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Design of Shallow and Deep Foundations for Earthquakes D. Roy

DESIGN OF SHALLOW AND DEEP FOUNDATIONS FOR EARTHQUAKES Prepared by

Debasis Roy Department of Civil Engineering Indian Institute of Technology, Kharagpur 1. INTRODUCTION Foundations may undergo severe distress during an earthquake. One such example of foundation failure involving toppling of apartment blocks due to liquefaction during the 1964 Niigata Earthquake is presented in Figure 1. Earthquake effects on shallow and deep foundations are accounted for by designing them structurally to provide necessary strength and ensure serviceability. Strength considerations essentially involves ensuring that the foundation loads remain well below that dictated by the allowable bearing capacity under seismic conditions and serviceability is ensured by designing the substructure for the estimated permanent ground deformation. Simple procedures for estimating bearing capacity and permanent ground deformation under earthquake conditions are presented in this note.

Figure 1. Tilted apartment buildings 2. STATE OF STRESS WITHIN A SOIL DEPOSIT DURING AN EARTHQUAKE The states of stress within a soil element in static and earthquake conditions and the corresponding Mohr’s Circles are shown on Figure 2, from which it is apparent that the Mohr’s Circle representing a stable element in static condition (Element A, Figure 2a represented by Mohr’s Circle I, Figure 2c) may expand and translate towards the failure envelope because of cyclic shear and normal stress imposed during an earthquake (Element B, Figure 2b represented by Mohr’s Circle II, Figure 2c). As the ground motion further intensifies, Mohr’s Circle II may evolve into Mohr’s Circle III for which the failure plane is horizontal. Any further increase in the amplitude of ground motion will lead to the failure of soil layer without any further increase in resistance. It needs to be emphasized that the response discussed here can be reached irrespective of earthquake-related pore water pressure increase or liquefaction.

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

Figure 2. Subsurface state of stress Liquefaction is triggered when earthquake-related increase of pore water pressure causes a remarkable reduction of effective stress. Liquefaction is often functionally as a state in which large deformations (say, 5% double amplitude shear strain) develop within the deposit due to pore water pressure rise. The notion of liquefaction used here is thus not identical to the classical viewpoint that defines liquefaction as the state of zero effective stress. Saturated loose to medium dense sands and soft and sensitive clays of low plasticity are susceptible to liquefaction. The procedures for estimating the ultimate bearing capacities under earthquake loads at non-liquefied and liquefied sites are discussed below. 3. SHALLOW FOUNDATION DESIGN FOR EARTHQUAKES 3.1. NON-LIQUEFIED SITES Reduction in bearing capacity is mainly due to the inclination effects resulting from cyclic earthquake shear and normal loads because of structural inertia. A simple approach to account for these effects is to reduce the static bearing capacity factors using Figure 3. In Figure 3 subscripts “E” and “S” signify earthquake and static conditions. The ratio of seismic to static bearing capacity factors depend on the acceleration ratio, k h 1 k v , where kh and kv are the horizontal and vertical seismic coefficients within the failure zone. The seismic coefficients are often assumed according to k h 0.5 ah max and k v 0.5 k h , where ahmax is the average peak ground horizontal acceleration within the failure zone conservatively assumed to be identical to the peak horizontal ground acceleration at surface if the founding depth is not substantial. Alternatively, the average acceleration over the zone affected by shear failure can be estimated from a free-field site-response calculation using, e.g., SHAKE91. The usual value of the factor of safety for estimating the allowable seismic bearing capacity for shallow footings is 2. 3.2. LIQUEFIED SITES Many sites are underlain by a non-liquefiable crust of variable thickness depending on soil type and depth of groundwater. If the thickness of non-liquefiable layer below the bottom of footing is thin, shallow foundations supported within the layer may “punch” through. Shallow foundations in a site affected by liquefaction may also fail because of reduction of

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

Figure 3. Ratio of seismic to static bearing capacity factors (from Richards et al., 1993) bearing capacity due to earthquake-related pore water pressure rise. The foundation designer must ensure adequate factor of safety against such possibilities as indicated below. Punching The ultimate resistance for a strip footing against punching can be estimated using:

qult 2T su1

(1)

where T is the thickness of non-liquefiable crust below the footing base and su1 is the undrained shear strength of the non-liquefiable crust. For footings of limited length, multiplier 2 on the right hand side of Equation 1 should be replaced with the perimeter of the footing footprint. A factor of safety of safety of 2 should be provided in this regard. Bearing Capacity The bearing capacity problem related to liquefaction is essentially an undrained problem. The problem is conveniently treated using the static bearing capacity factor, Nc, for layered soils shown on Figure 4, in which Layer 1 represents the non-liquefiable crust and Layer 2 represents liquefied soil. Since liquefaction of Layer 2 is likely to cause a significant reduction in the amplitude of ground motion at surface, the static value of Nc may be used to estimate the ultimate bearing capacity even under earthquake condition. However, if triggering of liquefaction fails to damp out the ground motion at surface, NcE should be estimated using the chart on the right side of Figure 4. The undrained strength for non-liquefiable crust can be estimated from a field Vane Shear Test or the CPT if the layer is comprised of fine-grained soils. For coarse grained soils, the SPT or the CPT data can be used together with Equations 2 and 3 (Olson and Stark, 2003). For the liquefiable layer, the post-liquefaction undrained shear strength can be estimated using Equations 4 and 5 (Olson and Stark, 2003). su v0 0.205 0.0143qc1

(2)

su v0 0.03 0.0143qc1

(4)

su v0 0.205 0.0075( N1 ) 60

(3)

su v0 0.03 0.0075( N1 ) 60

(5)

where su is the undrained shear strength, v0 is the free field effective vertical overburden 0.5 0.5 pressure, qc1 qc Pa v0 , ( N1 ) 60 N Pa v0 ER , qc is the cone tip resistance, Pa is the atmospheric pressure and ER is the energy ratio of the SPT hammer. The usual

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

value of the factor of safety for estimating the allowable bearing capacity for shallow footings in a site underlain by liquefiable soils is 2.

Figure 4. Undrained bearing capacity factor, Nc, for layered soils (NAVFAC 1982) 3.3. DESIGN DISPLACEMENTS Since the factor of safety for estimating allowable bearing capacity under earthquake loads is about 50% smaller than that under usual dead load plus live load design conditions, allowable bearing capacity under earthquake loads may not be smaller than those in dead load plus live load design cases. However, footings tend to undergo continually increasing permanent vertical deformation (settlement) with the progress of earthquake-related cyclic moment and shear loading. Published centrifuge data indicate that total permanent vertical deformation can be as large as 1% of the footing width in areas not affected by liquefaction (Gajan et al. 2005) or 6% of the thickness of the liquefied layer when liquefaction is triggered. Consequently, permanent displacements may become the critical consideration in structural design for earthquake loads instead of bearing capacity. For sites not affected by liquefaction, Richards et al. (1993) presented a simple framework for estimating settlements because of earthquake-related unidirectional horizontal ground motion by extending the Newmark (1965) methodology developed originally for estimating permanent deformation of earth embankments. A similar simple framework is not available for multi directional earthquake ground motion. At liquefiable sites vertical settlement is usually estimated using the correlations presented in Figure 5. In this figure symbols Dr, N1 and qc1 (expressed in MPa) have been used to denote relative density, stress normalized SPT blow count and stress normalized cone tip resistance, respectively. Factor of safety against liquefaction is estimated following the procedures outlines in Youd et al. (2001). It should be noted that Japanese SPT data, based on which Ishihara and Yoshimine (1992) originally proposed these correlations, are typically obtained with hammers that deliver about 30% more energy than those employed in India. Figure 5 has been prepared accounting for this difference. The total permanent ground settlement related to liquefaction is obtained by multiplying the thicknesses of soil layers by the appropriate of the volumetric strain read out from Figure 5 and summing up the results for all individual layers within the soil column underlying a site.

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

Figure 5. Volumetric strain due to liquefaction (after Ishihara and Yoshimine, 1992) Differential settlements rather than total settlements usually govern structural design. The differential settlement is approximately 50% of the total settlement for isolated footings and 33% of that for mat foundations. 4. PILE FOUNDATION DESIGN FOR EARTHQUAKES Pile foundation is among the most widely used foundation types in areas affected by earthquakes. Several case histories involving failure of piles can nevertheless be found in the literature, two of which are shown on Figure 6. Most earthquake-related failure of pile foundations is due to permanent ground displacement (e.g., Figure 6a) or because of loss of lateral support (e.g., Figure 6b)

Figure 6. Earthquake effects on pile foundations

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

4.1. QUASI-STATIC DESIGN Piles are designed for earthquake loads focusing mainly on their bending behavior. The interaction between the pile and the surrounding soil is approximated by idealizing the soil resistance to relative movement between pile and soil by the so-called “p – y,” “t – z,” and the “Q – z,” springs, representing horizontal translation, vertical translation of the pile shaft and vertical translation of the pile tip, respectively. Symbols p, t and Q have been used here to represent the horizontal force, vertical force along pile shaft and the vertical force at the pile tip, respectively, while y and z represent vertical and horizontal displacements, respectively. A widely used empirical procedure for constructing these nonlinear springs for cyclic loading conditions like earthquakes can be found in API RP2A (American Petroleum Institute 2000). A simplified, quasi-static analytical includes the following steps: (a) estimation of the free field deformation (without considering the existence of the piles), (b) applying these deformations across the “p – y,” “t – z,” and the “Q – z,” springs to the piles, (c) recalculating the deformations, (d) applying the recalculated deformations across the “p – y,” “t – z,” and the “Q – z,” springs to the piles and (e) iterating through steps c and d until the input deformation field becomes compatible with the pile deformation within an acceptable range of tolerance. A very simple method of pile design for earthquake-related permanent ground deformation used by the Japanese Road Association (JRA 1996) involves consideration of a distributed load along the pile shaft as shown on Figure 7 along with other structural loads.

Figure 7. Lateral load for pile design for earthquake-related permanent ground deformation Concerns have been raised over recent years regarding the adequacy of this design procedure because it neglects the possibility of bucking resulting from the remarkable reduction of lateral restraint within the liquefied layer (Bhattacharya et al. 2004). However, to take proper account of liquefaction-related loss of lateral restraint development of an elaborate numerical model based on finite element or finite difference becomes necessary. It should be noted that several case histories describing earthquake-related failures of structures due to loss of lateral restraint for piles in cohesive deposits can also be found in the literature. Although finite difference computer codes have been developed to account for this possibility (Matlock and Foo 1980), a simple empirical procedure for estimating gap formation as a function of soil strength and number of cycles of earthquake load is not yet available.

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

4.2. DYNAMIC ANALYSIS An elaborate numerical model based on finite element (based on software package such as FLUSH, PLAXIS, QUAKE/W, ABAQUS, LSDYNA) or finite difference (FLAC) is also sometimes used to estimate the pile behavior. A suite of earthquake accelerograms are used in these analyses. Sourcing information and a brief description of the capabilities of these packages can be found at www.ggsd.com, www.itascg.com and www.lstc.com. 5. SELECTION OF FOUNDATION TYPE IN EARTHQUAKE-PRONE AREAS Isolated shallow foundations do not work well during earthquakes particularly because of differential settlements. However, lightly-loaded structures can be adequately supported using shallow foundations connected by grade beams and/or structurally designed floor slabs provided that sufficient depth of non-liquefiable (and/or insensitive) soils are present below the bottom of the footing. The grade beams are typically designed to carry one tenth of the maximum column load. Mat foundation is often considered a viable foundation option under earthquake loading conditions especially in areas underlain by liquefiable deposits. Uneven permanent ground deformations in such situations are bridged relatively easily by an appropriately designed mat foundation. Pile foundations also perform well under earthquake loads and are therefore commonly used in seismically active areas. Pile caps are also often interconnected with grade beams and structurally designed floor slab. 6. SUMMARY Structural design of foundations involves satisfying two requirements: (a) a factor of safety of 2 or more is available against bearing capacity failure under seismic loading and (b) the permanent ground deformation can be accommodated by the foundation system and superstructure. Some of the simple empirical procedures available to account for these issues for common foundation types have been discussed in this note. Common strategies adopted by geotechnical engineers in foundation design have also been briefly discussed. REFERENCES American Petroleum Institute. 2000. Recommended practice for planning, desigining and constructing fixed offshore platforms – Working stress design. API RP 2A. Washington, DC, USA. Bhattacharya S., Madabhushi, S.P.G. and Bolton, M.D. 2004. An alternative mechanism for pile failure in liquefiable deposits during earthquakes. Géotechnique, 54(3): 2013-213. Gajan, S., Kutter, B.L., Phalen, J.D., Hutchinson, T.C., and Martin, G.R. 2005. Centrifuge modeling of load-deformation behavior of rocking shallow foundations. Soil Dynamics and Earthquake Engineering, 25, 773-783. Ishihara, K., and Yoshimine, M. 1992. Evaluation of settlements in sand deposits following liquefaction during earthquakes. Soils and Foundations. 32(1), 173-188. JRA. 1996. Japanese Road Association Specification for Highway Bridges, Part V, Seismic Design. Matlock, H. and Foo, S. 1980. Axial analysis of piles using a hysteretic and degrading soil model. Proceedings, 1st International Conference on Numerical Methods in Offshore Piling, London, 127-133.

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Geotechnical Earthquake Engineering IITGn – March 4 – 8t, 2013

Design of Shallow and Deep Foundations for Earthquakes D. Roy

Newmark, N.M. 1965. Effects of earthquakes on dams and embankments. Géotechnique, 15, 139-160. Olson, S.M. and Stark, T.D. 2003. Yield strength ratio and liquefaction analysis of slopes and embankments. Journal of Geotechnical and Geoenvironmental Engineering. ASCE. 129(8), 727-737. Richards, R., Elms, D.G., and Budhu, M. 1993. Seismic bearing capacity and settlements of foundations. Journal of Geotechnical Engineering. 119(4): 662-674. Yuminamochi, F. 1999. Air photographs of the Niigata City immediately after the earthquake of 1964. Japanese Geotechnical Society.

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