diagram of the cumulative pore water pressure distribution along a depth in the bed. (Note: this figure was first proposed byIshihara and Yamazaki (1984) and is modified on the basis of Gao et al. (2011). In the figure, c0 is the initial cohesion of the bed; σ is the overlying stress; φ0 is the initial internal friction angle; ce is the cohesion after attenuation under the continuous wave load; φe is the in ternal friction angle after attenuation under the continuous wave load).
4.1. The analysis of shear failure of the seabed under wave action Without considering the soil viscosity, the shear strength of the soil is
τ ¼ σ ⋅tan φ0 (where σ is the overlying stress and φ is the internal friction
angle). For this type of soil, regardless of the distribution of the excess pore water pressure in the soil in the bed, failure occurs from the surface. However, for silty soil, because there is a certain amount of clay in it, the cohesion of the soil should be considered and the shear strength should be τ ¼ c0 þ σ⋅tan φ0 . For silty soil with a continuous wave loading, when the bottom bed is not damaged, the cohesion c and internal fric tion angle φ of the silty soil decrease with increasing load times and tend to gradually stabilize (Xu et al., 2009a). In the process of the test, the influence of the cyclic wave load on the soil mass and on the bed depth is gradually weakened. At the same time, the excess pore water pressure in the seabed increases first and then increases from the surface of the seabed to the bottom. If it is assumed to be below the depth z ¼ zl , the influence of the wave load on the bed soil mass has been ignored. The distribution of the excess pore water pressure and the change of the shear strength of the soil with depth after loading are shown in Fig. 9. Under the condition of a low wave height, no liquefaction occurs in the soil. This indicates that the excess pore water pressure in the bed does not reach the effective stress of the overlying layer, but this does not mean that there is no excess pore water pressure in the bed. Under the continuous load of the wave, the cumulative pore water pressure in the bed first increases and then decreases with increasing depth. At the same time, with the continuous load, the cohesion and internal friction angle inside the bed soil are also decreasing, which leads to a decrease in the shear strength of the soil. This change occurs at the same time as the change of the accumulated pore water pressure in the bed and under the action of the overlying wave shear force, which in theory can cause the bed to shear at a certain depth (the weak point of the bed). The theo retical diagram of the arc shear failure of the bed is shown in Fig. 10: After the shearing of the weak point of the bed, the soil around the shearing point is destroyed. Then, under the action of the shearing force generated between the wave trough and wave crest, the surface of the soil is stretched when the wave trough arrives and compresses when the wave crest arrives. Shear failure occurs in the whole block after several periods of oscillation.
Fig. 11. Arc shearing failure diagram (Henkel, 1970).
4.2. Initial damage area of the silty seabed under wave action Low-grade slopes or flat seabeds experience shear sliding under wave action (Henkel, 1970; Xu et al., 2009b), and the limit equilibrium method can be used to calculate the range of the sliding area. For tests 1 and 2, the initial mode is assumed to be shear failure, and the calculation of the failure area is performed using Henkel’s (Henkel, 1970) wave-induced seabed slip calculation model (Fig. 11). When the soil is in the limit equilibrium state, the soil stability safety factor can be expressed as F ¼ Mr/Md. Where Mr is the anti-skid torque 0 0 and can be expressed as Mr ¼ 2x3 ðcu =γ zÞγ ðsin θ θ cos θÞ=sin3 θ; and 0 Md is the slip torque and can be expressed as Md ¼ 2x3 βγ =3 þ ðL2 ΔPÞðsin α α cos αÞ=2π2 . The relationship between x, d, and θ can be expressed as follows: d= x ¼ ð1 cos θÞ=sin θ. In this case, α ¼ 2πx=L, β is the slope angle of the 0 seabed, Δp is the wave pressure amplitude, and k ¼ cu =γ z is the soil strength characterization coefficient. Since the test bed was flat, the inclination angle β was zero. The wave and bed parameters at the time of the initial failure of the two tests are shown in Table 4. During test 1, the vane shear test was carried out, both when the soil was already liquefied and not liquefied. The k of the obtained soil was calculated using the vane shear strength cu obtained from the experiment. The seabed in test 2 was not consoli dated, and its shear strength is similar to the that of the liquefied seabed 6
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5. Conclusion
Table 4 Wave and seabed corresponding to the initial failure of the bed during the two experiments. Parameters
Test 1
Test 2
Water depth h Wave height H Wavelength L Density of soil ρ2 Soil strength characterization coefficient k
0.4 m 0.18 m 1.9 m 1.91 g/cm3 0.05–0.11 (The value is 0.07)
0.4 m 0.06 m 4.3 m 1.85 g/cm3 0.03–0.05 (The value is 0.04)
In this study, two wave flume tests are carried out. The difference between the two tests is the consolidation degree of the test beds. Under the wave action, the two tests show different results. Through the analysis and discussion of the test results, the following conclusions are obtained: (1) Under the wave actions, the initial failure pattern of the crusty silty seabed with different degrees of consolidation is obviously different. The concrete manifestation of this finding is as follows: the relatively dense seabed experienced shear failure under the action of the waves and the initial damage of the relatively soft seabed is due to cumulative liquefaction damage. (2) After the initial failure of the soil, the silty soil seabed continued to liquefy under the wave action in a top-down progression. (3) Under the action of a continuous wave load, the silty soil bed without damage appears to be damaged, which reduces its cohesion and internal friction angle and reduces the shear strength of the bed, thus providing conditions for the shear failure of the bed. (4) As a special type of soil, some structural changes will take place during the consolidation process, which will make the silty soil bed present different failure forms under the wave action; this topic will be the focus of subsequent research.
Table 5 Failure zone parameters calculated from the shear failure.
Test 1 Test 2
Parameters
Width
Difference ratio
Test value
1.70 m 1.50 m 0.30 m 1.50 m
11%
Calculated values Test value Calculated values
Depth 0.16 m
Difference ratio 0%
0.16 m 400%
0.085 m 0.15 m
76%
in the tests. The results can be calculated as follows: under the conditions of test 1, the calculated shear width is 1.5 m, and the shear depth is 0.16 m and under the conditions of test 2, the calculated shear width is 1.5 m, and the shear depth is 0.15 m. The comparison between the experimental results and the calculated results is shown in Table 5. From an the point of view of the error of the calculation results and test results, test 1 is in good agreement with the shear failure mode but test 2 is clearly not in agreement with the shear failure mode.
Author contributions section Yupeng Ren:Conceptualization, Methodology, Experiments, WritingOriginal draft preparation. Guohui Xu: Supervision, Writing- Reviewing and Editing, Guidance. Xingbei Xu: Experiments, Visualization, Software. Tianlin Zhao: Experiments, Editing, Validation. Xinzhi Wang: Experiments, Writing- Reviewing and Editing.
4.3. Analysis of the pore water pressure during the initial failure test
Declaration of competing interest
Two tests for the upper probe (probe A, probe a) that measured pore water pressure are shown in Fig. 7. Comparative analyses were per formed for the two pore water pressure data sets, when there is initial soil damage in the two tests, the pore water pressure has a certain jump, but the tests differ significantly in the time of the destruction process. In experiment 1, the pore water pressure began to increase until the initial failure of the soil and it has a certain time course, which lasted 10 s. In contrast, in experiment 2, the initial pressure of the soil was applied while the wave was applied, and the pore water pressure increased, but it lasted for 0 s. This indicates that the soil is destroyed because the pore water pressure increases. Then, the waves are subjected to several cycles of wave loading, and the soil becomes completely liquefied and con forms to the characteristics of shear failure. However, in test 2, the seabed has a certain structure before the wave loading, along with the beginning of the wave loading, the soil instantly loses its structure, and the initial destruction does not have a time course, so it does not meet the characteristics of shear damage. After the initial failure of the seabed, the change of the pore water pressure in the non-liquefied seabed is shown in Fig. 8. The pore water pressure in the non-liquefied seabed showed a slow, steady accumulation. Considering the characteristics of the pore water pressure change and the progress of the liquefaction depth after the initial failure of the two tests (Fig. 6), it can be seen that after the initial failure of the seabed, the liquefaction modes of both tests showed a gradual liquefaction process until the maximum liquefaction depth was reached.
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Jotisankasa, A., Mahannopkul, K., Sawangsuriya, A., 2015. Slope stability and porewater pressure regime in response to rainfall: a case study of granitic fill slope in northern Thailand. Geotech. Eng. 46 (1), 45–54. Lin, Z., Guo, Y., Jeng, D., Liao, C., Rey, N., 2016. An integrated numerical model for wave–soil–pipeline interactions. Coast. Eng. 108, 25–35. Lin, Z., Pokrajac, D., Guo, Y., Jeng, D.-s., Tang, T., Rey, N., Zheng, J., Zhang, J., 2017. Investigation of nonlinear wave-induced seabed response around mono-pile foundation. Coast. Eng. 121, 197–211. Luan, M., Zhang, C., Wang, D., Guo, Y., 2004. Numerical analysis of residual pore water pressure development and evaluation of liquefaction potential of seabed under wave loading. J. Hydraul. Eng. 2, 94–100. Miyamoto, T., Yoshinaga, S., Soga, F., Shimizu, K., Kawamata, R., Sato, M., 1989. Seismic prospecting method applied to the detection of offshore breakwater units settling in the seabed. Coast Eng. J. 32 (1), 103–112. Prior, D.B., Suhayda, J.N., 1979. Application of infinite slope analysis to subaqueous sediment instability, Mississippi delta. Eng. Geol. 14 (1), 1–10. Prior, D.B., Yang, Z., Bornhold, B.D., Keller, G.H., Lu, N., Wiseman, W.J., Wright, L.D., Zhang, J., 1986. Active slope failure, sediment collapse, and silt flows on the modern subaqueous Huanghe (Yellow River) delta. Geo Mar. Lett. 6 (2), 85–95. Ren, Y., Fang, H., Xu, G., Xu, X., 2017. Wave pressure on the boundary of liquefied silty seabed under wave loading. Acta Oceanol. Sin. 39 (1), 89–95. Sassa, S., Sekiguchi, H., 1999. Wave-induced liquefaction of beds of sand in a centrifuge. Geotechnique 49 (5), 621–638. Sassa, S., Sekiguchi, H., Miyamoto, J., 2001. Analysis of progressive liquefaction as a moving-boundary problem. Geotechnique 51 (10), 847–857. Sui, T., Zhang, C., Jeng, D., Guo, Y., Zheng, J., Zhang, W., Shi, J., 2019. Wave-induced seabed residual response and liquefaction around a mono-pile foundation with various embedded depth. Ocean. Eng. 173, 157–173. Sui, T., Zheng, J., Zhang, C., Jeng, D., Zhang, J., Guo, Y., He, R., 2017. Consolidation of unsaturated seabed around an inserted pile foundation and its effects on the waveinduced momentary liquefaction. Ocean. Eng. 131, 308–321. Sumer, B.M., Ozgur Kirca, V.S., Fredsøe, J., 2012. Experimental validation of a mathematical model for seabed liquefaction under waves. Int. J. Offshore Polar 22 (2), 133–141. Sumer, B.M., Truelsen, C., oslash, Freds, Oslash, R., 2006. Liquefaction around pipelines under waves. J. Waterw. Port Coast. 132 (4), 266–275.
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The initial wave induced failure of silty seabed: Liquefaction or shear failure Yupeng Ren a, b, Guohui Xu a, b, *, Xingbei Xu a, b, Tianlin Zhao a, b, Xinzhi Wang a, b a b
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, China Laboratory for Marine Geology, Qingdao National Laboratory for Marine Science and Technology, Qingdao, 266061, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Silty soil Pore-water pressure Consolidation time Initial failure Liquefaction development patterns
A silty seabed can be destabilized in two ways under wave loading: by liquefaction or shear failure. In this paper, the wave-induced initial failure mode of a silty seabed under different consolidation conditions is studied using flume experiments. Through a comparison of the pore water pressure, initial failure, and liquefaction develop ment patterns in a relatively soft and dense seabed, it is found that liquefaction is responsible for the initial failure of the soft seabed, while shear failure is responsible for the initial failure of the dense seabed. Liquefaction progresses from the surface and gradually downward in the soft seabed, but it propagates from the interface where the shear failure occurs in the dense seabed.
1. Introduction Silty seabed liquefaction caused by the cyclical loading of a hurri cane or storm on the seafloor is considered to be one cause of the damage to the subaqueous delta slopes of the Mississippi River and Yellow River. However, the exact mechanism of this damage has not been studied in depth (Coleman et al., 1998; Prior et al., 1986). The effect of wave action on the seabed can cause the liquefaction or sliding of the seabed, which will cause significant damage to marine structures. In 1969, channel 70 and platform 3 in the southern part of the Mississippi submarine delta were damaged by seabed sliding caused by Hurricane Camille (Prior and Suhayda, 1979). Research on the lique faction of seabed soils caused by waves is mainly based on the variation in the pore water pressure in the soil, and the identification of lique faction is based on the effective stress principle. The law of the variation in the pore water pressure in the soil can be obtained through the analysis of the dynamic response of the seabed soil under the effects of wave loading, which is based on the consolidation theory equation. Additionally, applications of the effective stress principle are used for liquefaction identification (Luan et al., 2004; Wang et al., 2001). In addition, many field measurements of the pore pressure were used to study wave-induced soil liquefaction problems (Groot et al., 2006; Jotisankasa et al., 2015; Miyamoto et al., 1989; Tang et al., 2015; Zen and Yamazaki, 1991). Sassa (Sassa and Sekiguchi, 1999; Sassa et al., 2001) used a centrifuge test and a calculation, which was based on the
effective stress principle, to propose that the liquefaction of the seabed under wave action propagates downward from the surface. Moreover, wave flume experiments have also indicated the validity of the devel opment model (Ren et al., 2017; Sumer et al., 2012). In addition, a numerical method was used to describe the downward progression of liquefaction in the loose sand of the seabed under wave action (Wang et al., 2015). With the development of marine resources and the con struction of marine structures, to increase the protection of these structures, recent research on liquefaction has mainly focused on the soils surrounding marine structures, such as submarine pipes and marine pile foundations. Previous studies have shown that, previous studies have shown that when pipelines are buried in the seabed, the soil around the pipelines is more prone to liquefaction (Lin et al., 2016, 2017; Sui et al., 2019; Sumer et al., 2006; Sun et al., 2019; Dunn et al., 2006; Zhao et al., 2016). When the bed liquefies, the pipelines buried in the bed will be exposed to the liquefied fluidized soil and face a greater threat of being damaged. The newly deposited soil has a high moisture content and a low strength. Under a long duration of wave action, the soil is consolidated. With the progress of consolidation, the moisture content of the soil de creases and the strength increases. This consolidation may lead to complex stress distributions in the bottom bed (Jian et al., 2017; Sui et al., 2017; Ye, 2012). The form of seabed failure that occurs under wave action depends on the type of soil, the state of soil consolidation, and the intensity of the wave action. In addition, the damage zones
* Corresponding author. Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, China. E-mail address: [email protected] (G. Xu). https://doi.org/10.1016/j.oceaneng.2020.106990 Received 22 August 2019; Received in revised form 15 January 2020; Accepted 17 January 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.
Please cite this article as: Yupeng Ren, Ocean Engineering, https://doi.org/10.1016/j.oceaneng.2020.106990
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Fig. 1. Schematic diagram of the flume test device.
caused by different failure modes and the methods of evaluating the failure also differ based on these factors (Taiba et al., 2016; Wang et al., 2016; Zen et al., 1998). The limit equilibrium method can be used to analyze the variation in the seabed wave pressure. The results of this method show that the seabed can be sheared, causing damage from submarine sliding (Henkel, 1970; Zhang et al., 2016). Many methods have been used to judge the shear slip of the seabed, in which the effect of excess pore water pressure in the soil cannot be ignored (Gu, 1989). Especially when the pile foundation and other structures are buried in the bed, the change of pore water pressure around the pile foundation is different from that of the soil in other places, and the shear failure is more likely to occur around the pile foundation, rather than at the lower part of the pile foundation (Sui et al., 2017). Experimental and computational studies have shown that even for a flat seabed, arc shear failure may occur under the conditions of a pres sure difference between the wave crest and trough. Some scholars have also described the process and morphology of the circular arc shear failure of the seabed (Chang and Jia, 2010; Xu et al., 2009b). Especially when there are structures such as piles in the seabed after consolidation, shear failure is more likely (Chang and Jeng, 2014; Sui et al., 2017). In summary, the present study shows that a flat silty soil seabed can not only undergo liquefaction damage but also shear damage. However, the reasons for this difference are not clear. Whether or not it is due to the initial consolidation state of the seabed soil is worth considering. For silty soil, if it has undergone consolidation, it is well constructed due to the interaction of fine particles and clay, and its internal structure will
produce cohesion. Damage to a consolidated silty seabed under wave cyclic loading is the result of the constant undermining of its structure. In the case where the volume of the soil is not compressed, the process of soil structural failure does not necessarily produce an increase in the pore water pressure. However, if the silty seabed is not consolidated, the soil particles cannot form a structural connection, so the pore water pressure accumulates, and the response of the soil under wave loading should be similar to that of sand. Thus, for a silty seabed, the initial failure pattern may be different under wave loading due to the difference in the degree of consolidation. When the degree of consolidation is high, shear failure may occur first. However, if the seabed is not consolidated, the loose seabed material may accumulate pore water pressure, and liquefaction failure may occur first. Therefore, in this paper, flume experiments were carried out on a silty seabed with different degrees of consolidation to study the initial failure mode. The results of these experiments provide an explanation for the initial failure mechanism of the subaqueous deltas of the Mis sissippi River and the Yellow River. 2. Flume experiments The experiments were carried out in a wave flume that was 0.5 m in width, 1.2 m in depth, and 14 m in length. Uniform regular waves were produced using a piston-type wave generator. The water depth was maintained at 40 cm, and the soil was placed in a 0.6 m deep and 2.6 m long box (Fig. 1). Two tests were carried out. In test 1, the seabed
Fig. 2. Schematic diagram of the probe placements. 2
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Table 1 The order in which the waves were applied in the tests. Test 1
Test 2
H ¼ 6 cm (low wave height) for 90 min H ¼ 10 cm (medium wave high) for 240 min H ¼ 18 cm (high wave height) to the end of the test
H ¼ 6 cm (low wave height) for 11 min H ¼ 9 cm (medium wave high) for 60 min H ¼ 14 cm (high wave height) to the end of the test
Table 2 Liquefaction process in the seabed. Test 1
Test 2
No liquefaction was observed at the initial wave height H ¼ 6 cm No liquefaction was observed at the wave height H ¼ 10 cm
Liquefaction was observed at the initial wave height H ¼ 6 cm liquefaction displayed downward development at the wave height H ¼ 9 cm liquefaction displayed downward development at the wave height H ¼ 14 cm
Liquefaction was observed at the wave height H ¼ 18 cm and liquefaction developed downward
Fig. 3. Particle size grading curve of the test soil.
with d50 ¼ 0.052 mm and a clay content of 10% (Fig. 3). The silty soil retrieved from the Yellow River Delta is screened for impurities and then, in the form of a remolded soil, a certain percentage of the silty soil and water are mixed into a slurry, ensuring a water content of approximately 32% (as close to 32% as possible to produce an even test bed). Then, we transferred the slurry into the flume in batches to create a seabed measuring 2 m � 0.5 m � 0.6 m. After laying the seabed, we added water to a depth of 40 cm. Test 1 was left standing for 7 days, and the consolidation time was long. In test 2, the seabed was left to stand for only 4 h, and it did not undergo consolidation. Before the wave was initiated, the content and penetration resistance were measured at different depths in the two experiments (Fig. 4a). In addi tion, the cohesion c and internal friction angle φ of the soils in the two test beds were determined by a direct shear test (Fig. 4b). The results show that the consolidation, strength, and compactness of the seabed in test 1 were higher than those in test 2 (the bottom bed of test 1 was “dense” and the bottom bed of test 2 was “soft”). In addition, in the early stage of test 1, the application of small waves resulted in the dynamic consolidation of the test bed bedrock soil, which made the soil more compact than that at the beginning of the test. The waves imposed by the two tests mainly simulate three wave conditions: low wave height, medium wave height and high wave height. The wave height was gradually increased according to the observed state of the soil and pore pressure changes (in test 1, the wave height was increased after the point at which the seabed was unbroken and the pore pressure of the soil stabilized). The sequence applied in the two experiments is shown in Table 1.
(a) Comparison of the soil moisture and penetration resistance of the two tests
3. Test results In the two experiments, the differences in the initial failure range and the variation of the pore water pressure in the seabed were due to the different consolidation degrees of the test seabed. 3.1. Initial failure of the seabed and the development of liquefaction
(b) Cohesion of soil in two tests
The initial failures of the tests of seabed 1 and 2 were significantly different (Table 2). In test 1, in which the degree of consolidation of the seabed was relatively high, the bottom bed did not liquefy under the action of the smaller waves, and the soil at a depth of 16 cm was observed to fluctuate from the sidewall of the flume when the wave height was 18 cm. In test 2, in which the seabed consolidation was relatively low, we observed that the soil at a depth of 8.5 cm fluctuated under the action of the waves with a wave height of 6 cm. After the
Fig. 4. Soil parameters of the bottom bed in two tests.
underwent consolidation, but for test 2, it did not. The pore pressure probe is fixed in the vertical direction at different depths of the seabed (Fig. 2). To ensure the authenticity of the test results, the soil used for the experiments was an original sample of silt from the Yellow River Delta 3
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Fig. 5. Liquefaction progress of the seabed in the two tests.
The beginning of the initial failure of the seabed was taken at time 0, and the liquefaction depths of tests 1 and 2 were plotted versus time to display the evolution of the liquefaction depth (Fig. 6). In test 1, after the initial failure of the seabed, the liquefaction depth gradually increased and finally reached the maximum liquefaction depth for a wave height of 18 cm. For test 2, the depth of liquefaction increased rapidly since the initial failure of the seabed occurred at H ¼ 6 cm, reached a stable depth, and then for the larger wave heights of 9 cm and 14 cm, the liquefaction depth continued to increase until the maximum liquefaction depth was reached. 3.2. Pore water pressure variation in the test seabed For test 1, at wave heights of 6 cm and 10 cm, the pore water pressure value was stable at different depths of the seabed. When the wave height increased to 18 cm, the soil structure was destroyed, and the pore water pressure increased rapidly at a depth of the 21 cm of the seabed. After the initial failure of the seabed, the pore water pressure of the under lying non-liquefied soil accumulated for a long duration of time. In test 2, when the wave action was applied at a height of H ¼ 6 cm, the pore water pressure at all depths increased rapidly. The accumulated soil pore water pressure in the upper layer (25 cm deep) was larger than that in the lower layer (35 cm and 45 cm deep). When the wave height was 9 cm, the pore water pressure in the soil continued to accumulate, and the growth rate of the upper soil layer was smaller due to its ten dency to liquefy, while the growth of the lower soil mass was larger. When the wave height was 14 cm, the upper soil had already liquefied, so the pore water pressure remained stable, while the pore water pres sure of the lower soil (because it had not liquefied) continued to
Fig. 6. Variation in the liquefaction depth with time in the two tests.
initial failure of the two soils in the test seabed, the liquefaction process exhibited a gradual downward development. In the experiments, the liquefaction depth was determined by observing the fluctuation through the wall of the flume. The depth of the soil liquefaction development is represented by the position of the soil fluctuation as observed through the wall of the flume. The initial liquefaction depth and the depth of the downward evolution of the liquefaction observed in the test are indicated on the sidewalls of the flume depicted in Fig. 5. 4
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During test 1, the initial failure of the soil was accompanied by a rapid increase in the pore water pressure. However, in test 2, when the wave was applied, the pore water pressure increased. When the wave became stable, the pore water pressure continued to accumulate. Thus, before the initial failure of the bed, the pore water pressure will increase. Then, the internal pore water pressure will continue to accumulate after the wave height increases, and the accumulation will be slower and will last longer. After the initial failure of the seabed soil in the two tests, the lique faction of the bottom of the seabed develops under the cyclic loading of the waves, and the pore water pressure in the undrained soil increases. After the initial failure of the seabed in the two tests, the change in the pore water pressure with time under the continuous load of the wave is shown in Fig. 8. It can be seen from Fig. 8 that with the continuous loading of the waves, after the initial failure, the increase in the pore water pressure of the undrained soils of the two tests are stable and accumulate slowly and continuously.
Table 3 Changes in the pore water pressure of the seabed during the tests. Test 1
Test 2
When H ¼ 6 cm the pore water pressure of the soil remained stable, and no obvious increase was observed. When H ¼ 10 cm the soil pore water pressure still remained stable.
When H ¼ 6 cm the pore water pressure began to obviously increase in all layers of the seabed. When H ¼ 9 cm the pore water pressure of the soil continued to increase, and the accumulative velocity accelerated. When H ¼ 14 cm the pore water pressure of the upper soil layer was stable, while that of the lower soil layer continued to increase.
When H ¼ 18 cm, the pore water pressure began to increase in all layers of the seabed.
accumulate(See. Table 3). When the soil liquefied, the pore pressure was characterized by a rapid increase and a large fluctuation amplitude. According to these characteristics, the time of liquefaction recorded by the probe inside the soil is earlier than that observed through the wall of the flume. In view of the constraining effect of the fixed wall on the soil, the fluctuation of the liquefaction of the soil observed through the wall should lag behind the fluctuation of the interior soil. The initial failure observed in the two tests and the variations in the pore water pressure of the seabed were significantly different. The change in the pore water pressure with time as recorded by the upper most probe for the two tests is shown in Fig. 7.
4. Discussion The mechanism of the initial failure of the seabed is shear failure or liquefaction, and the failure mechanism is different depending on the consolidation of the soil. There should be differences in the failure morphology and pore water pressure in the soil (Zen et al., 1998).
Fig. 7. The change in the pore water pressure with time as recorded in the uppermost layer of the seabed.
Fig. 8. Changes in the pore water pressure with time at different depths. 5
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Excess pore water pressure
Fig. 10. Schematic diagram of the Arc shear failure mode (Note: This figure was first seen in Xu (2006), and this article has been revised on this basis).
Fig. 9. Schematic diagram of the cumulative pore water pressure distribution along a depth in the bed. (Note: this figure was first proposed byIshihara and Yamazaki (1984) and is modified on the basis of Gao et al. (2011). In the figure, c0 is the initial cohesion of the bed; σ is the overlying stress; φ0 is the initial internal friction angle; ce is the cohesion after attenuation under the continuous wave load; φe is the in ternal friction angle after attenuation under the continuous wave load).
4.1. The analysis of shear failure of the seabed under wave action Without considering the soil viscosity, the shear strength of the soil is
τ ¼ σ ⋅tan φ0 (where σ is the overlying stress and φ is the internal friction
angle). For this type of soil, regardless of the distribution of the excess pore water pressure in the soil in the bed, failure occurs from the surface. However, for silty soil, because there is a certain amount of clay in it, the cohesion of the soil should be considered and the shear strength should be τ ¼ c0 þ σ⋅tan φ0 . For silty soil with a continuous wave loading, when the bottom bed is not damaged, the cohesion c and internal fric tion angle φ of the silty soil decrease with increasing load times and tend to gradually stabilize (Xu et al., 2009a). In the process of the test, the influence of the cyclic wave load on the soil mass and on the bed depth is gradually weakened. At the same time, the excess pore water pressure in the seabed increases first and then increases from the surface of the seabed to the bottom. If it is assumed to be below the depth z ¼ zl , the influence of the wave load on the bed soil mass has been ignored. The distribution of the excess pore water pressure and the change of the shear strength of the soil with depth after loading are shown in Fig. 9. Under the condition of a low wave height, no liquefaction occurs in the soil. This indicates that the excess pore water pressure in the bed does not reach the effective stress of the overlying layer, but this does not mean that there is no excess pore water pressure in the bed. Under the continuous load of the wave, the cumulative pore water pressure in the bed first increases and then decreases with increasing depth. At the same time, with the continuous load, the cohesion and internal friction angle inside the bed soil are also decreasing, which leads to a decrease in the shear strength of the soil. This change occurs at the same time as the change of the accumulated pore water pressure in the bed and under the action of the overlying wave shear force, which in theory can cause the bed to shear at a certain depth (the weak point of the bed). The theo retical diagram of the arc shear failure of the bed is shown in Fig. 10: After the shearing of the weak point of the bed, the soil around the shearing point is destroyed. Then, under the action of the shearing force generated between the wave trough and wave crest, the surface of the soil is stretched when the wave trough arrives and compresses when the wave crest arrives. Shear failure occurs in the whole block after several periods of oscillation.
Fig. 11. Arc shearing failure diagram (Henkel, 1970).
4.2. Initial damage area of the silty seabed under wave action Low-grade slopes or flat seabeds experience shear sliding under wave action (Henkel, 1970; Xu et al., 2009b), and the limit equilibrium method can be used to calculate the range of the sliding area. For tests 1 and 2, the initial mode is assumed to be shear failure, and the calculation of the failure area is performed using Henkel’s (Henkel, 1970) wave-induced seabed slip calculation model (Fig. 11). When the soil is in the limit equilibrium state, the soil stability safety factor can be expressed as F ¼ Mr/Md. Where Mr is the anti-skid torque 0 0 and can be expressed as Mr ¼ 2x3 ðcu =γ zÞγ ðsin θ θ cos θÞ=sin3 θ; and 0 Md is the slip torque and can be expressed as Md ¼ 2x3 βγ =3 þ ðL2 ΔPÞðsin α α cos αÞ=2π2 . The relationship between x, d, and θ can be expressed as follows: d= x ¼ ð1 cos θÞ=sin θ. In this case, α ¼ 2πx=L, β is the slope angle of the 0 seabed, Δp is the wave pressure amplitude, and k ¼ cu =γ z is the soil strength characterization coefficient. Since the test bed was flat, the inclination angle β was zero. The wave and bed parameters at the time of the initial failure of the two tests are shown in Table 4. During test 1, the vane shear test was carried out, both when the soil was already liquefied and not liquefied. The k of the obtained soil was calculated using the vane shear strength cu obtained from the experiment. The seabed in test 2 was not consoli dated, and its shear strength is similar to the that of the liquefied seabed 6
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5. Conclusion
Table 4 Wave and seabed corresponding to the initial failure of the bed during the two experiments. Parameters
Test 1
Test 2
Water depth h Wave height H Wavelength L Density of soil ρ2 Soil strength characterization coefficient k
0.4 m 0.18 m 1.9 m 1.91 g/cm3 0.05–0.11 (The value is 0.07)
0.4 m 0.06 m 4.3 m 1.85 g/cm3 0.03–0.05 (The value is 0.04)
In this study, two wave flume tests are carried out. The difference between the two tests is the consolidation degree of the test beds. Under the wave action, the two tests show different results. Through the analysis and discussion of the test results, the following conclusions are obtained: (1) Under the wave actions, the initial failure pattern of the crusty silty seabed with different degrees of consolidation is obviously different. The concrete manifestation of this finding is as follows: the relatively dense seabed experienced shear failure under the action of the waves and the initial damage of the relatively soft seabed is due to cumulative liquefaction damage. (2) After the initial failure of the soil, the silty soil seabed continued to liquefy under the wave action in a top-down progression. (3) Under the action of a continuous wave load, the silty soil bed without damage appears to be damaged, which reduces its cohesion and internal friction angle and reduces the shear strength of the bed, thus providing conditions for the shear failure of the bed. (4) As a special type of soil, some structural changes will take place during the consolidation process, which will make the silty soil bed present different failure forms under the wave action; this topic will be the focus of subsequent research.
Table 5 Failure zone parameters calculated from the shear failure.
Test 1 Test 2
Parameters
Width
Difference ratio
Test value
1.70 m 1.50 m 0.30 m 1.50 m
11%
Calculated values Test value Calculated values
Depth 0.16 m
Difference ratio 0%
0.16 m 400%
0.085 m 0.15 m
76%
in the tests. The results can be calculated as follows: under the conditions of test 1, the calculated shear width is 1.5 m, and the shear depth is 0.16 m and under the conditions of test 2, the calculated shear width is 1.5 m, and the shear depth is 0.15 m. The comparison between the experimental results and the calculated results is shown in Table 5. From an the point of view of the error of the calculation results and test results, test 1 is in good agreement with the shear failure mode but test 2 is clearly not in agreement with the shear failure mode.
Author contributions section Yupeng Ren:Conceptualization, Methodology, Experiments, WritingOriginal draft preparation. Guohui Xu: Supervision, Writing- Reviewing and Editing, Guidance. Xingbei Xu: Experiments, Visualization, Software. Tianlin Zhao: Experiments, Editing, Validation. Xinzhi Wang: Experiments, Writing- Reviewing and Editing.
4.3. Analysis of the pore water pressure during the initial failure test
Declaration of competing interest
Two tests for the upper probe (probe A, probe a) that measured pore water pressure are shown in Fig. 7. Comparative analyses were per formed for the two pore water pressure data sets, when there is initial soil damage in the two tests, the pore water pressure has a certain jump, but the tests differ significantly in the time of the destruction process. In experiment 1, the pore water pressure began to increase until the initial failure of the soil and it has a certain time course, which lasted 10 s. In contrast, in experiment 2, the initial pressure of the soil was applied while the wave was applied, and the pore water pressure increased, but it lasted for 0 s. This indicates that the soil is destroyed because the pore water pressure increases. Then, the waves are subjected to several cycles of wave loading, and the soil becomes completely liquefied and con forms to the characteristics of shear failure. However, in test 2, the seabed has a certain structure before the wave loading, along with the beginning of the wave loading, the soil instantly loses its structure, and the initial destruction does not have a time course, so it does not meet the characteristics of shear damage. After the initial failure of the seabed, the change of the pore water pressure in the non-liquefied seabed is shown in Fig. 8. The pore water pressure in the non-liquefied seabed showed a slow, steady accumulation. Considering the characteristics of the pore water pressure change and the progress of the liquefaction depth after the initial failure of the two tests (Fig. 6), it can be seen that after the initial failure of the seabed, the liquefaction modes of both tests showed a gradual liquefaction process until the maximum liquefaction depth was reached.
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