1
Centrifuge modelling of liquefaction-induced effects on
shallow foundations with different bearing pressures
Marques, A.S., Department of Civil Engineering, University of Coimbra, Portugal, as.silvamarques@gmail.com
Coelho, P.A.L.F., Department of Civil Engineering, University of Coimbra, Portugal, pac@dec.uc.pt Cilingir, U., Department of Engineering, University of Sheffield, UK, u.cilingir@sheffield.ac.uk Haigh, S.K., Department of Engineering, University of Cambridge, UK, skh20@cam.ac.uk
Madabhushi, S.P.G., Department of Engineering, University of Cambridge, UK, mspg1@cam.ac.uk
Abstract: Liquefaction-induced effects are a major threat to shallow foundations built on saturated sand
deposits, in seismically active regions. This type of structure is frequently used to support different structures, namely bridges, buildings, gravity walls, etc. Currently, there are few procedures in practice with limited scientific basis for estimation of the liquefaction-effects on foundations built on liquefiable soil. Therefore it is very important to develop more reliable predictions of the performance of shallow foundations built on liquefiable ground and, even more importantly, to develop more efficient techniques to improve that performance.
This paper aims at describing a preliminary investigation carried out as part of a research project- SERIES- involving dynamic centrifuge modelling of seismic liquefaction effects and mitigation in shallow foundations. The observations from a centrifuge model test performed at Cambridge University Engineering Department’s Schofield Centre are used to evaluate the settlements of two shallow foundations applying different bearing pressures to the soil. Also, the results presented aim at evaluating the development of excess pore pressures during the seismic simulations, post-earthquake response to the high transient hydraulic gradients, and the propagation of the accelerations under the footings and free-field during the seismic motion.
The results obtained enhance current understanding on liquefaction effects and provide valuable information that can be used to examine current design procedures. This will hopefully contribute to design safer and cheaper structures built on shallow foundations in regions prone to earthquake-induced liquefaction.
Keywords: Shallow Foundations; Liquefaction effects; Centrifuge Modelling; Earthquake.
1
INTRODUCTION
Many existing structures are located in areas where strata of loose, saturated, cohesionless soils are common due to the geologic setting. When these deposits are subjected to earthquake shaking, the soil particles have a tendency to move into a denser configuration, but are initially restrained from doing so by the presence of relatively incompressible water in the soil voids. As a result, there is a temporary transfer of load from the soil particles to the pore water, which results in an increase in pore water pressure and decrease in effective stress. The reduction of effective stress can be substantial and results in a large loss of strength until the excess pore water pressure (i.e. the pore water pressure above static conditions) dissipates with time. This phenomenon of pore water pressure build-up and loss of strength, which primarily occurs in saturated sands, is generally known as liquefaction (Committee on Earthquake Engineering, 1985).
Liquefaction-induced ground deformations depend strongly on cyclic stresses produced by strong shaking and the engineering properties of the liquefiable soil layer. Estimation of the seismic response of shallow foundations during a strong earthquake has proven to be a difficult task throughout the years. The main cause of this difficulty arises from the fact that soil behaviour is highly non-linear when subjected to
2 large cyclic strains, it can deform substantially and, when saturated, can develop high pore pressures and finally liquefy. Liquefaction consequently leads to severe loss of bearing capacity, which often causes serious damage to the superstructure. Extensive damage to shallow foundations due to liquefaction has been reported in numerous cases in the past, from Niigata (1967) earthquake to the more recent 1999 M 7.4 Kocaeli earthquake. Since the earliest times that earthquake-induced liquefaction was responsible for widespread destruction, in the 1967 Niigata earthquake for instance, engineers facing structural and foundation design in seismic active areas consider this phenomenon as a major threat to structure stability during an earthquake. As shallow foundations are often used as footing of structures, particularly bridges and other constructions built on loose granular deposits, their situation is particularly critical, as they are sometimes located in flooded areas that form the ideal conditions for liquefaction to occur.
In view of the limitations of full scale observations during real events, resulting from temporal and spatial unpredictability of earthquakes, and the difficulties involved with numerical modelling of these problems, due to the complex behaviour of liquefiable soil, centrifuge modelling emerges as a very important tool in research. In fact, taking into account that the soil physical and stress conditions are mimicked, centrifuge modelling is able to capture the true soil behaviour under realistic loading, provided that the boundary conditions of the problem are appropriately set.
The work presented in this paper is based on a single centrifuge experiment. The main objective of this test was to evaluate the fundamental behaviour of the system through the analysis a benchmark problem for further comparison with subsequent tests. The input motion, surface motion, ground conditions, ground response, and structural response were closely monitored and documented, thereby providing insight into ground behaviour and its impacts on the footings.
2
PREVIOUS STUDIES
Recent earthquakes have provided countless examples of the damaging effects of liquefaction on shallow foundations built under different structures. However, as field case histories provide limited amount of information on building settlement, vertical ground strain, and the level, depth, and lateral extent of ground improvement when used, physical modelling is a high-quality alternative to study the performance of shallow foundations subjected to liquefaction's phenomenon. Therefore, many researchers used 1-g shaking table experiments and centrifuge tests in order to study the seismic performance of shallow foundations (e.g., Yoshimi and Tokimatsu, 1977; Liu and Dobry, 1997; Hausler, 2002; Dashti et al, 2010).
The influence of foundation width on the average settlement of buildings founded on a liquefied sand stratum was recognized by Yoshimi and Tokimatsu (1977) after the Niigata Earthquake and was confirmed by their 1-g shaking table tests and later by the findings of Adachi et al. (1992) after the Luzon Earthquake. Most of the settlements of buildings were shown to occur during strong shaking, with smaller contributions resulting from post-shaking soil reconsolidation due to excess pore water dissipation (e.g., Hausler 2002). Foundations settled in an approximately linear manner with time during shaking and commonly settled more than the free-field soil. As a result, building settlements were recognized to be strongly influenced by the structure’s inertial forces (Liu and Dobry, 1997). According to Dashti et al. (2010), buildings started to settle after one significant ground-motion loading cycle in an approximately linear manner with respect to time, quickly surpassing free-field ground settlements.
The state-of-the-practice for estimating liquefaction-induced settlements relies heavily on empirical procedures developed to estimate post-liquefaction consolidation settlement in the free-field (i.e., without the influence of structures). Hence, there is a lack of reliable and well-calibrated analysis tools for use in engineering practice. Still, as the seismic response of a shallow foundation on a saturated granular soil due to seismically induced liquefaction is a very complicated issue, better understanding of the response and interaction of the mechanisms involved is essential, so further studies and more complex issues can be studied in other centrifuge tests.
3
3
CENTRIFUGE EXPERIMENT
The 10-m Turner Beam Centrifuge is the main focus of centrifuge based geotechnical modelling at Cambridge's Schofield Centre. This machine has a 150 g-tonne capacity, achieving a maximum centrifugal acceleration of approximately 130 g. It has two arms of equal length - nominally 4.125 meters, one end supporting the model and the other carrying a counterweight mass. More details on the centrifuge can be found in Schofield (1980).
The actuator used in this centrifuge test is known as SAM – Stored Angular Momentum. It is a simple and reliable mechanism actuator that works by spinning two flywheels up to the required speed. However, it is not able to reproduce real seismic actions. More details can be found in Madabhushi et al. (2001). The centrifuge modelling was prepared inside an ESB container (more details can be found in Schofield and Zeng, 1992).
A single centrifuge experiment was performed to gain insight into the effects provided by two different shallow foundations with different bearing pressures applied on to the soil. A scheme of the model experiment, built at a 1:50 scale, is presented in Figure 1. The model was spun at a nominal centrifuge acceleration of 50 g. As shown in Figure 1, the centrifuge experiment included a liquefiable soil layer thickness (HL) of 360 mm and nominal relative density (Dr) of approximately 50%, representing
a prototype of 18 meters deep. The sand was placed with the help of an automatic sand pourer, whose performance is depicted by Madabhushi et al. (2006). The sand used in the model is a fine, uniform Hostun sand, with a D50 of 150 μm. A solution of Hydroxypropyl Methylcellulose in water was used as
the pore fluid with a viscosity of approximately 50 (±2) times that of water, in order to obtain the so-called viscosity scaling and overcome the conflict between time scale in flow and dynamic phenomena (Stewart et al., 1998). The model was placed under vacuum and de-aired fluid was slowly introduced into the sand from the bottom, using small water pressure gradients. The saturation process is controlled by a computation program, thus avoiding constant human presence during this procedure.
The models of structures consist of single-degree-of-freedom structures and were designed for static bearing pressures of 58 kPa and 95 kPa for structures L (light) and H (heavy), respectively. The dimensions of both structures are represented in Table 1.
Table 1 – Dimensions of the structures.
Structure width (mm) length (mm) height (mm) H 60 60 24.5 L 60 60 15
The g-level was increased in 10 g intervals, at the end of each taking readings from instruments. One shaking event was applied to the base of the model of selected amplitude and frequency which was fired at a 50 g level centrifuge acceleration. The earthquake fired had a 50 Hz frequency and lasted for 0.5 seconds, in order so simulate a real event lasting 25 s and having a predominant frequency of 1 Hz. The peak accelerations were +0.324g / -0.302g in prototype scale. Shaking was applied parallel to the long side of the model.
4
EXPERIMENTAL RESULTS AND FINDINGS
As stated before, the behaviour of the structure-soil system is evaluated through a conveniently designed centrifuge model representing two similar shallow foundations, with different bearing pressures, built on a saturated deposit of loose sand. The excess pore pressures along with the resulting settlements and acceleration motions under the footing and in the free field are described. The behaviour of the model is considered both during and after the earthquake. From now on, and unless indicated otherwise, all units used are presented in prototype scale.
4
Figure 1 - Centrifuge Model Layout (Cross Section View, model dimensions) – all units are in mm. 4.1 Settlements due to liquefaction
In principle, it would be expected that increasing the bearing pressure of the footing would result in larger settlements occurring. Figure 2, which represents the settlements of the structures and free-field in long-term, proves this to be true. Also, in the data collected in Figure 2, it is possible to visualize that the settlements continue for a significant period of time after the earthquake shaking ends, and so they must be taken in consideration.
Figure 3 shows the settlements until shortly after the end of the earthquake. The difference between the settlements of the two structures is about 0.25 m shortly after the seismic loading ends. On the other hand, the slopes of the curves for the two structures tend to become significantly parallel through time, not only in short-terms but also in long-term results (Figure 2). For a bearing pressure ratio of 1.64 between the two structures, a ratio in the settlements of 1.36, immediately after the earthquake was achieved. In terms of total settlements, the ratio obtained was 1.20. It can also be mentioned that the settlements usually obtained in a real situation are lower, but this is probably due to the fact that the simulated seismic event is very long (25 s).
5
Figure 2 - Settlement of Structures and Free-field – During and After the Earthquake.
Figure 3 - Settlement of Structures and Free-field – During and Shortly after the Earthquake. 4.2 Excess-pore pressure generation
In Figure 4 are depicted the excess pore pressures (epp) measured during the earthquake simulation, at different positions in the model, under the centre of the footings and in the free-field. The corresponding data for the instruments located under the structures show that the initial static shear stress induced by the footings influences the excess pore pressure at different depths during and after the earthquake. This is particularly perceptible at shallower depths and in the case of the heavier structure.
Immediately after the earthquake, it is interesting to notice that the excess pore pressure variation under both footings is dictated by the hydraulic gradient existing between the structures and the free-field – phenomenon known as excess pore pressure migration. Where the earthquake-induced excess pore pressure is reduced by the presence of the structures (in the first layer of instruments), the pore-pressure increases once the seismic event ends, this phenomenon is particularly visible in the data corresponding to the instruments closer to the surface. Contrarily, on the second level of instruments, no significant excess pore pressure variation occurs immediately after the earthquake ends, probably because the instruments are deep enough for the structures to have no influence in the results.
-1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0 500 1000 1500 2000 Sett leme nt ( m) time (s) Free-field Light Structure Heavy Structure ≈0,25 m ≈0,25 m -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0 10 20 30 40 50 60 70 80 Set tl em ent ( m ) time (s) ≈0,25 m ≈0,25 m Free-field Light Structure Heavy Structure
6
Heavier structure Free-field Lighter structure
Figure 4 - Excess Pore Pressure (epp) at Different Depths under Both Footings and in the Free-field during the Earthquake.
Figure 4 shows that the final value for the excess pore pressure in the shallower region under structure H is slightly higher, when comparing to the results obtained under the lighter footing. This is not a surprising result since the heavier structure induces on the soil a higher initial effective stress, and so it can develop a higher final pore water pressure. However, the difference is much smaller than one should expect if full liquefaction would have occurred under both footings). On the other hand, during the seismic loading it can be noticed that for the first layer of instruments the initial excess pore pressure developed under the lighter footing is higher, tending the results of both structures to the approximately same amount as the earthquake extends.
One final observation that can be seen in the data, this time related to the free-field results, is that the PPT closer to the base tends to dissipate the excess pore pressure faster than in the other levels, which remain almost constant until the final readings. This phenomenon is normally observed in this type of tests, where liquefaction occurs and is caused by the re-sedimentation of the liquefied sand that starts at the bottom of the container and creates an upward water flow that keeps the sand on the other levels liquefied for a longer period.
4.3 Ground motion propagation in the ground and structures
The horizontal and vertical accelerations measured at different locations in the model are plotted in Figures 5 and 6.
Analysing the horizontal motions recorded in the walls of the model ESB container (Figure 5), it is interesting to see that the propagation of the horizontal accelerations progressively increases as the motion propagates upwards the model box. On the contrary, the peak horizontal accelerations measured in the ground under the centre of each structure exhibit, in both cases, progressive attenuation as the motion propagates upwards through the soil. Attenuation intensifies near the surface and after the first couple of loading cycles (Figure 6), which is also visible in the data concerning to the free-field. This phenomenon reflects the change of soil behaviour as liquefaction occurs.
-15 -10 -5 0 5 10 15 20 0 20 40 60 80 E . p . p . a t z=1 m (k Pa ) -15 -10 -5 0 5 10 15 20 0 20 40 60 80 -15 -10 -5 0 5 10 15 20 0 20 40 60 80 -20 0 20 40 60 80 0 20 40 60 80 E . p . p . a t z=6 m (k Pa ) Time (s) -20 0 20 40 60 80 0 20 40 60 80 -20 0 20 40 60 80 0 20 40 60 80 Time (s) -10 40 90 140 190 0 20 40 60 80 E . p . p . a t z=1 7 ,5 m (k Pa ) Time (s)
7 Horizontal Acc
Vertical Acc
Figure 5 – Propagation of Horizontal and Vertical Accelerations at Different Depths outside the Model Box during the Earthquake.
On the other hand, the time histories of the horizontal accelerations in the ground under the footings suggest that the characteristics of the structures (heavier or lighter) influence the motion propagation in the soil during the first cycles (Figure 6). In the first layer of instruments the peak horizontal motion visible in the first cycles is higher under the lighter structure. After these initial cycles both data tend approximately to the same values, implying that the difference in bearing pressure between the two structures does not result in significant differences in the acceleration results.
With respect to the dynamic behaviour of the structures, the time histories of the horizontal accelerations show that their responses cause larger accelerations in the lighter structure, as shown in Figure 7, where the accelerations in the layer of the footings are measured by MEMS - Microelectromechanical system accelerometers. Actually, the peak horizontal accelerations in the lighter structure are about twice as large as those in the heavier structure. This result could eventually be anticipated, assuming that the maximum force applied by the sand on the structures is the same in both cases, which is probably roughly true except when the different settlement of the structures during the earthquake affects the vertical area of contact between the foundation and the surrounding soil. In this case, and because the heavier structure weights nearly twice as much, Newton's 2nd law of motion suggests that the acceleration in the heavier structure would be about half of the acceleration in the lighter structure. Thus, the use of a heavier structure for a shallow foundation seems to cause smaller seismic loading of the structure.
-0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=0 m ( g ) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=9 m ( g ) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=1 8 m (g ) time (s) Input h⬚ -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) Input v
8
Heavier structure Free-field Lighter structure
Figure 6 – Propagation of Horizontal Accelerations at Different Depths under Both Footings and Free-field during the Earthquake. -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=1 m ( g ) time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=6 m ( g ) time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=1 1 ,5 m ( g ) time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) Instrument malfunction -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 a cc h a t z=1 7 ,5 m ( g ) time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s) -0,4 -0,2 0,0 0,2 0,4 0 10 20 30 40 50 time (s)
9
Heavier structure Lighter structure
Figure 7 – Propagation of Horizontal Accelerations in the Structures and Ground under the Footings.
5
CONCLUSIONS
A single centrifuge experiment was made in order to study the effects of two shallow foundations applying different bearing pressures to the soil. The results obtained revealed that:
1. The settlements continued after the earthquake shaking;
2. For a bearing pressure ratio of 1.64 between the two structures, it was achieved a ratio in the settlements of 1.36, immediately after the earthquake. In terms of total settlements, the ratio obtained was 1.20;
3. The initial static shear stresses induced by the footing influences the excess pore pressure at different depths during and after the earthquake - phenomenon particularly perceptible at shallower depths and in the case of the heavier structure;
4. Final value for the excess pore pressure in the shallower region under the structure H is slightly higher, when comparing to the results obtained under the lighter footing, but the difference is much smaller than one should expect if full liquefaction would occur under both footings;
5. Post-earthquake excess pore pressure variation under both footings is dictated by the hydraulic gradient existing between the structures and the free-field – phenomenon known as excess pore pressure migration. This phenomenon is slightly more visible under structure H;
-0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 a a c M E M S h a t F o o ting s (g ) -0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 -0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 a cc h a t z=1 m ( g ) -0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 -0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 a cc h a t Inp ut (g ) time (s) -0,8 -0,4 0,0 0,4 0,8 0 10 20 30 40 50 time (s)
10 6. PPT closer to the base in the free-field tends to dissipate the excess pore pressure faster than in the other levels, which remain almost constant until the final readings, as usually observed in similar tests. This means that the excess pore pressure dissipation of the sand starts at the bottom and travels from there upwards. Comparable results are found in static liquefaction experiments (Bezuijen and Mastbergen, 1989);
7. Although the horizontal motions tend to increase in the walls of the model ESB container as the motion propagates upwards, the peak horizontal accelerations measured in the ground exhibit progressive attenuation, which reflects the change of soil behaviour as liquefaction occurs;
8. The different bearing pressures of the structures influence the motion propagation in the soil in the first cycles. However, after that, both data tend approximately to the same values, suggesting that the two structures are not different enough to present significant differences in the accelerations motions;
9. Higher horizontal accelerations are measured in the lighter structure, which are about twice as large as those that reach the other footing, showing that importance of soil-structure-interaction in these cases.
ACKNOWLEDGMENTS
The authors would like to acknowledge the valuable assistance of the technicians at the Schofield Centre, as well as the financial research scholarship provided by FCT – Fundação para a Ciência e a Tecnologia.
The research leading to these results has received funding from the European Community’s 7th Framework Programme [FP7/2007-2013] for access to Turner Beam Centrifuge, Cambridge, UK, under Grant Agreement nº 227887.
REFERENCES
Adachi, T., Iwai, S., Yasui, M., and Sato, Y. (1992). “Settlement and inclination of reinforced concrete buildings in Dagupan City due to liquefaction during the 1990 Philippine earthquake.” Proc., 10th World Conf. on
Earthquake Engineering, International Association for Earthquake Engineering (IAEE), Madrid, Spain, 147– 152.
Bezuijen A., Mastbergen D.R. (1989), “Liquefaction of a sand body constructed by means of hydraulic fill”. Proc.
12th. Int. Conf.on soil mechanics and foundation engineering, Rio de Janeiro.
Committee on Earthquake Engineering (1985). Liquefaction of Soils During Earthquakes, Committee on
Engineering and Technical Systems, National Research Council, 240 pp.
Dashti, S., Bray, J. D., Pestana, J. M., Riemer, M. and Wilson D. (2010). "Mechanisms of Seismically Induced Settlement of Buildings with Shallow Foundations on Liquefiable Soil". Journal of Geotechnical and
Geoenvironmental Engineering, Volume 137: 151-164.
Hausler, E. A. (2002). “Influence of ground improvement on settlement and liquefaction: A study based on field case history evidence and dynamic geotechnical centrifuge tests”. Ph.D. thesis, University of California,
Berkeley, Chap. 5, 271.
Liu, L. & Dobry, R. (1997) Seismic response of shallow foundations on liquefiable saturated sand, Journal of
Geotechnical and Geoenvironmental Engineering, ASCE, 123(6):557-567.
Madabhushi, S.P.G., Houghton , N.E. and Haigh S.K. (2006). "A new automatic sand pourer for model preparation at university of Cambridge". In 6th International Conference on Physical Modelling in Geotechnics.
Madabhushi, S.P.G., Teymur, B., Haigh, S.K. & Brennan, A.J. (2001). "Modelling of Liquefaction and Lateral Spreading". International Workshop on Earthquake Simulation in Geotechnical Engineering, Cleveland.
Schofield, A. N. And Zeng, X. (1992). Design and Performance of an equivalent-shear-beam (ESB) container for earthquake centrifuge modelling. Tech. Rept. CUED/D-SOILS TR245. Cambridge Unuiversity, UK.
Schofield, A.N (1980). "Cambridge geotechnical centrifuge operations". Géotechnique, 30(3):227–268, 1980. Stewart, D. P., Chen, Y. R., and Kutter, B. L. (_1998_. ). “Experience with the use of methylcellulose as a viscous
pore fluid in centrifuge models.” ASTM Geotech. Test. J., 21(4), 365–369.
Yoshimi, Y. & Tokimatsu, K. (1977) Settlement of Buildings on Saturated Sand During Earthquakes, Soils and
