This article highlights the development of a large shaking table test for sand liquefaction analysis. Two soil containers of different sizes were fabricated. The first one was small (0.87 m × 0.87 m × 1.20 m) in which the reconstitution and saturation methods could be easily tested. The dry tamping (DT) method was used to fabricate a model specimen. The subsequent field measurements suggested that the DT method provided a good distribution of sand grains in different cross sections. Before supplying the model specimen with water, carbon dioxide was flushed to replace air bubbles. This helped in obtaining a good degree of saturation, later verified by a digital moisture meter. For a given inlet water flux, the recorded pore water pressure displayed a quasi-linear trend, suggesting a good internal void system. This reconfirms the effectiveness of the DT method to yield homogeneous model specimens. The second soil container was huge (4 m × 4 m × 2 m) and used to explore liquefaction behavior in real engineering dimensions. Flexible foams were mounted on the side walls to mitigate the boundary effect. Although the boundary effect still manifested itself near the edges of the container during base shaking, half of the model specimen underwent a correct simple shear condition. For further analysis, vane shear tests were carried out before and after the liquefaction test. It was found that the intermediate layer, in general, suffered from the most severe liquefaction failure.

Research activities into sand liquefaction have been conducted since the 1964 Niigata earthquake in Japan [1, 2]. In the laboratory, monotonic and cyclic triaxial tests are widely adopted to investigate liquefaction responses. As for laboratory element tests, the state parameter (considering both relative density and consolidation stress [3, 4]) and degree of saturation are two decisive indicators [5, 6] for examining the liquefaction potential. Besides, the soil fabric [7, 8] formed in different specimen reconstitution methods [9-11] has recently been proven to be another influential factor in controlling liquefaction triggering.

Although triaxial tests certainly provide valuable insights into the mechanism of sand liquefaction, the understanding based on these tests is still limited by the size effect and thus only represents the liquefaction behavior of a unit soil element. This is far from representing a natural soil extent subjected to seismic loading in a semi-infinite space. Therefore, shaking table tests play an increasingly important role in the context of geotechnical earthquake engineering and contribute to improving the understanding of the liquefaction phenomenon. Many successful configurations have been presented in the literature [12-17]. Teparaksa and Koseki [18] performed a series of liquefaction tests on a shaking table to assess the effect of liquefaction history on liquefaction resistance of level ground. Ko and Chen [19] investigated the evolution of mechanical properties of saturated sand during the process of liquefaction via shaking table tests. Due to convenience, the sectional areas pertaining to these configurations (usually lower than 10 m2) are still too conservative to involve full-scale structural components directly in the liquefaction process. For engineering purposes, it is of great importance to develop a large shaking table test capable of considering complete soil–structure interactions. For such a test, a satisfactory internal homogeneity (related to the applied reconstitution method) and degree of saturation of the model sand specimen are two basic requirements for further investigation. However, the above studies usually developed their own experimental procedures according to their specimens’ sizes and available equipment. Due to the authors’ limited knowledge, a pertinent reconstitution and saturation program remains a paucity in the literature, especially for large shaking table tests involving sand liquefaction. In addition, an in-depth assessment method for the quality of the fabricated model specimen is still needed.

To fill these knowledge gaps, this study presents the development of a large shaking table test (more than 28 m3) for sand liquefaction analysis with the fabrication of two soil containers. The first one was small (0.87 m × 0.87 m × 1.20 m) with the objective of seeking the correct reconstitution and saturation methods. Two preliminary tests were then conducted so as to establish the relationship between the internal homogeneity and field measurements, as well as to check the obtained degree of saturation. The second one was huge in size (4 m × 4 m × 2 m) so as to investigate liquefaction responses in actual engineering dimensions. To ensure that most of the model specimen could undergo a correct simple shear condition during base shaking, an economical and practical method was employed to mitigate the boundary effect. The method consisted of attaching flexible foams to the side walls to suppress the reflection of incident waves. A complete liquefaction experiment was finally performed to check the effectiveness of the above mitigation strategy and detect the sensible region to sand liquefaction.

The remainder of this article is organized as follows. The index properties of the used sand are first given. In the third section, the developed reconstitution and saturation methods are introduced with the small soil container, followed by a detailed discussion about their performances. In the next section, the experimental results of the huge shaking table liquefaction test in the large soil container are presented. Finally, we discuss the observed boundary effect during base shaking and the relevant field results.

2.1. Hostun 31 Sand

In this study, a poorly graded French reference sand Hostun 31 (HN31) was used for liquefaction analysis. This sand is characterized by a mean grain size of D50 = 0.35 mm, a uniformity coefficient of Cu = D60/D10 = 1.57, a minimum void ratio of emin = 0.656, a maximum void ratio of emax = 1.00, and a special gravity of Gs = 2.65 [20, 21]. The grain size distribution curve measured by the laser diffraction method is provided in Figure 1.

2.2. Reconstitution Method

Besides void ratio and consolidation stress [3, 22, 23] , the depositional method [9, 24] has been recognized as another decisive factor influencing the evolution of sand liquefaction. In a general sense, air pluviation is a convenient method widely adopted to fabricate homogenous sand specimens on shaking tables. However, the free fall of sand grains under gravity for large-scale experiments unavoidably causes thick sand dust in the testing hall, which is harmful to the MTS load cells. In addition, the realization of a sand hopper able to house such a voluminous granular assembly, as in this study, is almost impossible. As an alternative, the dry tamping (DT) method was selected and first examined with the small container to check the homogeneity of the reconstituted specimen. Zhu et al. [25] used the DT method to fabricate an element specimen in undrained triaxial tests and thus confirmed the repeatability of this approach. To gain a complete insight into the internal homogeneity, the vane shear test has been taken as a yardstick to recognize the quality of specimens yielded by the DT method [26]. In geotechnical engineering, the vane shear test is a convenient field method to estimate the shear strength of a soil unit at a given depth [27]. The experiment is quick and cost-effective for field measurements. Commercially available vane shear equipment (manufactured by YING AN YANG) was adopted, mainly composed of (i) several extension bars to attain a maximum depth of 3 m and (ii) a torsiometer with a precision greater than 10%.

Prior to assessing the internal homogeneity directly in the small container, it was of great importance to first understand the shear strength profile of a uniform sand column. Therefore, an element specimen of 18.7 cm in diameter and 40 cm in height was fabricated in the laboratory with five layers using the DT method, as shown in Figure 2(a). The mass of each layer was controlled to achieve a medium-dense state with a relative density Dr of 50%. Afterward, each layer was successively placed into a split-mold and carefully compacted in order to meet the required thickness of 8 cm using a handheld tamper. The vane shear readings were performed at the central part of the specimen to avoid size and boundary effects as much as possible, and the reading frequency was set to be every 5 cm. It can be seen from Figure 2(b) that the vane shear resistance τf increases in a general linear manner with the depth, although a slight parabolic tendency can be observed between 10 and 20 cm. This phenomenon can be reasonably explained by the fact that granular material such as sand usually has a greater effective friction angle subjected to a lower consolidation stress due to a shallow depth. However, this small deviation does not change the conclusion that the shear strength of soil should quasi-linearly increase with the increment in depth if this soil column is relatively uniform [26].

In the small container, a model sand column of 60 cm in the initial height was reconstituted with the DT method to meet a dense state of Dr = 70%. The tamping technique consisted of (i) first placing a strong wooden plate on the surface of each layer and (ii) then dropping a heavy hammer to densify the model specimen, as shown in Figure 3(a). For a better result, this procedure was repeated by altering the position of the plate. The vane shear tests were carried out at five positions (central part and four corners) and at four depths (10, 20, 30, and 40 cm). Because the obtained vane shear values at the same depth fell within a narrow dispersion range (i.e. ±15%), all experimental data were consequently averaged. In Figure 3(b), it can be seen that the mean values can be satisfactorily fitted by a straight line, consistent with the previous observation in the element size. This reveals that the DT method is still capable of yielding relatively homogeneous model specimens for shaking table tests. Although the final settlement after the compaction was hard to measure accurately in such a configuration, the authors acknowledge that the final value was certainly an underestimation for the attainment of Dr = 70%. Therefore, this model specimen was further subjected to a white noise excitation on a small shaking table Vésuve at French Alternative Energies and Atomic Energy Commission (CEA), as shown in Figure 4. The white noise was terminated when a relative density of about Dr = 66% was reached and vane shear measurements were immediately performed after the excitation. Two phenomena can be observed in Figure 3(b): (i) the subsequent base shaking continued to densify the model specimen since τf slightly increased as compared with the previous curve; and (ii) the “quasi-linear” pattern was not destroyed by the subsequent loading, indicating a satisfactory soil homogeneity. From these two experiments, it can be deduced that the DT method can be viewed as beneficial to meet the uniformity requirement. However, the tamping procedure is too time-consuming for higher densities, and some mechanical vibrations are sometimes necessary to enhance the compaction effect.

2.3. Saturation Method

With the purpose of examining the feasibility of the saturation method, a preliminary test was designed, as shown in Figure 5. In the small container, an inlet tube and a drainage layer were installed to introduce and diffuse water in a uniform manner, respectively. After placing a thin geotextile, a model specimen (80 cm) with Dr = 50% was built using the DT method. A pore water transducer was placed at the bottom of the model specimen to detect the variation of waterhead during saturation. Afterward, the container was completely closed with an air-proof cover, as shown in Figure 6. Carbon dioxide (CO2) was first flushed across the dry specimen to replace regular air. The inlet flux was controlled to be only 15 kPa in order not to destroy the fragile soil fabric [21, 28]. To ensure safety, an aeration device was activated and kept working during the injection. The complete filling of CO2 was checked by a sensible detector: the color of the device changed to red if the CO2 concentration at the top part of the container was greater than 2000 ppm. Using the same inlet line, water was then injected to saturate the model specimen. The inlet flux was set to only 2 L per minute through a fluxmeter (Figure 6).

Figure 7 displays the relationship between the pore water pressure (at the bottom recorded by the pore water transducer), the water level (manual recorded roughly every 10 minutes), and the injection time. As for the initial parts in Figure 7, both curves remain null since the entry water needed approximately 1 hour to pass through the drainage layer. After this, a linear tendency is suggested by both curves. For a given inlet flux, this linear tendency implies that the internal void ratios at various depths can be considered to be roughly the same; namely, the uniformity of the model specimen built by the DT method is reconfirmed here. After about 3 hours, the pore water pressure reached a value of about 8 kPa, corresponding well to a model specimen of 80 cm in height. Finally, the moisture content (i.e. the mass of pore water divided by the total surrounding soil mass) was measured with a digital moisture meter DM300L (with the precision of about 0.01% in double precision mode) to derive the degree of saturation Sr, as shown in Figure 8. And the final value was very close to 100%, indicating good saturation.

3.1. Earthquake Simulation Facility

In this study, a huge shaking table Azalée developed at the Tamaris experimental platform at CEA was employed to produce base shaking. As shown in Figure 9, the table has an upper plate of about 25 tons in square form (6 m × 6 m), able to generate excitations with 6 degrees of freedom (3 degrees in translation and another 3 in rotation) using four vertical actuators and four horizontal actuators, each with a capacity of 1000 kN. In practice, a maximum acceleration of about 1 g can be generated with a model specimen of up to 100 tons.

In the context of sand liquefaction simulation on shaking tables, model specimens need to be reconstituted within finite boundaries provided by a model container. A poorly chosen artificial boundary condition may primarily influence the stress and strain fields [13, 14, 17] that are not present in the real field since soil mass is commonly supposed to be in a semi-infinite half space. In an ideal situation, the side walls of the soil container should (i) behave exactly as soil mass in field conditions, maintaining the stress field as closely as possible; and (ii) further capable of altering its mechanical characteristics during base shaking. Provided that sand liquefaction involves important soil stiffness and modulus degradation with the increase in excess pore water pressure [29, 30], the above requirements are often difficult to meet. Although there is no perfect technical solution to overcome the above dissimilarity, a general consensus regarding model container designs has been achieved. Some examples have already been reported in the literature such as (i) equivalent shear beam container [31] and (ii) laminar shear box [15, 16] , to name a few of them. As for the scale of interest in this study, these successful applications, however, are too costly to help in mitigating boundary effects, especially for mimicking the “zero-stiffness” state after liquefaction triggering. To this end, several flexible foams of 20 cm were first mounted following the shaking direction in the soil container (4 m × 4 m × 2 m) to restrain the generation of wave reflections on both sides, as displayed in Figure 10. A customized water-proof geomembrane of 5 mm in thickness was later installed in order to prevent pore water from seeping out of the model specimen. A detailed discussion about the boundary effects will be given in the following section.

Prior to depositing sand grains, a drainage layer composed of gravels was placed on the bottom to serve as a macro “porous stone,” as shown in Figure 11(a). The DT method was applied to yield a model specimen with Dr of around 50% (4 layers). The interfaces between two layers in contact were deconstructed in order to increase the cohesion between them. For such a heavy mass, base shaking of high frequency to densify the model specimen is beyond the power of current facilities; thus, a dynamic compactor was employed to replace manual compaction. The same saturation technique (Figure 11(b)) as that in the small container was then initiated. And the final degree of saturation Sr was confirmed by the same digital moisture meter.

3.2. Typical Liquefaction Responses

In this study, a sine-based wave (peak ground acceleration = 0.4 g, loading frequency f = 2 Hz) was used as base excitation, as shown in Figure 12. The input motion was subjected to trapezoidal correction between 5 and 20 seconds to enhance waveform reproducibility through the servo system. In addition, two secure time intervals without motion of about 5 seconds each were allocated at both the beginning and the end although the shaking table indeed experienced some slight motions owing to the resonance of high-pressure oil. In the process of reconstitution, three arrays (L = left, ML = middle left, and C = center) of pore water transducers were buried in the model specimen to capture the liquefaction evolution. The detailed instrument plan is provided in Figure 13(b). The second half of the model specimen in Figure 13(a) was reserved for field investigations (vane shear test) before and after shaking.

Figure 14 displays the time histories of excess pore water pressure (EPWP) Δu at three different depths. In the graph, the triggering of liquefaction is depicted by the gray discontinued lines. As for the bottom part in Figure 14(c), all three curves are almost overlapping with one another. This indicates that the soil elements at the bottom underwent almost the same loading history and their responses were not affected by the boundary effect. As for the middle part in Figure 14(b), the curve at the center is close to that at ML. However, they are visibly different from the curve at the left corner, contrary to what was observed at the bottom. Near the top free surface in Figure 14(a), similar conclusions can be drawn. Two curves (C and ML) near and at the center follow almost the same trend and visibly differ from that near the left corner. The above phenomena imply that the boundary effect at the bottom is so weak that it can be ignored. With the decrease in depth, the boundary effect plays a more important role, especially near the top free surface. This is consistent with the previous results in the literature [15, 16, 32]. More importantly, about half of the model specimen around the center is free of the boundary effect since the attached flexible foams could properly reduce wave reflections at the side walls so as to guarantee the needed simple shear condition for liquefaction analysis.

For further comparison, vane shear tests were performed at three locations (see Figure 15) immediately after base shaking. After base shaking, the pore water pressure dissipation commenced immediately. Figure 14 indicates that the dissipation of EPWP was nearly achieved, with ru approaching 0 by t = 60 seconds. This means that EPWP dissipation played only secondary importance for the subsequent vane shear tests, particularly following an equipment preparation stage lasting about 1 hour. Figure 16 presents the relationship between the vane shear reading and the depth. In the graph, it can be seen that the two-thirds part of the model specimen experienced the most severe loss of shear strength. This phenomenon can be explained by the following two independent factors. First, there is a distance between the two-thirds part of the model specimen and the free drainage surface at the top. This certainly enhances the undrained condition in favor of the accumulation of excess pore water pressure Δu. Second, the overburden effective stress at that part is not as high as that at the substratum. Thus, a moderate increase in Δu is sufficient to trigger sand liquefaction.

In this study, two soil containers were manufactured to develop a large shaking table test for sand liquefaction analysis. The first one was small and the objective was to seek the suitable reconstitution and saturation methods. The second one was huge and designed for exploring sand liquefaction at an almost actual engineering size. We can draw the following conclusions from the obtained results.

  1. The DT method is beneficial for building model specimens since it generally provides a good distribution of sand grains to ensure internal homogeneity. For large model specimens especially in a dense state, the manual tamping process can be replaced by base shaking or mechanical vibrations without significantly undermining the homogeneity.

  2. Similar to triaxial tests, the passage of CO2 before saturating model specimens helps in replacing regular air, which can lead to a good degree of saturation. For a given inlet flux, the linear pattern of waterhead during saturation can be set as a criterion by which to judge the internal homogeneity.

  3. For large shaking table tests, the attachment of flexible foams is a cost-effective method to control the boundary effect. Generally, half of the model specimen is free of the boundary effect and undergoes a correct simple shear condition for liquefaction analysis. Both the evolution of excess pore water pressure during base shaking and field investigation suggest that the intermediate layer suffers from the most severe liquefaction failure. Meanwhile, the intermediate layer of the specimen experienced the most severe loss of shear strength through the vane shear tests.

Data will be made available on request.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The financial supports provided by the ANR (Agence Nationale de la Recherche) ISOLATE and the National Natural Science Foundation of China (grant no. 42307190, 52109133) are deeply acknowledged.

The authors thank the technicians at French Alternative Energies and Atomic Energy Commission (CEA) who contributed to this experimental program.

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