Foundations under seismic loads Fondations sous charges sismiques Shamsher Prakash1 Professor Emeritus, Department of Civil Engineering,Missouri University of Science and Technology, Rolla, MO 65401,USA,
[email protected] Vijay K Puri2 Professor , Civil Engineering Department, Southern Illinois University, Carbondale, IL 62901, USA,
[email protected]
ABSTRACT Shallow foundations may experience a reduction in bearing capacity and increase in settlement and tilt due to seismic loading as has been observed during several earthquakes. Shallow foundations for seismic loads have generally been designed by the equivalent static approach. Foundations are considered eccentrically loaded and the ultimate bearing capacity is estimated accordingly. Building Codes generally allow an increase of 33% in bearing capacity when earthquake loads, in addition to static loads are used in the design of the foundation. Considerable research effort has been devoted to the determination of the dynamic bearing capacity in recent years. Significant developments in determination of dynamic bearing capacity are presented in the paper. RÉSUMÉ Fondations superficielles peuvent expérience une réduction de capacité portante et augmentation de règlement et d'inclinaison en raison de la charge sismique comme a été observé au cours de plusieurs tremblements de terre. Fondations superficielles pour les charges sismiques ont généralement été conçues par l'approche statique équivalente. Fondations sont considérés comme excentrique chargées et la capacité portante ultime est estimée en conséquence. Les Codes du bâtiment permettent généralement une augmentation de 33 % de la capacité portante lorsque les charges de tremblement de terre en plus de charges statiques sont utilisées dans la conception de la Fondation. Recherche un effort considérable a été consacré à la détermination de la capacité portante dynamique au cours des dernières années. Des développements importants dans la détermination de la capacité portante dynamique sont présentées dans le document.
Keywords: Capacity, Bearing, Dynamic, Settlement, Tilt, Determination
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INTRODUCTION
Structures subjected to earthquakes may be supported on shallow foundations or on piles depending on the load transmitted and the soil conditions at the site. The foundation must be safe both for the static as well for the dynamic loads imposed by the earthquakes. The earthquake associated ground shaking can affect the shallow foundation in a variety of ways:
Cyclic degradation of soil strength may lead to bearing capacity failure during the earthquake. Large horizontal inertial force due to earthquake may cause the foundation to fail in sliding or overturning. Soil liquefaction beneath and around the foundation may lead to large settlement and tilting of the foundation.
Softening or failure of the ground due to redistribution of pore water pressure after an earthquake which may adveslersly affect the stability of the foundation post-earthquake. Bearing capacity failures of shallow foundations have been observed in Mexico City during Michoacan earthqake of 1985 [1,2] and in city of Adapazari due to 1999 Kocaeli earthquake [3,4,5]. Typical examples of bearing capacity failure in Adapazari are shown in Fig. 1. The surface soils at the site of foundation damge belong to CL/ ML group which are generally considered non-liquefiable. Settlemets as much as 0.5-0.7m have been observed in loose sands[6] in Hachinohe during the 1968 Tokachioki earthquake of magnitude 7.9. Settlements of 0.5 -1.0 m were observed at Port and Roko Island in Kobe due to the Hygoken Nanbu (M=6.9) earthquake.
(b) Tilting of Buildings after Bearing Capacity Failure Figure 1. Examples of Bearing Capacity Failures of shallow foundations in Adapazari[5]
Several research investigations, mostly analytical have been conducted in the area of dynamic bearing capacity of foundations in the recent years. The more significant of these studies are presented his paper.
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(a)Bearing Capacity Failure
DEVELOPMENTS IN DYNAMIC BEARING CAPACITY
The response of a footing to dynamic loads is affected by the (1) nature and magnitude of dynamic loads, (2) number of pulses and (3) the strain rate response of soil. Shallow foundations for seismic loads are usually designed by the equivalent static approach. The foundations are considered as eccentrically loaded with inclined load (combination of vertical + horizontal load) and the ultimate bearing capacity is accordingly estimated. To account for the effect of dynamic nature of the load, the bearing capacity factors are determined by using dynamic angle of internal friction which is taken as 2-degrees less than its static value [7]. Building Codes generally permit an increase of 33 % in allowable bearing capacity when earthquake loads in addition to static loads are used in design of the foundation. This recommendation may be reasonable for dense granular soils, stiff to very stiff clays or hard bedrocks but is not applicable for friable rock, loose soils susceptible to liquefaction or pore water pressure increase, sensitive clays or clays likely to undergo plastic flow [8].
Behavior of small footing resting on dense sands and subjected to static and impulse loads was experimentally investigated by Selig and McKee [9]. It was observed that the footing failed in general shear in static case and local shear failure occurred in the dynamic case. Large settlements at failure were observed for the dynamic case. These experimental results indicate that for given value of settlement, the dynamic bearing capacity is lower than the static bearing capacity. This observation is further supported by results of experimental studies on small footings on surface of sand [10] wherein dynamic bearing capacity was about 30 % lower than static bearing capacity. Therefore, the increase in bearing capacity permitted by codes should be taken with a caution. Recently several analytical studies on seismic bearing capacity of shallow footing have been reported. These studies used limit equilibrium approach with varous assumptions on the failure surface. A plain failure surface shown in Fig. 2 was assummed by Richard et al [11] and equations and charts were developed to estimate seismic bering capacity and settlement using foundation width, depth, soil properties and horizontal and vertical acceleration components. This approach is used for simplicity although the assumption of a plane failure surface may not be realistic.
Figure 3. Failure surface used by Budhu and al-karni for static and dynamic case[12]
Logaritmic failure surfaces shown in Fig. 3 were assumed by Budhu and Al-karni [12] to determine the seismic bearing capacity of soils. They suggested modifications to the equations commonly used for static bearing capacity to obtain the dynamic bearing capacityas follows: qud = c Nc Sc dc ec +q Nq Sqs dq eq + 0.5 γ B Nγ Sγ d γ eγ
(1)
Where, Nc, Nq, Nγ, are the static bearing capacity factors. Sc, Sqs, Sγ are static shape factors.
dc, dq, dγ are static depth factors ec , eq and eγ are the seismic factors estimated using following equations
ec exp 4.3k hl D Figure 2. Failure surface in soil for seismic bearing capacity assumed by Richard et al [11]
5.3k h1.2 eq (1 kv ) exp 1 k v 9k h1.2 2 e (1 kv ) exp 3 1 kv
(2) (3)
(4)
Where, Kh and Kv are the horizontal and vertical acceleration coefficients respectively. H= depth of the failure zone from the ground surface and D= c/ γH
H
0.5B exp tan D f 2 cos 4 2
(5) Df = depth of the footing and φ = angle of internal friction
(a) Ncd
c=cohesion of soil An experimental study was also conducted by Al-Karni and Budhu [13] on model footing to study the response under horizontal acceleration and compared the results with the approach suggested in [12].
(b) Nqd Figure 4. Failure Surfaces under static and Seismic Loading [14]
[11,12 or 14]) may be expected to provide reasonable estimates of seismic bearing capacity. Gajan and Kutter [15] provided the concept of contact interface model to estimate the load capacities, stiffness degradation, energy dissipation and deformation of shallow foundations under combined cyclic loading. The „contact interface model‟ provides a nonlinear relation between cyclic loads and displacements of the footing–soil system during combined cyclic loading (vertical, shear, and moment).
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(c) Nγd Fig. 5 Values of bearing cacity factors (a) Ncd (b) Nqd and (c) Nγd [14]
A study of the seismic bearing capacity of shallow strip footing was conducted by Chaudhury and Subba Rao [14]. The failure surfaces for the static and dynamic case are shown in Fig.4. They used the limiting equilibrium appraoach and the eqivalent static method to repesent the seismic forces and obtained the seismic bearing capacity factors. The dynamic bearing capacity „qud‟ is obtained as: qud = c Ncd + q Nqd + 0.5 γ B Nγd (6)
Where, Ncd, Nqd and Nγd are seismic bearing capacity factors. Values of Ncd, Nqd and Nγd are shown in Fig. 5 for various combinations of kh , kv and Φ. As there is general lack of experimental data, it is difficult to verify which one of the analytical appraoaches (namely those given in
SHALLOW FOUNDATIONS IN LIQUEFIABLE SOILS
Gazezas et al [16] studied tilting of buildings in 1999 Turkey earthquake. Detailed scrutiny of the “Adapazari failures” showed that significant tilting and toppling were observed only in relatively slender buildings (with aspect ratio: H / B > 2), provided they were laterally free from other buildings on one of their sides. Wider and/or contiguous buildings suffered small if any rotation. for the prevailing soil conditions and type of seismic shaking; most buildings with H / B > 1.8 overturned, whereas building with H / B < 0.8 essentially only settled vertically, with no visible tilting.(Figure 6 shows a plot of H/B to tilt angle of building). Soil profiles based on three SPT and three CPT tests, performed in front of each building of interest, reveal the presence of a number of alternating sandy-silt and silty-sand layers, from the surface down to a depth of at least 15 m with values of point resistance qc ≈ (0.4 – 5.0) MPa . Seismo–cone measurements revealed wave velocities Vs less than 60 m/s for depths down to 15 m, indicative of extremely soft soil layers. Ground acceleration was not recorded in Tigcilar. Using in 1-D wave propagation analysis, the EW component of the Sakarya accelerogram (recorded on soft rock outcrop, in the hilly outskirts of the city) leads to acceleration values between 0.20 g -0.30 g, with several significant cycles of motion, with dominant period in excess of 2 seconds. Even such relatively small levels of acceleration would have liquefied at least the upper-most loose
sandy silt layers of a total thickness 1–2 m, and would have produced excess pore-water pressures in the lower layers [16]
Only the dynamic bearing capacity aspect has been presented in the paper. Settlement and tilt of the foundation are very important will be discussed separately in future.
REFERENCES
Fig. 6. Finite element used by Tolga and Bakir [15]
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CONCLUSION
Shallow foundations subjected to combined static and seismic loads are commonly designed using the pseudostatic approach. Most research effort in recent years has been directed towards better defining the failure surface under combined static and seismic loading and efforts have been made to understand the behavior of the foundations under seismic loading Analytical solutions need validation on model, full scale and/or centrifuge tests. There has been some effort in this direction also. The codal provisions permitting 33% increase in static bearing capacity for the seismic case need to be re-examined in view of the test results cited in this paper [9,10] and the settlement and tilt that may be experienced by the footings due to earthquake loading.
[1] M.J. Mendoza and G. Avunit, The Mexico earthquake of September 19,1985-behavior of building foundations in Mexico city, Earthquake Spectra, 4(4): 835853, 1988 [2] L. Zeevart, Seismosoil dynamics of foundations in Mexico city earthquake , September 1985, Journal of Geotechnical Engineering, 117(3): 376-427, 1991 [3] G. Karaca, An investigation into large vertical displacement experienced by the structures in Adapazari during 17 August 1999 earthquake, MS thesis, Middle East Technical University , Ankara, Turkey 2001. [4] B.S. Bakir, H. Sucuoglu and T. Yilmaz, An overview of local site effects and the associated building damage during 17 August 1999 Izmit earthquake, Bulletin of seismological Society of America, 92(1): 509-526, 2002. [5] M.T. Yilmaz, O. Pekcan and B.S. Bakir, Undrained cyclic shear and deformation behavior of silt-clay mixtures of Adapazari, turkey, Soil Dynamics and Earthquake Engineering, 14(7) : 497-507, 2004 . [6] Y. Ohsaki, Effects of sand compaction on liquefaction during Tokachioki earthquake. Soils and Foundations. Vol. 10(2): 112-128, 1970. [7] B.M. Das, Principles of Soil Dynamics, PWS Kent, 1992. [8] R.W. Day, Foundation Engineering Handbook, McGraw Hill, 2006. [9] E.T. Selig and K. E. McKee, Static and dynamic behavior of small footing, Journal Soil Mechanics and Foundation Engineering, ASCE, 87(6), pp. 29-47, 1961. [10] A.S. Vesic, D.C. Banks and J. M. Woodward, An experimental study of dynamic bearing capacity of footing on sand, Proc. 6th INCSMFE, Vol. 2, pp. 209-213, Montreal, Canada, 1965. [11] R. Richards, D.G. Elms and M. Budhu, Seismic bearing capacity and settlement of foundations, Journal of Geotechnical Engineering Division, ASC, 119(4) , pp 662-674,1993. [12] M. Budhu and A.A. al-Karni, Seismic bearing capacity of soils, Geotechnique, 43(1), pp. 181-187, 1993. [13] A.A. Al-Karni and M. Budhu, An experimental study of seismic bearing capacity of shallow footings, Proc. 4 th International Conference on Recent advances in Geotechnical earthquake Engineering and soil dynamics and symposium in honor of professor W.D. Liam Finn, CD-ROM, San-Diego, CA, 2001. [14] D. Chaudhury and K.S. Subba Rao, Seismic bearing capacity of shallow strip footings, Geotechnical and geological engineering, 23(4), pp. 403-418, 2005. [15] S.Gajan and B.L.Kutter, Contact interface model for shallow foundations subjected to combined cyclic
loading", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 135 (3), pp 407-419, 2009. [16] G. Gazetas, M. Apostou and J.Anasta- Sopoular, Seismic bearing capacity failure and overturning of Terveler Building in Adapazari 1999”, Proc.Fifth Inter.Conf on Case histories in Geotechnical. Engineering. New York CD ROM –SOAP11(1-51), 2004.
