Centrifuge Modeling of Liquefaction Effects on Shallow Foundations

Abstract

Earthquake-induced liquefaction is a major concern for structures built on saturated cohesionless soils in seismically active regions, as it often causes failure of critical structures such as bridges and quay walls, which severely restricts post-earthquake emergency response and economic recovery. The destructive consequences of this phenomenon have remarkably increased since it was firstly identified in US and Japan in 1964. This paper describes an investigation on the performance of shallow foundations susceptible to seismic liquefaction, considering the particular vulnerability that this type of foundation has shown in the field during past earthquakes. The research program included three dynamic centrifuge experiments, conducted at the Schofield Centre, University of Cambridge, UK, as part of a SERIES’ TNA Use Agreement focusing on the magnitude of liquefaction effects on shallow foundations, under different conditions, including interaction effects between adjacent structures, and on the assessment of the performance of innovative mitigation techniques, particularly narrow densified zones combined with selectively positioned high-capacity vertical drains.

24.1 Introduction

Earthquake-induced liquefaction is a major concern for structures built on saturated deposits of cohesionless soils in seismically active regions, the phenomenon being so complex that even its definition remains ambiguous (Boulanger 2005). Throughout the last 50 years, liquefaction has proven to be a major source of economic losses, often resulting in vast structural damage to buildings, infrastructures and even ground failure, which often severely restricts post-earthquake emergency response and economic recovery. Damage to shallow foundations can be particularly severe, mitigation measures being poorly understood (Mitchell 2003; Bardet et al. 1997).

The research previously carried out on the behavior of shallow foundations built on liquefiable ground undergoing seismic events identified major shortcomings affecting our fundamental understanding of the problem and our ability to model and to mitigate its effects. In view of the limitations of the data obtained from case histories and alternative experimental tools able to deal with such problems, centrifuge modeling was selected as the main research tool for this project.

Considering the key limitations of our current understanding of the problem and the critical requirements from practitioners working in this field, namely those employing sophisticated methodologies including performance-based design and risk analysis, the following objectives were defined for this research: establish the fundamental behavior of the soil-structure system through the analysis of a benchmark problem; evaluate the influence of the bearing pressure induced by the shallow foundation on the liquefiable ground on the performance of the system under seismic loading; assess the effectiveness of narrow densified zones with selectively positioned high-capacity vertical drains in the mitigation of earthquake-induced liquefaction effects. The results obtained through centrifuge modeling will be complemented with elementary tests carried out on the modeling sand and a judicious assessment of selected advanced numerical tools to perform realistic numerical predictions of the behavior of the shallow foundations affected by seismic loading inducing ground liquefaction. The results of the numerical simulations will be compared between various researchers and institutions to clarify the limitations and strengths of different numerical tools.

This paper describes the part of the research employing dynamic centrifuge modeling, which was made possible through the financial support obtained through a Transnational Access (TA) Use Agreement granted within a project funded by the European Commission (7th Framework Program): Seismic Engineering Research Infrastructures for European Synergies- SERIES. The international research team involved in the TA Research Project is led by the University of Coimbra and includes the University of Rome, the Polytechnic of Madrid and the Slovenian National Building and Civil Engineering Institute. The dynamic centrifuge experiments were carried out at the experimental facilities of the Schofield Centre – Cambridge University Engineering Department.

24.2 Characteristics of the Dynamic Centrifuge Models

A series of three centrifuge experiments were carried out on models similarly built and submitted to comparable earthquake simulations, to investigate the magnitude of liquefaction effects, under different conditions, and to assess the performance of innovative mitigation techniques, particularly combining densification and high-capacity vertical drains. The only factors varying in each test were the model structures and, where applicable, the depth of the densified zone created in the soil foundation under the footing and the length of the surrounding material simulating high-capacity vertical drains. Four different combinations for the improved zone were tested and compared to the behavior of the benchmark test where no ground improvement was carried out.

24.2.1 Model Structures

Considering the aim of the tests, structural models had a simple design, consisting of solid steel blocks with scale dimensions of 60 × 60 mm in plan view and a thickness of 24.5 and 15 mm, for the heavier (H) and lighter (L) model structures, respectively. In the tests under consideration, performed at 50-g centrifuge acceleration, the pressures transmitted through the foundations basis, at prototype scale, were 58 and 95 kPa for structures L and H, respectively. Figure 24.1 shows the model structures used to perform the centrifuge experiments.

Fig. 24.1

Structures used in the centrifuge experiments

24.2.2 Dynamic Centrifuge Model A (CT-A)

The series of dynamic centrifuge tests included an experiment (CT-A) intended to evaluate the fundamental behavior of the system through the analysis of a benchmark problem for further comparison with the subsequent tests. This test was also carried out to establish the influence of the bearing pressure induced by the shallow foundation on the liquefiable ground on the performance of the soil-structure system under seismic loading and to assess potential interaction effects between the structures placed in the same model. Figure 24.2 presents a scheme of the model experiment, where the units are at prototype scale. As the figure shows, no ground improvement was simulated in CT-A, which intends to establish the performance during the earthquake simulation of shallow foundations directly on liquefiable ground. CT-A was performed using two different structures placed in opposite sides of the model – structures H and L. The ground foundation represented a fully saturated liquefiable sandy layer of 18 m deep with relative density of 50 %.

Fig. 24.2

Centrifuge model layout in experiment CT-A (cross section view)

To perform the subsequent tests, two different structures could be used to compare the results with CT-A – H or L structure. By using the heavier structure it might show the effects of the mitigation methods more clearly, while using the lighter structure might give a better representation of real structures built on liquefiable ground. Consequently, the footing chosen to perform subsequent tests was the H structure.

24.2.3 Dynamic Centrifuge Model B (CT-B)

Test CT-B was carried out with model structure H, to maximize liquefaction effects, and employing ground conditions similar to those used in benchmark test CT-A, except for the fact that some ground improvement was carried out under the footings. In this test, two equal shallow foundations were placed resting on narrow densified zones having the same depth as the layer of loose sand (Fig. 24.3). As the figure shows, one densified zone under one of the structures was also embedded by vertical drains extending to the bottom of the deposit, simulated through a particular geotextile. The geometry of the densified zone was established following the guidelines suggested by Coelho (2007). This centrifuge test intended to assess the effectiveness of narrow densified zones with selectively positioned high-capacity vertical drains in the mitigation of earthquake-induced liquefaction effects, as proposed by Coelho (2007).

Fig. 24.3

Centrifuge model layout in experiment CT-B (cross section view)

24.2.4 Dynamic Centrifuge Model C (CT-C)

Centrifuge model CT-C (Fig. 24.4) tests different configurations for the hybrid resistance measure initially tested in model CT-B, to evaluate the influence on the performance. As the figure shows, the geotextile extends in both cases to half the depth of the liquefiable deposit (9 m) while the narrow densified column encased in the geotextile extends to the bottom of the liquefiable layer, in one case, and to the same depth as the geotextile in the other.

Fig. 24.4

Centrifuge model layout in experiment CT-C (cross section view)

24.3 Experimental Techniques and Materials

24.3.1 Materials Used

Hostun sand, selected as the modeling sand for this experimental investigation, is a clean and uniform sand (Table 24.1) with a particle size distribution (PSD) curve that lies well within the bounds of soils most susceptible to liquefaction (Fig. 24.5). Its properties are described in detail by Flavigny et al. (1990).

Table 24.1 Properties of Hostun sand (Stringer 2008)

Fig. 24.5

PSD for Hostun sand, superimposed on liquefaction susceptibility curves (After Tsuchida (1970) – Adapted from Stringer (2008))

To simulate the effect of drainage systems, a specific geotextile was chosen to be rigid enough to avoid squeezing of the vertical drainage paths once the final horizontal stresses were installed in the model (Fig. 24.6). The geotextile used in the tests as part of the proposed hybrid liquefaction resistance measure may eventually be materialized in the field by closely-spaced high-capacity vertical drains.

Fig. 24.6

Geotextile used to simulate high-capacity vertical drains

24.3.2 Equivalent Shear Beam Container

As the boundary conditions are extremely important in the results observed, the container where the models were prepared need to be carefully chosen. Thus, the models were prepared and tested within an Equivalent Shear Beam (ESB) container, described by Schofield and Zeng (1992), having flexible walls intended to replicate the soil dynamic behavior and minimize boundary effects. However, due to the large degradation of soil properties during liquefaction caused by pore pressure build-up and subsequent effective stress reduction, the container cannot exactly match the soil behavior at all times during the test.

24.3.3 Model Preparation Techniques

24.3.3.1 Sand Deposition

The soil deposit was prepared using an air dry pluviation technique, by means of an automatic sand pourer (Fig. 24.7). This equipment allows different sized nozzles to be placed at the bottom of the hopper in order to control the flow rate, while a selected drop height is kept constant through a computational program used to control the equipment. The relative density achieved using this technique, which depends on the flow rate and drop height, is usually up to ±5 % of the desired value. Sand is poured in pairs of steps, passing in each one of them along the model and along one axis in a single step. More details on the automatic sand pourer can be found in Madabhushi et al. (2006). Calibration was carried out before pouring the model to determine the correct drop height and nozzle size to achieve the desired relative density, varying from 50 to 80 % (Table 24.2).

Fig. 24.7

Automatic sand pourer

Table 24.2 Drop height and nozzle diameter for each desired relative density

In the cases where a densified block had to be created in the model, under the footing, a box made of thin metallic sheet was employed to temporarily support that zone while the model was built. This temporary formwork, which was removed during the pouring process, was not required when the densified zone was encased within a geotextile, in which case the dense sand could be placed directly inside the geotextile. Taking into account the disturbance that could be caused by the formwork removal, as well as the larger difficulty in creating a narrower denser zone with the automatic sand pourer, the geotextile and the formwork were 20 mm wider (at model scale), in each direction, than the width of the model structures. The relative density of the sand in the models was in every case about 50 and 80 % in the loose and densified zones, respectively.

24.3.3.2 Instrumentation

The instruments’ position, represented for each test in Figs. 24.2, 24.3 and 24.4, were maintained in all the tests to ensure that results can be compared. A series of PPTs, Acc and LVDTs were installed to assess the soil behavior during the centrifuge tests. A series of MEMS were carefully attached to the footings to measure the vertical and horizontal accelerations. Several Acc were installed at the bottom and walls of the container to measure the vertical and horizontal input motions and to evaluate the horizontal motion propagation through the ESB walls. Special arms were designed to place LVDTs over each footing to measure its vertical displacements.

The amount, distribution and placement of the instruments installed in the centrifuge models and the flexibility of the connecting cables are carefully chosen to minimize the disturbance on soil behavior. In general, large concentration of instruments was avoided and cables were positioned so that soil reinforcement and creation of preferential flow paths was hampered. The loading of the model was carefully performed to minimize the 1-g vibrations induced in the model, which could affect the instruments position.

24.3.3.3 Model Saturation

Model saturation with a viscous fluid is an essential part of a model preparation in centrifuge-based liquefaction research, requiring strict control for superior results. A solution of Hydroxypropyl Methylcellulose in water was used as the pore fluid with a viscosity of ≈50 times that of water, in order to achieve the so-called viscosity scaling at 50-g and overcome the conflict between time scaling in flow and dynamic phenomena. The model was placed under vacuum and de-aired viscous fluid was slowly introduced through the bottom of the sand, using small water pressure gradients. The saturation system (Fig. 24.8), which is controlled by a computational program – CAM-Sat – that ensures its smoothness, is described in detail by Stringer et al. (2009).

Fig. 24.8

Model saturation

24.3.3.4 Footings Positioning

To minimize model disturbance during transportation to the beam, the structures were only installed after the model was loaded in the swing of the centrifuge beam. The positioning of the footings was very careful and involved verification of the evenness of each structure by means of a leveler.

24.3.4 Centrifuge Facilities

The three dynamic centrifuge experiments were conducted using the 10-m diameter Turner Beam Centrifuge at the Schofield Centre, University of Cambridge, UK, which is described in detail by Schofield (1980). The machine has a 150g-tonne capacity and it is capable of achieving a maximum centrifugal acceleration of approximately 120g at 4,125 radius. The actuator used in the centrifuge tests to generate seismic simulations is known as Stored Angular Momentum (SAM) actuator (Madabhushi et al. 1998), which is a simple and reliable mechanical actuator that uses the energy stored in a pair of flywheels to generate the input motion. Despite not being able to reproduce real seismic actions, it is able to generate nearly sinusoidal horizontal acceleration motions of chosen duration and amplitude, which is considered valuable for fundamental research on earthquake effects.

24.4 Earthquake Simulations

All the centrifuge models were submitted to a similar input seismic motion at the base, applied parallel to the long side of each model and designed to replicate a relatively strong real earthquake motion, planned to last about 25 s, have a predominant frequency of 1 Hz and impose maximum peak horizontal accelerations close to 0.3-g.

The time histories and FFTs of the earthquake simulations applied to the centrifuge models are depicted in Fig. 24.9, confirming that the planned loading was achieved in tests CT-B and CT-C. Although the input simulation in test CT-A was not measured, due to an instrument malfunction, there is no reason to believe this simulation was different. It should also be noted that the seismic simulation is not single-frequency, although as required the predominant frequency matches the desired value (1 Hz).

Fig. 24.9

Time histories of the seismic loading applied to all the models

24.5 Main Results

This section presents the data recorded in the centrifuge tests, the behavior of the models being successively compared in terms of the excess pore-pressure generation and dissipation in the granular ground, the horizontal accelerations induced on the structures and the footings settlements. In the data presented in the following, Foot.^left and Foot.^right refer to the structures placed on the left and right-hand sides of the model, respectively, as described in Sect. 24.2 for each model. The zone between the structures is regarded as free-field, although this hypothesis requires verification from analysis of the experimental data, since the structures and/or the ground improvement may influence the behavior at that location. A scheme of the particular configuration tested, as summarized in Table 24.3, is presented in the figures to facilitate the analysis.

Table 24.3 Different configurations tested in each centrifuge experiment

24.5.1 Excess-Pore-Pressure Generation

Figure 24.10 presents the excess-pore-pressure (epp) measured in the liquefiable ground during shaking in all the tests, showing that, as the earthquake starts, the epp increases in the free-field (z = 17.5 m) from the first loading cycles. Under the footings, however, the epp generated during the seismic simulations strongly depend on the characteristics of the footing and the ground improvement carried out in the model, even if when the shaking ends, a more or less significant positive epp is observed in every location. The data also suggests that the epp developed in the so-called free-field location in the model may not be absolutely independent of the structure and/or ground improvement existing in the model. This is particularly true in model CT-B, where the epp generated in the free-field, at a depth of 17.5 m, seems to be restricted by the ground improvement extending to the full depth of the deposit under both left and right structures. The epp dissipation, in model CT-B, immediately after the end of shaking, also seems to be slightly accelerated by the surrounding liquefaction resistance measures.

Fig. 24.10

Excess pore pressure at different depths under the footings during the earthquake simulation

When no ground improvement exists (CT-A), the final value for the epp at 1-m depth is slightly higher under H structure than under L structure. This probably results from the fact that footing H induces on the soil a higher initial effective stress, being able to develop a higher final epp. When liquefaction resistance measures are present (tests CT-B and CT-C), important negative epp are observed under the footing once the first couple of cycles take place. As permanent negative pore-pressure variation can only be induced by monotonic loading, this suggests that vertical stress concentration occurs under the footing at this stage. Also, the results show that the configuration H:D results in the longer period of negative epp induced under the footing, which continues far longer than the first loading cycles. Another main conclusion that can be drawn from the results is that, except when vertical drains were simulated with a geotextile, the epp tends to rise again immediately after the end of shaking (CT-A and CT-B’s H:D). On the other hand, the data from CT-C shows that the epp reaches the maximum value after a few cycles once the seismic loadings starts. This suggests that hybrid techniques combining narrow densified zones with vertical drains mitigate faster the epp developed under footings during earthquake shaking.

24.5.2 Propagation of Accelerations

Figure 24.11 shows the horizontal motions measured at the footings for all the models tested. CT-A data shows that the peak horizontal accelerations measured in the lighter structure (L) are about twice as large as those in H, which may be eventually explained by Newton’s 2nd Law of Motion, assuming that the horizontal force transmitted by the liquefied sand to footings L and H is similar (Marques et al. 2012). Figure 24.11 also shows that by increasing the soils’ relative density under structure H, the peak horizontal acceleration induced on the structures is also increased. This phenomenon is even visible in situation H:D in CT-B, since the instrument only start to malfunction after the first loading cycles. In configuration H:(D + G) (CT-B), there is no significant attenuation with the number of cycles, which is consistent with a less pronounced soil stiffness degradation that may result from the combination of a full-depth densified zone (H:D in Fig. 24.9) with vertical drains.

Fig. 24.11

Horizontal accelerations at the foundations and imposed to the base

Observations in configurations H:(D + G) in CT-B, and H:(D + G/2) in CT-C, prove that by using a hybrid technique with narrow densified zones throughout the liquefiable soil layer and vertical drains until half of it results in almost half of the horizontal accelerations in the footing after the first loading cycles. As expected, by densifying the ground only up to half the full depth of the liquefiable deposit and encasing it with vertical drains (situation H:(D/2 + G/2) in CT-C), the horizontal accelerations measured in the footing are considerably smaller. However, the peak horizontal motions recorded in the first loading cycles still reach approximately the same high values irrespective of the depth the resistance measure employed.

24.5.3 Footing Settlements

Figure 24.12 shows the settlements measured in each case during the seismic simulations. The settlements of the footings built on densified ground with or without vertical drains are in all cases significantly reduced in comparison with any of the footings presented in CT-A, where no ground improvement was carried out. However, the footings suffer significantly different settlements during the earthquake, which range approximately from 0.10 to 0.50 m, for configurations H:(D + G) and H:D (CT-B); and from 0.40 to 0.30 m, for configurations H:(D/2 + G/2) and H:(D + G/2) (CT-C).

Fig. 24.12

Settlements of the footings measured during the period of the earthquake simulation

In configuration H:D the structure suffers a fairly non-even settlement with an average value of approximately 0.50 m, which is about 50 % smaller than the one measured with no improvement under structure H (≈0.90 m). However, this structure did not remain in its original position during the seismic loading, moving towards the looser sand. Consequently, the co-seismic settlement measured in this case would possibly be reduced if the structure had rested exclusively on the dense zone. In contrast, in situation H:(D + G) in CT-B, the footing suffers an even settlement of approximately 0.10 m, which is about 90 % smaller than the one measured with no improvement. With respect to the experiments where hybrid mitigation techniques were used, Fig. 24.12 shows that the footing settles visibly more in situation H:(D/2 + G/2) in CT-C, as loose sand exhibits a much softer response to dynamic plus monotonic loading than dense sand.

The total settlements measured at the end of each centrifuge test for every footing is depicted in Table 24.4. Comparing the results obtained for the cases where mitigation techniques were used, it is clear that the total settlements in CT-C are noticeably larger than in H:(D + G) but much smaller than in H:D, the configurations tested in centrifuge experiment CT-B. However, the total settlements observed when liquefaction resistance measures are employed are always reduced in comparison to the benchmark case (H in CT-A), the reduction reaching almost 90 % when the tested hybrid technique is carried out up to the bottom of the deposit (Table 24.4).

Table 24.4 Total settlements of the footings

24.6 Conclusions

A centrifuge-based research program was carried out at Cambridge University Engineering Department’s Schofield Centre to characterize the behavior of shallow foundations built on saturated deposits of loose sand during seismic events, as part of a TA agreement established within the EU funded SERIES project. The performance of hybrid mitigation techniques, combining densification with vertical drainage was also assessed by considering different geometries for a narrow densified zone under the footings with and without geotextile surrounding it.

This paper describes the design of all the centrifuge tests, the test setup and the experimental techniques used to prepare the models, as well as the materials used. The experimental observations are also presented and analyzed, revealing the importance of centrifuge modeling in research aiming at highlighting the effects of earthquake-induced liquefaction. The results also prove the effectiveness of hybrid mitigation techniques combining vertical drains with narrow densified columns in mitigating liquefaction effects.