Wave-Induced Liquefaction and Floatation of a Pipeline in a Drum Centrifuge

The development and dissipation of residual pore pressure $u_e$ in the soil under wave loading may be represented by the following equation (Sassa and Sekiguchi 1999):where $K$ = intrinsic permeability coefficient; $m_v$ = coefficient of compressibility of soil skeleton; $\mu$ = dynamic viscosity of pore fluid; $\omega$ = angular frequency of waves; $\kappa$ = wave number $2\pi /L$, where $L$ = wave length; ${\epsilon }_{\mathrm{vol}}$ = plastic volumetric strain due to cyclic shearing; $z$ = vertical coordinate; and $t$ = time. To satisfy the time-scaling law of the soil consolidation, the following relation should hold for both the model and the prototype:

For the wave test of a $1/N$ scaled model under $N\mathit{g}$ condition, ${\kappa }_m=N{\kappa }_p$ and ${\omega }_m=N{\omega }_p$. The latter is derived from Froude’s law. The intrinsic permeability coefficient $K$ should be constant if the same soil with the same initial state of packing is used in the model and the prototype. The parameter $m_v$ of the model is the same as that of the prototype, because it depends essentially on the effective confining pressure. Therefore, by using pore fluid with viscosity ${\mu }_m=N{\mu }_p$, Eq. (2) is satisfied. With this technique, called viscous scaling, one can satisfy the time-scaling laws for fluid wave propagation and the consolidation of the soil (Sassa and Sekiguchi 1999).

For the wave test of a $1/N$ scaled model under $1g$ condition, the equations ${\kappa }_m=N{\kappa }_p$ and ${\omega }_m=N^{0.5}{\omega }_p$ hold. The viscosity of pore fluid usually is ${\mu }_m={\mu }_p$. To satisfy Eq. (2), under assumptions of essentially the same compressibility $m_v$ between the model and the prototype, although the scaled $1g$ model cannot reproduce the effective confining pressure as in the prototype, $K_m=N^{(-1.5)}{K}_p$ needs to be satisfied. This indicates that the same material used in the prototype could not be used in the experiment. However, the use of different soil material brings about a difference in the compressibility $m_v$ as well as in the mechanical characteristics of the soil. Thus, the soil response observed in $1g$ wave tests cannot be properly extrapolated to field conditions.

Sumer (2014) compared the buildup of residual pore pressure at shallow soil depth obtained from a $1g$ wave test on the bed of silt (Sumer et al. 2006b) with that of centrifuge wave test on a bed of sand (Sassa and Sekiguchi 1999). Because the coefficient of consolidation [Eq. (2)] was of the same order between them, the pore-pressure response of the $1g$ test was in good agreement with that of the centrifuge test. However, silt was used as the soil material instead of sand in the field (Sumer et al. 2006b), as described previously.

Consider a soil bed with a horizontal surface under wave loading. The time-averaged vertical and horizontal effective stresses at a generic point arewhere subscript_ave indicates the period-averaged value; ${\sigma }_{v0}^{\prime }$ = initial vertical effective stress; and ${\sigma }_{h0}^{\prime }$ = initial horizontal effective stress. Under initial $K_0$-consolidation, ${\sigma }_{h0}^{\prime }=K_0{\sigma }_{v0}^{\prime }$, where $K_0$ is the coefficient of lateral earth pressure at rest. The value $u_e$ is the residual pore pressure due to cyclic loading, and $\mathrm{\Delta }{\sigma }_{h\_\mathrm{ave}}$ is the period-averaged increment of horizontal total stress. The increment of vertical total stress $\mathrm{\Delta }{\sigma }_{v\_\mathrm{ave}}$ may be considered to be zero, but $\mathrm{\Delta }{\sigma }_{h\_\mathrm{ave}}$ can increase under laterally confined conditions as in the seabed ground. Ishihara and Li (1972) performed triaxial torsion shear tests and showed that under the laterally confined condition, the principal stress ratio defined by $K={\sigma }_3/{\sigma }_1$ increased in the course of cyclic loading from $K_0$ to unity ($K=K_0\to 1$) due to the increase in the horizontal total stress ${\sigma }_3$ in association with buildup of residual pore pressure. This aspect was also shown in the analysis of wave-induced liquefaction, in which the mean total stress increased due to the increase in the horizontal total stress ${\sigma }_3$, whereas the mean effective stress decreased during wave loading (Sassa and Sekiguch 2001).

From Eqs. (3) and (4), principal total stresses are

The hydrostatic pressure is excluded for representation. When residual pore pressure builds up, and the principal stress ratio $K$ reaches unity, ${\sigma }_{3\_\mathrm{ave}}$ reaches ${\sigma }_{1\_\mathrm{ave}}$. From this and Eqs. (5) and (6)

Liquefaction is defined as the state in which the period-averaged mean effective stress is zero, that is, ${\sigma }_{m\_\mathrm{ave}}^{\prime }=0$. Here, ${\sigma }_{m\_\mathrm{ave}}^{\prime }=({\sigma }_{v\_\mathrm{ave}}^{\prime }+2{\sigma }_{h\_\mathrm{ave}}^{\prime })/3$. From Eqs. (3), (4), and (7) and ${\sigma }_{h0}^{\prime }=K_0{\sigma }_{v0}^{\prime }$, when residual pore pressure $u_{\mathrm{e}}$ reaches the level of ${\sigma }_{v0}^{\prime }$, the mean effective stress ${\sigma }_{m\_\mathrm{ave}}^{\prime }$ becomes 0 (${\sigma }_{m\_\mathrm{ave}}^{\prime }=0$). It thus follows that when liquefaction occurs, $u_e={\sigma }_{v0}^{\prime }$.

When residual pore pressure $u_e$ reaches the level of initial mean effective stress level ${\sigma }_{m0}^{\prime }$, mean effective stress does not reach zero (${\sigma }_{m\_\mathrm{ave}}^{\prime }\ne 0$) in the seabed ground, because the principal stress ratio $K$ increases in the laterally confined condition in association with increasing $u_e$. The criteria for the onset of liquefaction by comparing ${\sigma }_{m0}^{\prime }$ with $u_e$ was adopted by several studies (e.g., Sumer et al. 2006b; Jeng and Seymour 2007; Jeng 2013; Sumer 2014). In this criteria, however, there is room for further buildup of residual pore pressure after the residual pore pressure $u_e$ reaches ${\sigma }_{m0}^{\prime }$ and therefore, although marginal, some effective stress remains [Sumer (2014), with reference to Sassa and Sekiguchi (2001)], and thus the soil is not in the state of liquefaction, as adopted in this study.

A water channel installed inside the 2.2-m-diameter drum centrifuge of Toyo Construction (Nishinomiya, Japan) is shown in Fig. 1. The generation and propagation of waves in a drum centrifuge first was studied by Sekiguchi and Phillips (1991). Baba et al. (2002) developed a wave generation system based on a plunger-type device in a drum centrifuge, permitting the soil bed to be subjected to regular waves of constant and moderate amplitude. However, waves of varying amplitude or irregular waves could not be generated, and the severity of the waves generated was below the critical value at which liquefaction occurs. Miyamoto et al. (2018) introduced a piston-type wave maker in the drum channel so that the sequence of storm waves started from relatively small waves and increased to very intense ones, in which liquefaction occurred. Irregular waves, similar to real storm waves, also could be reproduced. Here, the piston-type wave maker was driven by an AC servomotor and feedback system in which the data from a laser-type displacement transducer was used to continuously vary the stroke of the wave paddle (Fig. 1).

Two sets of centrifuge wave tests were performed on loosely packed, fresh deposits of fine sand (Table 1). Three tests (Cases 1, 2, and 5) absent from the table were the cases of a sand bed without a pipe, in which the fundamental characteristics of wave-induced liquefaction were observed, and essentially had the same behavior as in Sassa and Sekiguchi (1999). The present paper describes and discusses the cases of a sand bed with a pipe in Table 1. All the tests were carried out under a centrifuge acceleration of $70g$.

The fundamental cases (F-cases) addressed the floatation process of a pipeline, associated with wave-induced liquefaction. The characteristics of liquefaction were investigated under both regular and irregular waves. In the regular-wave experiment, a sinusoidal wave with gradually increasing amplitude was generated. The period $T$ of the sinusoidal wave was equal to 0.1 s, corresponding to a period of 7 s in the field. In the irregular wave experiment, in which realistic storm waves were assumed, irregular wave forms were generated based on the standard frequency spectra (modified Bretschneider–Mitsuyasu equation). The forms of wave paddle motion in the regular-wave test (Case 3) and irregular-wave test (Case 4) are shown in Figs. 2(a and b). These are measured forms obtained from the laser-type displacement transducer. The wave conditions of the regular- and irregular-wave tests are listed in Table 2. The values of wave height $H$ in the table were calculated from the wave pressures measured at the soil surface using the linear wave theory.

The countermeasure cases (C-cases) was designed to investigate the effects of gravel layer replacement as a countermeasure against wave-induced liquefaction and pipe floatation. In the experiments, a sinusoidal wave, whose amplitude gradually increased and then gradually decreased, was imposed on the soil surface as one severe wave group. The frequency of the sinusoidal wave was equal to 10 Hz, which corresponded to that in the regular wave tests in the F-cases. The representative form of wave paddle motion from the laser-type displacement transducer is shown in Fig. 2(c). The wave conditions of the C-cases of wave tests are listed in Table 2.

The cross section of a sand deposit model with a buried pipe in the F-cases is shown in Fig. 3(a). Water was used as the exterior fluid, and Metolose (Shin-Etsu Chemical, Tokyo) with a viscosity of $7.0\times {10}^{-5}{\mathrm{m}}^2/\mathrm{s}$ was used as the pore fluid in order to match the time-scaling laws of soil consolidation and fluid–wave propagation (Sassa and Sekiguchi 1999). The sand used was silica sand No. 7 (specific gravity of sand grains $Gs=2.66$, maximum void ratio $e_{\max }=1.16$, minimum void ratio $e_{\min }=0.70$, and median grain size $d_{50}=0.15\mathrm{mm}$). The loosely formed sand beds had relative densities $Dr$ of 35%–38%, and the initial soil depth of 102 mm corresponded to a 7-m-thick sand bed on a prototype scale. The fluid depth was kept at 100 mm, equivalent to a 7-m water depth on a prototype scale.

The pipeline model was made of aluminum pipe (diameter of 25 mm) and urethane foam. The specific gravity of the pipe model was 1.35, which was smaller than the measured specific gravity of liquefied soil, 1.83 [$={\gamma }_{\mathrm{sat}}/{\gamma }_w$, where ${\gamma }_{\mathrm{sat}}$ is saturated unit weight of soil; ${\gamma }_{\mathrm{sat}}=(G_s+e)/(1+e){\gamma }_w$, where $e$ is void ratio of the sand bed; and ${\gamma }_w$ is unit weight of fluid]. Here, the value of ${\gamma }_{\mathrm{sat}}$ is the value before wave loading, which may not exactly represent that of liquefied soil. In this respect, it is instructive to refer to Sassa et al. (2001). Namely, the wave-induced liquefied soil exhibited significant vibratory motion that centered around the original soil surface before wave loading. This shows that the volume, and thus the void state, of liquefied soil remained essentially the same as that before wave loading. The burial depth of the pipe, which represents the distance between the soil surface and top of the pipe, was 27 mm, corresponding to a 1.9-m soil depth on a prototype scale. This burial depth was nearly the same as the pipe diameter, whose experimental condition was set to be practical in view of the actual problems of buried-pipe floatation (Sumer 2014).

The sand deposit model with a gravel layer over the loose sand bed in the C-cases is shown in Fig. 3(b). The soil surface was partially improved by the gravel layer. The outline of the model was the same as that in the F-cases except for the gravel layer replacement of the soil surface. The thickness of the gravel layer was selected to be 15 mm, corresponding to about 1 m on a prototype scale. The width of the gravel layer varied in Cases 7 and 8. In Case 7, the ground surface in the range of 60° above the pipe was replaced with the gravel layer. In Case 8, the surface layer in the range of 120° above the pipe was replaced with the gravel layer. The gravel layer ranges in Cases 7 and 8 are illustrated schematically in Fig. 3(c). The gravel used had $Gs=2.61$ and grain size $d=2.0–4.75\mathrm{mm}$ ($d_{50}=3.1\mathrm{mm}$).

The setup method for the pipe was as follows. The sand bed was formed by gently pouring sand into a sea of Metolose. When the sand thickness was 50 mm, the pipe model was placed on the sand surface. Silicone grease was applied to the pipe ends to make the friction between the pipe and the wall of the water channel sufficiently small. By continuing to pour sand, a sand bed with a thickness of 102 mm was finally formed. In the case of the gravel cover, when the thickness of the sand was 85 mm, the gravel layer was carefully formed on the soil surface.

The wave pressures acting on the soil surface were measured using pressure transducers. Wave-induced pore-pressure changes in the soil bed were measured with two vertical arrays, and upper and under surfaces of the pipe. The pore-pressure transducers (PPTs) in the arrays were fixed in space using string so that they would not sink into the liquefied soil, and the PPTs on the pipe surface were fixed there. The movements of the pipe and the soil surface were observed using a high-speed charge-coupled device (CCD) camera at an image rate of $250\mathrm{frames}/\mathrm{s}$.

The measured time histories of the excess pore pressures at three different soil depths are shown in Fig. 4, together with the wave pressure at the soil surface. These measurements were from Array A near the pipe [Fig. 3(a)]. Fig. 4(b) shows the response at a shallow soil depth ($z=22\mathrm{mm}$). No significant buildup of residual pore pressure occurred during the moderate level of wave loading ($t=3.0–3.6\mathrm{s}$). The increase in wave severity brought about a buildup of residual pore pressure. When the wave pressure at the soil surface reached 8.1 kPa, the residual pore pressure reached the level of the initial vertical effective stress ${\sigma }_{vo}^{\prime }$, indicating the occurrence of liquefaction at this depth. Because the amplitudes of the wave pressure at the soil surface $u_{0+}$ (trough) and $u_{0-}$ (crest) were slightly asymmetric due to the nonlinearity of the wave, their average pressure was adopted as the wave pressure on the occurrence of liquefaction.

In this study, liquefaction occurred at the wave pressure 8.1 kPa as a result of the increase in amplitude of wave pressure. Under constant wave loading, liquefaction might occur at a lower level of wave pressure, because the occurrence of liquefaction depends not only on the maximum shear stress arising from wave pressure but also on the number of effective waves pertaining to liquefaction. The effective number of waves, together with the conventional maximum shear stress, is capable of representing the severity of given cyclic loading on liquefaction due to the buildup of residual pore pressure (Sassa and Yamazaki 2016). The effective number of waves of constant regular waves with a certain wave pressure becomes larger than that of regular waves whose amplitude increases.

After liquefaction occurred at the shallow soil depth, it occurred at the middle soil depth and then at the bottom, indicating a downward advance of the liquefied zone [Figs. 4(c and d)]. The process of the downward progress of liquefied zone is more clearly illustrated in Fig. 5, in which the advance of liquefaction is based on the time records of the occurrence of liquefaction at three different soil depths.

The pore-pressure responses in Array B far from the pipe [Fig. 3(a)] also indicated the downward progress of liquefaction. The rate of progressive liquefaction was essentially the same as that observed in Array A.

The floatation process of the buried pipe under severe wave loading was observed using a high-speed camera. Photos of the floatation at four different times are shown in Fig. 6. After the occurrence of liquefaction in the sand bed, the pipe gradually moved upward. In the course of wave loading, the pipe finally reached the soil surface. A closer observation of the movement of the pipe is shown in Fig. 6(e). The trajectory of the pipe movement was in the shape of an ellipse, showing that the pipe advanced upward in the significant fluidized motion of liquefied sand under severe waves. Therefore, the behavior of the pipe essentially was caused by the dynamic interaction between the waves and liquefied soil.

Floatation of the buried pipe to the soil surface was a consequence of liquefaction. This is illustrated in Fig. 7, which shows the vertical movement of the top of the pipe during wave loading based on the observations using the high-speed camera. No significant movement of the pipe occurred before the soil bed underwent liquefaction. Upon the occurrence of liquefaction at the shallow soil depth the buried pipe started to move upward. The motion of the pipe increased markedly with the downward progress of the liquefied zone in the course of continued wave loading and the pipe eventually reached the soil surface. Because the pipe moved upward with an elliptical motion [Fig. 6(e)], the vertical vibratory motion of the pipe in Fig. 7 represents the vertical component of the elliptical motion of the pipe. The period of the elliptical motion of the pipe corresponded to that of the input waves, indicating that the vibratory motion of the pipe was induced by the significant vibratory motion of the liquefied sand caused by wave loading.

The observed pipe behavior had a certain similarity to the previous observation in a $1g$ wave test. Namely, the video of the $1g$ test (Sumer 2014) showed that in the course of wave loading, the pipe moved upward and reached the soil surface in association with the significant vibratory motion of liquefied soil. However, the detailed process of the pipe motion could not be observed from the video, because the pipe was in the liquefied soil. In addition, there was a significant difference in the velocity of pipe floatation: $20\mathrm{mm}/\mathrm{s}$ in the present study (Case3) and $0.5\mathrm{mm}/\mathrm{s}$ in the $1g$ test (Sumer et al. 1999, Fig. 10). As stated previously, scaling laws of wave–soil interactions involving the time-scaling law of the soil consolidation as well as the mechanical similarity have not yet been established for $1g$ wave tests, so no further quantitative discussion should be made here.

The measured time histories of the excess pore pressures at the shallow soil depth from Cases 6–8 are shown in Fig. 11 together with the wave pressures at the soil surface, $u_0$. These measurements were from Array A near the pipe [Fig. 3(b)]. Fig. 11(a) shows the waveform from Case 6 for the no-countermeasures case. The residual pore pressure developed continuously with the increase in wave severity, and liquefaction occurred at a wave pressure of 7.3 kPa. A closer observation of the soil response shows that the pore pressure decreased after the onset of liquefaction, indicating the dilatancy of the soil induced by the movement of the pipe. In other words, the decrease in the pore pressure was a consequence of dynamic interaction between the pipe movement and the liquefied soil. Such a decrease in residual pore pressure after the occurrence of liquefaction was not measured by Array B, which was far from the pipe. Array A in the C-cases [Fig. 3(b)] was closer to the pipe than in F-cases [Fig 3(a)]. In F-cases, the effects of pipe movement were not detected by Array A.

Fig. 11(b) shows the soil response for Case 7, in which the gravel layer was laid in a 60° range. As in Case 6, the residual pore pressure developed gradually and liquefaction occurred at a wave pressure of 7.8 kPa. This suggests that the effect of the gravel layer in Case 7 on the onset of liquefaction was marginal. Finally, Fig. 11(c) shows the soil response for Case 8, in which the gravel layer was laid in a 120° range. The rate of development of residual pore pressure was much lower than that in Case 6, and liquefaction occurred at a wave pressure of 10.2 kPa. The wave pressure level at which liquefaction occurred in Case 8 was greater than that in Cases 6 and 7. This comparison means that the liquefaction resistance became much greater owing to the gravel layer replacement in a sufficient range over the soil surface.

The onset of liquefaction was accompanied by wave pressure attenuation. The waveform on the soil surface in Fig. 11(a) shows that the amplitude of the wave pressure increased gradually before the soil bed underwent liquefaction. However, upon the occurrence of liquefaction at the shallow soil depth, the rate of increase of the wave pressure amplitude at the soil surface decreased. This indicates a wave damping effect of the liquefied sand bed, which is one form of wave–soil interaction. Wave pressure damping was also seen after the occurrence of liquefaction in Cases 7 and 8.

The increase in liquefaction resistance caused by the gravel layer now is discussed. The severity of the action of travelling sinusoidal waves on a given soil deposit may be expressed in terms of the cyclic stress ratio ${\chi }_0$ (Sassa and Sekiguchi 1999), which is expressed in terms of poroelasticity theory (Madsen 1987; Yamamoto et al. 1978) aswhere $\tau$ = wave-induced maximum shear stress in soil; $u_0$ = amplitude of fluid pressure fluctuation at soil surface ($z=0$); $\kappa$ = wavenumber; ${\gamma }^{\prime }$ = submerged unit weight of soil; and $z$ = vertical coordinate taken downward from soil surface.

The relationship between the cyclic stress ratio ${\chi }_0$ and the residual pore pressure ratio $u_e/{\sigma }_{v0}^{\prime }$ at the shallow soil depth is depicted in Fig. 12 on the basis of the results from three cases: the no-countermeasures case (Case 6), the case of gravel layer in the 60° range (Case7), and the 120° case (Case 8). Looking first at the soil response in the no-countermeasures case (Case 6) (Fig. 12, hollow circles), the residual pore-pressure ratio $u_e/{\sigma }_{v0}^{\prime }$ increased with increasing ${\chi }_0$ and reached unity at a critical value ${\chi }_{cr}$, 0.106; $u_e/{\sigma }_{v0}^{\prime }=1.0$ indicates the occurrence of liquefaction, and the critical value ${\chi }_{cr}$, beyond which liquefaction occurs, indicates the liquefaction resistance of a given sand bed. Looking at the soil response in the case of the 60° gravel layer (Case 7) (Fig. 12, hollow diamonds), the critical value ${\chi }_{cr}$ was 0.112, which was somewhat higher than the ${\chi }_{cr}$ value in the no-countermeasures case (Case 6). This means that the liquefaction resistance became slightly higher when the gravel layer was applied in the 60° range. Finally, looking at the soil response in the case of 120° gravel layer case (Case 8) (Fig. 12, solid circles), the critical value ${\chi }_{cr}$ was considerably higher than that in the no-countermeasures case. The critical value in Case 8 was 0.146, whereas the value in the no-countermeasures case (Case 6) was 0.106. This indicates that the liquefaction resistance of the sand bed increased by 40% owing to the gravel layer replacement in a 120° range over the soil surface.

The process of wave-induced liquefaction is progressive in nature. This section discusses the progressive nature of liquefaction in a soil bed with gravel layer replacement. Measured time histories of the downward progress of the liquefied zone in the course of wave loading are shown in Fig. 13, in which the advance of liquefaction is based on the time records of the occurrence of liquefaction at three different soil depths. In these tests, the differences in the time of occurrence of liquefaction at the shallow soil depth corresponded to those in the liquefaction resistance ${\chi }_{cr}$ of each case, which was discussed in the previous section. The form of progressive liquefaction in the case of a 60° gravel layer (Case 7) was the same as that of the no-countermeasures case (Case 6). By contrast, in the case of a 120° gravel cover, liquefaction at a shallow soil depth occurred significantly later than in the no-countermeasures case. This is because of the increase in the liquefaction resistance ${\chi }_{cr}$ caused by gravel layer replacement. However, the rate of downward progress of the liquefaction was more rapid because the sand at the greater depth was not improved by the gravel layer at the soil surface. This indicates that it is important for practical designs to prevent the onset of liquefaction against design waves by increasing the liquefaction resistance ${\chi }_{cr}$ in a sufficient manner by effective countermeasures, such as gravel layer replacement.

The instability of the buried pipe under severe wave loading was observed using the high-speed camera. Figs. 14(a–d) show the pipe–soil–gravel behavior during wave loading at four different times in the case of a gravel layer in the 120° range (Case 8). A gravel cover with a sufficient range brought about less development of floatation of the pipe and prevented it from reaching the soil surface. Closer observation of the sand–gravel–pipe behavior shows that after the occurrence of liquefaction in the sand bed, the soil surface started vibrating. Both ends of the gravel layer began to sink in association with the vibratory soil motion [Fig. 14(b)]. The gravel layer directly above the pipe prevented the liquefied sand from enhancing the vibratory motion, leading to less movement of the pipe [Fig. 14(c)]. Thus, the pipe did not float to the soil surface [Fig. 14(d)].

By contrast, a gravel cover with an insufficient range could not prevent the pipe from floating to the soil surface. This aspect can be clearly seen in Figs. 14(e–h), which show the floatation of the pipe in Case 7. The insufficient gravel layer could not prevent the liquefied sand from enhancing vibratory motion, leading to significant pipe floatation.

The elliptical trajectory of the pipe movement of Case 7 is shown in Fig. 15. As a result of the dynamic interaction between the waves and liquefied soil near the soil surface, the pipe moved laterally in the same direction as the progressive wave. The pipe passed the end of the gravel, reached the soil surface, and was exposed. Thus, a gravel layer with an insufficient range could not prevent pipe exposure.

The effects of a gravel layer on floatation of the pipe are clearly shown in Fig. 16, which shows the time histories of vertical movement of the pipe centre during wave loading for Cases 6, 7, and 8 and the measured wave pressure at the soil surface for Case 8. The rate of development of pipe displacement in Case 8, which had a gravel layer in the 120° range, was much lower than that in the no-countermeasures case (Case 6). The vertical displacement of the pipe in Case 8 was 18 mm after passage of the storm wave group, and it remained at 15 mm below the soil surface, corresponding to a 1-m depth of burial on a prototype scale. Closer observation of its development indicates that the amplitude of pipe vibration of this case was much smaller than that in the no-countermeasures case, indicating that the sufficient range of the gravel layer prevented liquefied soil motion caused by severe wave loading. By contrast, in Case 7, which had a gravel layer in the range of 60°, the pipe floated upward at the same rate as in the no-countermeasures case. This floatation was closely associated with the development of the elliptical motion of the pipe, which was brought about by the significant vibratory motion of the liquefied sand, and it finally reached the soil surface. It was found that a gravel cover with a range of 120° proved sufficient in preventing significant vibratory motion of the liquefied soil and floatation of the pipe and could thus be an effective countermeasure against wave-induced liquefaction and pipe floatation.