Performance assessment of prefabricated vertical drains in mitigating soil reliquefaction subjected to repeated seismic events using shaking table experiments

Abstract

The use of prefabricated vertical drains (PVD) in liquefiable deposits is gaining attention due to enhanced drainage. However, investigations on PVD in mitigating re-liquefaction during repeated shaking events are not available. This study performed a series of shaking table experiments on untreated and PVD-treated specimens prepared with 40% and 60% relative density. Repeated sinusoidal loading was applied with an incremental peak acceleration of 0.1g, 0.2g, 0.3g, and 0.4g, at 5 Hz shaking frequency with 40 s duration. The performance of treated ground was evaluated based on the generation and dissipation of excess pore water pressure (EPWP), induced sand densification, subsidence, and cyclic stress ratio. In addition, the strain accumulated in fresh and exhumed PVD was investigated using geotextile tensile testing apparatus aided with digital image correlation. No evidence of pore pressure was reported up to 0.2g peak acceleration for 40% and 60% relative density specimens. The continuous occurrence of soil densification and drainage medium restrained and delayed the generation of EPWP and expedited the dissipation process. This study demonstrates PVD can mitigate re-liquefaction, without suffering from deterioration, when subjected to medium to high intense repeated shaking events.

Graphical abstract

Keywords

prefabricated vertical drains / drainage / re-liquefaction / shaking table / digital image correlation.

1 Introduction

Liquefaction is a catastrophic geotechnical hazard that affects saturated sand deposits during seismic events and that can result in damage to infrastructure [1,2]. Over the last decade, earthquake swarms/repeated earthquakes have shown the destructive nature of soil re-liquefaction. For example, earthquakes, in 2011 Tohoku, Japan, 2016 Kumamoto, Japan, and 2019 Vancouver, Canada, induced soil re-liquefaction that severely damaged buildings and geotechnical structures. Cubrinovski and McCahon [3] reported a settlement of 1−2 m and an exceeding tilt of 2° in low to midrise structures during the 2010−2011 Christchurch, New Zealand, repeated earthquakes. Researchers worldwide have proposed several ground improvement techniques and have successfully mitigated liquefaction and associated ground deformations. However, the studies on ground improvement techniques to counteract re-liquefaction and associated deformations are limited.

Soil re-liquefaction is a complex and controversial phenomenon in geotechnical earthquake engineering that demands careful scientific investigation. Based on field observations and physical modeling experiments, a better understanding of the mechanism behind re-liquefaction has been achieved in recent years [4–10]. From the literature, it can be seen that, on the one hand, repeated shaking events increase the re-liquefaction resistance [11–13], while other studies imply repeated events decrease resistance to the liquefaction [14–16]. All these studies are valid for their particular soil and seismic loading conditions. Considering the re-liquefaction mechanism and damages reported from past repeated earthquakes, appropriate ground improvement techniques are required to counteract catastrophic damage in the future.

In recent years, few studies have reported on improvement of techniques for mitigating re-liquefaction. Padmanabhan and Shanmugam [17] explored the feasibility of mitigating liquefaction by means of sand compaction piles (SCP), which were subjected to repeated shaking events using a 1g shaking table apparatus. The authors reported a significant reduction in excess pore water pressure (EPWP) at an initial low acceleration amplitude (0.1g). However, SCP induced partial collapse/failure at the end of the final high-intense shaking event (0.4g). Vijay Kumar et al. [18] discussed the efficiency of composite skirted ground reinforcement in mitigating liquefaction subjected to repeated shaking. A significant increment in amplitude reduction and relative density, and an increase in the re-liquefaction resistance, were observed in loose and medium-dense specimens. However, the performance decreases as the repeated shaking events deteriorate the installed improvement technology due to the continuous generation of EPWP. The durability of these improvement techniques is a significant concern in mitigating soil re-liquefaction due to repeated shaking events.

Prefabricated vertical drains (PVD) are commonly used ground improvement techniques to expedite the dissipation of EPWP generated during liquefaction. Howell et al. [19] observed a reduction in r_u,max values, horizontal and vertical deformations in the liquefiable sand deposits using centrifuge experiments. The improvement was attributed to the faster dissipation of EPWP due to the installation of PVD. Paramasivam et al. [20] used centrifuge modeling to investigate the response of structures, and soil-foundation-structure with different embedment depths on PVD-treated deposits. The authors observed that the dynamic soil properties and input motion characteristics influenced the efficacy of PVD in reducing foundation tilt and minimizing EPWP. Farzalizadeh et al. [21] examined the performance of rubber and wall-type gravel drains to enhance the liquefaction resistance of sand specimens using 1g shaking table experiments. Both these drain systems can reduce the EPWP and deformations to a certain extent. However, rubber drains performed relatively better owing to a higher permeability. Other studies also reported, through field and laboratory investigations [22–24], that PVD possesses excellent durability and drainage characteristics. Though these studies substantiate the liquefaction resistance offered by the PVD and other vertical drains, no studies were available on counteracting soil re-liquefaction subjected to repeated shaking events.

The objective of the present study is to investigate the re-liquefaction resistance offered by PVD subjected to repeated incremental acceleration loading. In addition, strain induced by the PVD filter specimen due to repeated shaking events was also examined. A 1g shaking table apparatus mounted with a transparent Perspex container was used to perform the experiments. Saturated ground with 40% and 60% relative density was prepared and tested repeatedly with incremental 0.1g, 0.2g, 0.3g, and 0.4g sinusoidal acceleration loading at 5 Hz frequency and 40 s duration. The applied input motion simulates foreshocks, and the main shock event develops during earthquake incidence of medium to high intensity shaking. The strain induced in the PVD specimen was examined using a geotextile tensile testing machine together with an advanced two-dimensional digital image correlation (2D-DIC) technology. The performance of PVD-treated and untreated ground was evaluated based on EPWP generation, variation in ground density, subsidence, and cyclic stress ratio (CSR). A comparison has also been made with published results of the SCP technique and the PVD-treated ground.

2 Experimental study

This section describes the materials used in this study (Solani sand and PVD), followed by experimental setup and sample preparation. It also elaborates on the selection and design of PVD for experimental studies and the procedure followed during installation. The application of repeated loading and measurement of sand density is discussed in detail. Finally, the theory behind selecting DIC technology for strain measurement in PVD material is discussed.

2.1 Materials used

The sand used for the experiments was procured locally from the Solani riverbed, Roorkee, India (referred to as Solani sand). Tab.1 presents the tested Solani sand’s physical properties, which is categorized as poorly graded sand (SP) as per the guidelines of Ref. [25]. The grain size distribution curve for the Solani sand, along with the liquefaction boundary range, is shown in Fig.1. The obtained grain size distribution curve was found to fall within the range of gradation for liquefiable sand as suggested by Xenaki and Athanasopoulos [26], indicating that the sand is susceptible to liquefaction. From the findings of [27], it is understood that the Solani sand is vulnerable to re-liquefaction when subjected to repeated shaking events.

2.2 Experimental setup

The experimental setup consisted of a 1g uniaxial shaking table having dimensions of 2.0 m × 2.0 m (length × breadth), mounted on rails. The load-carrying capacity of the table was 3 t, and it was attached to a servo-hydraulic actuator that facilitates the movement of the table. The maximum stroke length of the actuator was ± 160 mm. The table worked with an operating frequency range of 0.01−50 Hz with a peak velocity of 2 m/s and acceleration from 0.001g to 1g. The entire operation of the shaking table was performed through a digital controlled data acquisition system. The control unit could accept sine, rectangular, triangular, and reduced-scale earthquake motions as input motions.

2.3 Sample preparation

A transparent Perspex model tank of dimensions 1.4 m × 1 m × 1 m (length × breadth × height) was mounted over the shaking table, as shown in Fig.2. To counteract the boundary effects, 50 mm thick polyurethane foam was placed at right angles to the shaking direction in the tank. Studies conducted by Ha et al. [16] and Punetha [28] reported that the polyurethane foam is sufficient to absorb the refracted wave forms. For simulating actual field conditions, the bottom surface of the model tank was made rough using a sandblasting technique. The saturated sand specimens, having 40% and 60% relative density, were prepared inside the tank to a height of 600 mm. A specially designed conical hopper arrangement was used for preparing the specimens. The wet sedimentation method was adopted for preparing the testing ground as this preparation technique replicates the behavior of alluvial soil deposition in actual ground conditions [29].

Repeated relative density tests were performed as per Ref. [30] for calculating the optimum height of fall for achieving the desired relative density chosen for the study. Fig.3 displays the optimum height of fall values for different relative densities.

The amounts of dry sand and water required to prepare the specimens were calculated for both the density values. Resultant relative density increases with the height of the fall of sand in the tank. As illustrated in Fig.3, dry sand was poured from 10 and 15 cm to achieve the required relative densities of 40% and 60%, respectively. Using, wet sedimentation technique the saturated ground was prepared. The specimen preparation was carried out in three layers. Initially, 1/3 of the water was poured into the tank, followed by the deposition of dry Solani sand. The sand was poured into the box containing water using a hopper arrangement. Since the terminal velocity of sand falling through water is lower than in air, the sand settlement took place slowly, which facilitated achieving uniformity in horizontal deposition during sample preparation. Further, the ground was prepared with alternate water and sand layers to achieve uniform saturation and homogeneity in sand deposition in horizontal conditions. The hopper was moved along the horizontal direction at a constant velocity (of approximately 5 mm/s based on the sand settlement rate as observed in trial tests). The homogeneity of the prepared ground was ensured by comparing the estimated height of each layer with the achieved height during sample preparation. Thus, the wet sedimentation technique simulates the deposition of sand through water that is found in many natural environments involving natural alluvial soils [31,32]. The sand samples prepared by using the wet sedimentation technique have similar fabric and behavior and hence the technique could simulate homogeneity in ground preparation. The procedure was followed up to a selected height of 600 mm. Fig.4(a)–Fig.4(c) display the stages of sample preparation. Proper care was taken throughout the sample preparation to maintain the height of the fall. Padmanabhan and Shanmugam [27] and Maheshwari et al. [33] followed a similar procedure for sample preparation. For monitoring pore pressure generation and dissipation, two pore pressure piezometers were used. The pore pressure piezometers were installed along the center line of the tank to avoid rigid boundary interferences, and at depths of 0.2 and 0.4 m from the base of the tank as shown in Fig.5. This method of pore pressure measurement was found to be successful by Varghese and Latha [29] and Maheshwari et al. [33] to counteract the refraction of waveforms in liquefaction instrumentation. The authors also attempted to use accelerometers during the trial tests for monitoring acceleration response of the saturated ground during repeated shaking. However, due to continuous incremental shaking and with continuous water expulsion from the ground, the accelerometers were displaced and malfunctioned repeatedly. Due to this, accelerometers were not installed in the study.

2.4 Selection and installation of prefabricated vertical drains

The PVD of dimensions 100 mm wide and 5 mm thick used in this study were procured from M/s Techfab India Industries Private Limited, Maharashtra, India. Fig.6(a) shows the PVD used in the study and the properties are presented in Tab.2. Fig.6(b) shows the cross-section of the PVD. As shown in Fig.6, PVD comprised two parts: 1) a plastic core to help to resist buckling and longitudinal stretching and to accelerate the drainage process; 2) a geotextile filter fabric encasing the plastic core, acting as a soil filter to prevent the entry of finer sand particles to avoid clogging [34,35]. The tensile strength of the PVD filter was examined using an electromechanical geotextile tensile testing (100ST) machine available in CSIR–CBRI, Roorkee, India. The machine tested the tensile strength of geosynthetics to a load of 100 kN with 0.001 to 500 mm/min test speed. Clearance between the two columns is 656 mm, and a maximum crosshead travel of 1198 mm. The machine contained an inbuilt ASTM code library for testing geosynthetics. For the present study, ASTM D4632 [36] was followed for testing the PVD filter specimen.

The re-liquefaction mitigation studies by Padmanabhan and Shanmugam [17] and Vijay Kumar et al. [18] observed partial collapse/failure of the selected treatment techniques at the end of the final shaking event. Therefore, attention was given to the selection of spacing and material, repeated shaking events and continuous generation of EPWP, which could have induced deformations to the PVD. A triangular pattern was adopted in the present study, as it possesses a better influence area [37] than a square pattern. The installation was performed using a specially designed mandrel shown in Fig.6(c). PVD was connected with the mandrel, so that the installation process would be easier in the saturated sand specimen as shown in Fig.6(d). The PVD connected with the mandrel was then pushed inside the prepared ground with minimum vibration. Fig.7(a) shows the installation of PVD in the prepared saturated sand specimen. The increment in sand density was observed after installation of PVD in the ground. Proper care was taken in installing the PVD specimen to the complete depth without causing damage. It refers to the minimum disturbances on the prepared saturated sand specimen during the installation of PVD. Similarly, during PVD exhume, the intervening soil was removed first after tests to minimize the surface rupturing of PVD samples. After complete removal of soil, the PVDs were exhumed and taken for the post strength evaluation studies. Fig.7(b) shows PVD improvement system.

2.5 Design of PVD

The critical parameters in designing a PVD improvement system are the equivalent drain diameter (d_e) and center-to-center spacing. Using Eq. (1), proposed by Ref. [38], d_e was estimated for PVD used in this study.

(1)d_{\mathrm{e}}= \frac{2\left(b+t\right)}{\text{π}}.

It was found that d_e was small (0.0668 m) for PVD compared with other forms of vertical drains installed in the field (circular drains are approximately 0.6 m), therefore the spacing will be less for PVDs. The center-to-center spacing of drains was calculated based on charts and equations proposed by Ref. [39], considering the 0.60 r_u,max as the threshold design limit. In general, spacing was selected as four times the effective diameter of the drain [38]. Based on the soil characteristics and shaking duration, the drain spacing was selected as 200 mm and ratio a/B≤ 0.3 (a = drain radius, B = half the effective spacing of drains) [40]. The installation layout of the PVD improvement system with spacing dimensions was shown in Fig.7(c). The authors believe the drain design can simulate the field conditions that can mitigate re-liquefaction and associated deformations. To avoid collision with installed pore pressure piezometers along center line of the tank, PVD was not installed centrally in the tank.

2.6 Application of repeated incremental acceleration loading to the ground bed

The sinusoidal waveform was selected as a base motion to study the behavior of PVD-treated and untreated sand specimens [19,30,41]. Repeated incremental shaking of 0.1g, 0.2g, 0.3g, and 0.4g peak acceleration with 5 Hz frequency and 40 s shaking duration was selected. This was to simulate a series of foreshock events followed by a main-shock event (e.g., 2016 Kumamoto earthquake series, Japan) [42]. The test matrix adopted in the present study is shown in Tab.3, where RD refers to the initial relative density of the prepared saturated sand specimen. The specimen was shaken four times in succession, and shaking was applied only after ensuring complete dissipation of EPWP generated during the previous shaking. Pore pressure response was measured with attached piezometers, and the time taken for generation and dissipation was monitored continuously for each shaking.

2.7 Evaluation of relative density

The relative density of ground was estimated using digital cone penetrometer test (DCPT). The penetrometer consists of drive cone assembly with a 60° cone angle and 1.5 cm² area and carefully driven at 10 to 15 mm/s [43]. The cone assembly was connected to an adjustable extension rod for deeper penetration. The penetration resistance at every 100 mm depth was measured on digital display and the relative density (RD) was estimated using Eq. (2) as proposed Ref. [44].

(2)RD=100\left[0.268\times \mathrm{l}\mathrm{n}\left(\frac{q_{\mathrm{t}}/{\sigma }_{\mathrm{a}\mathrm{t}\mathrm{m}}}{\sqrt{{\sigma }_{\mathrm{v}\mathrm{o}}/{\sigma }_{\mathrm{a}\mathrm{t}\mathrm{m}}}}\right)-0.675\right].

2.8 DIC measurement technique for strain monitoring and estimation

The displacement/strain in PVD filter material was tested using geosynthetic tensile testing apparatus aided with DIC technology. Fig.8 shows the 2D-DIC setup and geotextile tensile testing used in the study. DIC technology offers non-contact image analysis for measuring displacement/strain over the region of interest (ROI). The camera had a pixel resolution of 2048 × 1088 and is powered with a high-speed CMOS sensor (complementary metal-oxide semiconductor sensor). The camera and was equipped with a 50 mm lens that could capture images at up to 168 frames per second. In this study, images were captured at a rate of 30 frames per second. The camera was positioned perpendicularly to the plane of PVD and placed at a distance to capture ROI. Before testing, PVD was randomly speckled by spraying white paint on the ROI. Uniform illumination of the PVD was achieved using two light-emitting diodes (LED) floodlights placed at a 45° angle. The recorded digital images were then processed in terms of greyscale value using VIC-2D software, which offered an estimation of displacement or contours of a material subjected to loading.

3 Results and discussion

Liquefaction parameters such as EPWP generation and dissipation of untreated and PVD-treated specimens, together with the influence of induced sand densification and measured soil subsidence during repeated shaking on re-liquefaction remediation, are discussed in this section. Finally, CSR’s significance on treated and untreated ground subjected to repeated shaking events is elaborated.

3.1 Strain estimation using 2D digital image correlation technique

When saturated ground is subjected to earthquake motions, it may experience random variations in stress, strain, and frequency. The induced variation in strain response can affect the seismic resistance in repeated shaking events. Considering this, an attempt has been made in this study to compare the strain variation in PVD filter material. The comparison can be performed by estimating the strain response of a fresh PVD and an exhumed PVD after the shaking table experiments. The strain estimation was done by conducting a tensile strength test on the obtained PVD specimens. The strain development during tensile testing was monitored and estimated using the 2D-DIC technique. The detailed test arrangement is shown in Fig.8. For tensile testing, a speckled PVD filter specimen was placed in a tensile testing machine and tested at 300 mm/min speed as per [36]. Images were captured continuously using the previously described camera and analyzed using VIC-2D software. Typical strain contours obtained from DIC at different stages of loading are shown in Fig.9(a) and Fig.9(b). The elongation of PVD fabric is visible in each stage, as illustrated in Fig.9. The strain analysis was performed through VIC-2D software.

Fig.10(a) and Fig.10(b) present the tensile strength of the fresh and exhumed PVD specimen after the shaking tests. The maximum strains were 61.5% and 65.9%, corresponding to forces of 855 and 751 N for fresh and exhumed PVD filter material, respectively. A minimal reduction in tensile load capacity (about 12%) was observed in the obtained specimens. No surface distress/rupture was observed in the exposed filter and there was no evidence of significant damage in the PVD system after testing. Further, the obtained tensile load tests and strain response on the samples, estimated using 2D DIC, also confirmed no significant distress in the specimens. As reported by Deng et al. [45] and Bo et al. [46], tensile strength of PVD is critical in influencing the discharge capacity of the PVD. The observations demonstrated that the tensile characteristics of the PVD offer more flexibility during repeated shaking and were found to be durable even at higher shaking events.

3.2 Influence of repeated shaking events on penetration resistance and induced density for untreated and treated specimen

DCPT tests were performed at random locations (minimum 4), before testing and after the complete dissipation of generated EPWPs, for estimating penetration resistance and density of the ground. It was observed that the variations in penetration resistance values at the selected locations were within 3% to 5% and the authors used average penetration resistance values for estimating penetration resistance and relative density of the ground during testing. Fig.11 presents the observed cone penetration resistance and estimated relative density of the freshly prepared untreated and PVD-treated sand specimens. It can be seen from Fig.11 that, there is a slight improvement in initial relative density and penetration values for untreated ground. The increase may be attributed to the sample preparation method; that is, to the wet sedimentation method, where deposition of soil particles induces slight overburden pressure causing little increment in density. In the case of the treated ground, installation of PVD improved the relative density of saturated specimens for both the density conditions (i.e., 10 to 20% improvement for the 40% and for the 60% density specimens) due to the drainage characteristics of the installed member on the prepared ground. From Fig.11(b), it can also be seen that the prepared sand specimen maintains uniform sand density in both density conditions. The freshly prepared saturated ground has reported relative density in the range of (35%–40%) and (55%–60%) for 40% and 60% density specimens.

The variation of cone penetration resistance along the depth is presented in Fig.12 for both density conditions. From Fig.12(a), it can be seen that the penetration resistance increased with the application of repeated incremental acceleration loading. Compared to the 40% relative density ground, the 60% relative density ground showed considerably more resistance to penetration, as can be seen in Fig.12(b), after being subjected to repeated shaking events. The increase is due to the influence of the initial relative density of the sand specimens. Both Fig.12(a) and Fig.12(b) show that PVD-treatment increased cone penetration resistance. It can be inferred that drainage, together with in situ densification during repeated shaking, resulted in higher penetration resistance and in situ density in the case of treated ground.

Fig.13 illustrates the variation of estimated relative density along the depth of the soil specimen for both grounds subjected to repeated shaking events. It can be seen from Fig.13(a) and Fig.13(b) that the relative density of the specimens increases with the application of repeated incremental acceleration loading. From both these figures, it can be inferred that the non-uniformity in densification in untreated sand specimen stimulated the continuous generation of EPWP from bottom to top while applying incremental loading. Similar observations were also reported Refs. [47–49] using centrifuge modeling and large-scale shaking table experiments. Whereas in PVD-treated specimens, more uniformity in densification was observed, resulting in the increase of re-liquefaction resistance.

The induced densification is primarily associated with the dissipation of EPWP that resulted in the reconsolidation of the PVD-treated sand specimen. The reconsolidation process is a one-dimensional phenomenon that causes the deformation of the soil specimen in the water-saturated porous medium. The soil specimen undergoes a continuous process of reconsolidation after each repeated shaking event, whereas the induced densification can result in either increase or decrease of the resistance to soil re-liquefaction [6]. Due to the presence of an effective drainage layer, time for reconsolidation reduces, which causes more uniformity in soil densification which in turn mitigates the generation of pore water pressure. In the absence of a drainage medium, time for consolidation increases, resulting in non-uniformity of soil density with depth.

In the present study, the beneficial effect of induced sand densification was not observed in the case of untreated deposits. The influence of the reconsolidation on re-liquefaction resistance of PVD-treated and untreated sand specimens is further discussed in the following section, in terms of EPWP.

To validate the DCPT results, relative density values was estimated from the measured soil subsidence values (refer to Subsection 3.4) and the values are presented in Fig.14. The relative density was estimated using calculated soil volume after each shaking event together with the bulk density. Relative density values obtained from DCPT were slightly higher than values estimated using soil subsidence for both 40% and 60% relative density. About 1% to 5% variation was observed between DCPT and estimated values. The variation may be due to the driving energy of DCPT equipment during penetration. This was due to additional increment in penetration resistance showing few variations. However, the observations confirmed that the estimated density values were in good agreement and that DCPT can be useful for estimating the in situ density of the ground.

3.3 Pore water pressure response for treated and untreated ground during repeated shaking events

During experimental investigations, shaking was repeated only after ensuring the complete dissipation of generated EPWP measured from the installed piezometers. The pore pressure ratio (r_u) is the ratio between EPWP in kPa to the effective overburden pressure {\sigma }_{\mathrm{v}\mathrm{o}}^{\mathrm{\prime }} in kPa at that depth. Fig.15 presents the r_u time history of PVD-treated and untreated sand specimens prepared with 40% relative density. In general, it is observed that r_u was maximum at a depth of 0.4 m and minimum at 0.2 m. The difference was due to the soil overburden pressure, which was higher at the bottom and lower at the top. Fig.15(a) shows that r_u reached a value close to unity (almost liquefied state) for untreated specimen, whereas the r_u was completely restrained in the case of the PVD treated specimen. This is attributed to the following factors: (i) drainage offered by the PVD, which could minimize and dissipate the generation of EPWP, and (ii) soil densification due to quicker consolidation of disturbed soil grains during shaking conditions.

When the same specimen was shaken again at 0.2g acceleration, r_u reached a value close to 0.6 (within design limit) for the PVD-treated specimen as shown in Fig.15(b). However, the untreated specimen became reliquefied for the same loading due to undrained loading conditions with non-uniform soil densification. Although generation of pore water pressures was observed due to repeated shaking, installation of PVD’s expedited the dissipation process and made the soil stable by achieving a density increment at every successive shaking. Similar observations can be observed for the specimen shaken at 0.3g and 0.4g, where PVD specimens perform better than untreated sand specimens in resisting the generation of EPWP and expediting the dissipation process, as illustrated in Fig.15(c) and Fig.15(d). As also shown in Fig.15, untreated specimens completely liquefied and reliquefied in all the shaking events ranging from 0.1g to 0.4g peak acceleration loading. The PVD-treated specimen completely restrained pore pressure at 0.1g, limiting the pore pressure to within the design limit till peak acceleration became 0.3g. These values were slightly higher than the design limit for 0.4g acceleration values. The difference in induced relative density of untreated and PVD treated specimen is relatively small during the final shaking, since PVD improves the re-liquefaction resistance significantly by achieving quicker soil deposition together with drainage mechanism. The delay in soil compaction due to the absence of a drainage layer results in non-uniform soil densification in the case of untreated ground. Irrespective of the induced densification in both cases, the drainage effects influencing the soil resistance against reliquefaction during repeated shaking events.

Apart from the induced sand densification that resulted from the repeated shaking events and PVD installation, the influence of initial relative density was also examined for both treated and untreated sand conditions. For this, sand specimens were prepared at 60% relative density and tested under repeated incremental loading. As shown in Fig.16(a) and Fig.16(b), r_u was generated to a maximum of 0.70 and 0.75 for 0.1g and 0.2g, respectively, for untreated sand specimen, whereas r_u was completely restrained for both the peak acceleration values in the case of PVD treated ground. For PVD treated ground, initial sand density along with induced sand densification and drainage path offered more resistance to re-liquefaction during low to medium shaking conditions, than occurred in the case of 40% relative density ground. At 0.3g acceleration, r_u was significantly less in PVD-treated than in untreated sand specimen, as illustrated in Fig.16(c). Fig.16(d) shows that untreated specimen almost liquefied at shallow depth for 0.4g loading, whereas for the PVD-treated specimen r_u was within the threshold design limit. From results for both 40% and 60% density specimens, it can be inferred that PVD-treated specimens: 1) performed better at medium intense shaking events (up to 0.2g) depending on the ground conditions and, 2) enhanced drainage delayed EPWP generation, which improved the resistance of soil at shallow depth.

These observations are further validated using parameters such as maximum pore pressure ratio build-up time (t₁) duration (t₂) and dissipation time (t₃). Performance of PVD against re-liquefaction was examined based on r_u, on the time taken to attain r_u,max, and on the dissipation time. The liquefaction response time for both untreated and treated ground at 0.2 m and 0.4 m deep is presented in Tab.4. In general, it can be observed that: 1) t₁ decreased with the incremental acceleration loading and; 2) PVD treated specimen offered more time to attain r_u,max and for dissipation of EPWP. The higher relative density contributed to delaying t₁; however, its influence is not pronounced regarding t₃. In such cases, the drainage mechanism is influential in reducing the time taken for the pore pressure dissipation. Moreover, PVD-treated specimen effectively controls t₂ for both ground conditions. This enhances the sand resistance to re-liquefaction and improves structures’ stability on liquefied and potentially re-liquefaction behavior of sand deposits.

3.4 Soil subsidence

Fig.17 presents the cumulative soil subsidence observed after applying each incremental loading for both PVD-treated and untreated specimens. The influence of soil subsidence during liquefaction and re-liquefaction induces structure tilting, resulting in collapse and catastrophic damage [17,50]. Subsidence occurred due to the continuous generation and dissipation of EPWP and reconsolidation of soil specimens, which altered the ground after the shaking event. It can be observed that: 1) cumulative soil subsidence was reported to be less for a treated specimen and validating the performance of PVD in counteracting re-liquefaction-driven ground deformations; 2) specimens with higher relative density offered more resistance to cumulative soil subsidence. As seen from Fig.17, subsidence was not reported for some acceleration values (0.1g for 40% relative density specimen and up to 0.2g for 60% relative density specimen), highlighting the influence of PVDs against the generation of EPWP in saturated ground.

By relating pore pressure and subsidence values, it can be stated that the higher the pore pressure generation, the greater the occurrence of subsidence. In the PVD-treated specimen, subsidence was reported in the periphery of PVD as maximum dissipation occurred surrounding the drain.

3.5 Effect of cyclic stress ratio on reliquefaction potential

Due to the malfunctioning of accelerometers during the trial tests, caused by continuous water expulsion from the ground and associated displacement of installed accelerometers, the acceleration sensors were not used in the study. Accordingly, the CSR values were estimated based on the variation of in situ density obtained during the tests. The estimations were made by adopting the applied acceleration amplitude of the shaking event (a_max) as a given input motions. There have been similar studies that have discussed the influence of CSR on liquefaction resistance subjected to sinusoidal harmonic motions without provision of accelerometers, as was done in this study. CSR is the seismic demand of the sand specimen required to induce liquefaction [51] and was estimated using Eq. (3) proposed by [52],

(3)CSR=\left(\frac{{\tau }_{\mathrm{a}\mathrm{v}}}{{\sigma }_{\mathrm{v}\mathrm{o}}^{\prime }}\right)=0.65\times \left(\frac{a_{max}}{g}\right)\left(\frac{{\sigma }_{\mathrm{v}\mathrm{o}}}{{\sigma }_{\mathrm{v}\mathrm{o}}^{\prime }}\right)r_{\mathrm{d}}.

Stress reduction coefficient decreases along the depth and was calculated using Ref. [53] recommendations as given in Eq. (4)

(4)r_{\mathrm{d}}=1.0-0.00765 \mathit{\text{z}}, \mathrm{f}\mathrm{o}\mathrm{r}\mathit{\text{z}}⩽9.15 \mathrm{m}.

Fig.18 displays the r_u,max and corresponding CSR for a particular shaking event for 40% and 60% relative density specimens. In general, untreated specimens reported significantly higher r_u,max and CSR values compared to those for PVD-treated specimens. From Fig.18(a), it can be observed that a specimen at shallow depth (0.4 m) required less CSR to attain liquefaction and re-liquefaction than was required at larger depth (0.2 m). This results from higher overburden pressure and stress reduction coefficient that increases with depth. The findings show that drainage mechanism significantly resisted pore pressure and expedited the dissipation process. The cyclic stress induced was insufficient to generate liquefaction and subsequent re-liquefaction in treated specimens, despite being subjected to repeated medium to high intense acceleration amplitude. Similar observations were also reported for 60% relative density sand specimen for treated and untreated conditions as illustrated in Fig.18(b). The specimen prepared with 60% density reported lower r_u,max values, even for similar CSR values, demonstrating that the initial density of the sand specimen did not majorly influence CSR. Interestingly, untreated specimens prepared with 40% density reported similar r_u,max even for a considerable increase in CSR after being subjected to repeated shaking events. However, these characteristics were not observed in the case of PVD-treated and untreated specimens prepared with 60% density, as illustrated in Fig.18.

The time taken to attain r_u,max and the corresponding CSR for a given shaking event is presented in Fig.19, for both 40% and 60% density specimens. Fig.19(a) shows that untreated specimens reported significantly less time than PVD-treated specimens in achieving r_u,max values, at both depths. In addition to faster dissipation and resistance to the generation of EPWP offered by PVD, the rate of EPWP generation was also expected to be reduced. With repeated incremental shaking events, CSR increased, and time taken to attain r_u,max decreased for both partially reliquefied treated specimen and completely reliquefied untreated specimen. This demonstrated that the specimen gradually lost shear strength after being subjected to continuous generation and dissipation of EPWP, in both treated and untreated specimens. Fig.19(b) displays the values for 60% density specimen and shows similar observations reported by the 40% density specimen. Time taken to attain r_u,max reported an increase for 60% density specimens. In contrast, CSR values for both the density specimens were observed to be similar, as illustrated in Fig.19. It is interesting to note that the time taken to achieve r_u,max was greater than 40 s for a couple of shaking events in 60% density specimens, as illustrated in Fig.19(b).

4 Comparison with other Studies

In the present study, a comparison has been made with the published experimental results of Padmanabhan and Shanmugam [17]. That previous study was selected because the chosen loading conditions (incremental acceleration) and prepared ground conditions (40% and 60% density) match the present study. As discussed earlier, the soil at shallow depth was more prone to re-liquefaction. Tab.5 presents the reported r_u,max of untreated, SCP and PVD specimen for 40% and 60% density ground as observed at 0.2 m deep. It has to be noted that SCP works on the densification mechanism and PVD works by means of a drainage mechanism associated with densification induced during installation. From Tab.5, PVD treated specimens performed better in increasing the resistance to re-liquefaction (reduced r_u,max values) compared to SCP in both the ground conditions. Except for the 0.4g acceleration applied in 40% dense ground, the obtained r_u,max values lie within the design threshold limit. As illustrated in Tab.5, performance of PVD was more pronounced in 60% density specimen. It can also be inferred that PVD is a viable option even for high density sand deposits in preference to the SCP improvement technique. From these observations, it can be stated that densification mechanism alone is not sufficient to mitigate re-liquefaction. This is because the beneficial effect of the densification mechanism deteriorated due to the continuous generation of EPWP, attributed to repeated shaking events. In such cases, provision of PVD is a better option as it adopts benefits of both drainage and densification mechanism.

5 Conclusions

The main conclusions drawn from this study are as follows.

1) PVD installed ground showed significant improvement against soil re-liquefaction due to its improved drainage and associated reconsolidation characteristics. Further, the exhumed PVD, after the shaking table tests, showed minor variations in its tensile strength characteristics, highlighting that this treatment can be beneficial for liquefaction and re-liquefaction mitigation.

2) Increment in sand density due to PVD installation and drainage effectively mitigated the liquefaction and re-liquefaction of sand specimens. Installation of PVD facilitated the saturated ground to achieve its reconsolidation/compaction characteristics through its drainage mechanism. Without a drainage medium, soil compaction/deposition time increased, resulting in non-uniform densification. Due to this, the quicker generation of pore water pressures caused soil re-liquefaction in the untreated ground. Further, the beneficial effect of improvement in soil density due to continuous shaking reduced with incremental acceleration loading due to the induced continuous disturbances in the deposited ground.

3) PVD-treated specimens completely restricted EPWP, up to 0.1g and 0.2g acceleration values for 40% and 60% density specimens, respectively. Even at higher acceleration loading, PVD delayed and limited EPWP, not exceeding the threshold design limit (r_u,max≤ 0.6), whereas untreated specimens were completely reliquefied. Moreover, duration and dissipation time validated the influence of PVD regarding re-liquefaction.

4) The estimated cyclic stress ratio (CSR) of untreated and PVD-treated specimens were relatively similar, whereas r_u,max and time taken to attain r_u,max was significantly lower in treated specimens. This demonstrated that CSR values alone are insufficient to examine the strength of reliquefaction.

5) PVD-treated specimen performed well in limiting r_u,max than SCP-treated specimen for similar ground and loading conditions. This behavior can be attributed to drainage associated with the densification mechanism in improving seismic resistance and durability offered by PVD, without being deteriorated under repeated shaking events.

6) The experimental observations verified that selecting an effective treatment technique plays a significant role in improving the seismic response of liquefiable deposits. Though improvement in density enhanced resistance against liquefaction, continuous generation of EPWP during repeated shaking affected the strength of the soil. Considering this, drainage, together with soil densification, can be a viable option for improving the seismic response of saturated ground deposits, especially during repeated shaking events.

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