Shamsher Prakash

Foundations for Seismic Loads

Design of foundations in earthquake prone areas needs special considerations. Shallow foundations may experience a reduction in bearing capacity and increase in settlement and tilt due to seismic loading. The reduction in bearing capacity depends on the nature and type of soil and ground acceleration parameters. In the case of piles, the soil-pile behavior under earthquake loading is generally non-linear. The nonlinearity must be accounted for by defining soilpile stiffness in terms of strain dependent soil modulus. Several behavioral and design aspects of shallow foundations and pile groups subjected to earthquakes have been critically reviewed. Introduction Structures subjected to earthquakes may be supported on shallow foundations or on piles. The foundation must be safe both for the usual static loads as well for the dynamic loads imposed by the earthquakes and therefore the design of either type of foundation needs special considerations compared to the static case. Shallow foundations in seismic areas are commonly designed by the equivalent static approach. The observations during 1985 Michoacan-Guerero earthquake (Pecker, 1996) and the Kocaeli 1999 earthquake have shown that initial static pressure and load eccentricity have a pronounced effect on seismic behavior of foundations. The soil strength may undergo degradation under seismic loading depending on the type of soil. Pore pressure buildup and drainage conditions may result in decrease in strength and an increase in settlement. Most foundation failures due to earthquake occur due to increased settlement. However, failure due to reduction in bearing capacity have also been observed during Niigata earthquake (1964) in Japan and Izmit earthquake (1999) in Turkey (Day, 2002).Prasad et al (2004) made an experimental investigation of the seismic bearing capacity of sand. A practical method to account for reduction in bearing capacity due to earthquake loading was presented by Richard et al,(1993). The settlement and tilt of the foundation must also be considered. For analysis and design of pile groups under seismic loading a simple approach to account for nonlinear behavior of soil-pile system under dynamic loads and group efficiency factors are presented in the paper. In this approach strain dependent soil modulus is used to define soil-pile stiffness and radiation damping. GSP 160 Dynamic Response and Soil Properties Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics 2 Shallow Foundations 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 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 (Das, 1992). The settlement and tilt of the foundation may then be obtained using the method proposed by Prakash (1981). Building code such as International Building Code (2006) 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 is based on the assumption that the allowable bearing pressure has adequate factor of safety for the static loads and a lower factor of safety may be accepted for earthquake loads. 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 (Day, 2006). Figure 1. Failure surface in soil for seismic bearing capacity (After Richards et al, 1993) Richards et al (1993) observed seismic settlements of foundations on partially saturated dense or compacted soils. These settlements were not associated with liquefaction or densification and could be easily explained in terms of seismic bearing capacity reduction. They have proposed a simplified approach to estimate the dynamic bearing capacity que and seismic settlement SEq of a strip footing. Figure 1 shows the assumed failure surfaces. The seismic bearing capacity (quE) is given by Eq. 1: quE = cNcE + qNqE + 1⁄2 γ BNγE (1) where, γ = Unit weight of soil q= γDf and Df = Depth of the foundation NcE, NqE, and NγE = Seismic bearing capacity factors which are functions of φ and tanψ = kh / (1-kv) kh and kv are the horizontal and vertical coefficients of acceleration due to earthquake. For static case, kh = kv, = 0 and Eq. (1) becomes qu = cNc + qNq + 1⁄2 γBNγ (2) GSP 160 Dynamic Response and Soil Properties Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics 3 in which Nc, Nq and Nγ are the static bearing capacity factors. Figure 2 shows plots of NγE/Nγ, NqE/Nq and NcE/Nc with tan ψ and φ. tan ψ = kh/ (1-kv), tan ψ = kh/ (1-kv), tan ψ = kh/ (1-kv), Figure 2. Variation of N qE /Nq , NγE /Nγ and NcE/Nc with φ and tan ψ(After Richards et al 1993) Figure 3. Critical acceleration * h k (After Richards et al, 1993) GSP 160 Dynamic Response and Soil Properties Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics 4 Seismic Settlement of Foundations Bearing capacity-related seismic settlement takes place when the ratio kh/(1 kv) reaches a critical value (kh/1 – kv)*. If kv = 0, then (kh/1 kv)* becomes equal to kh * Figure 3 shows the variation of kh * (for kv = c = 0; granular soil) with the static factor of safety (FS) applied to the ultimate bearing capacity Eq, (2), for φ = 10°, 20°, 30°, and 40° and Df/B of 0, 0.25, 0.5 and 1.0. The settlement (SEq) of a strip foundation due to an earthquake can be estimated (Richards et al, 1993) as 4 2 * ( ) 0 .1 7 4 ta n k V h S m E q A E A g A α − = (3) where V = peak velocity for the design earthquake (m/sec),A = acceleration coefficient for the design earthquake, g = acceleration due to gravity (9.81 m/sec). tan αAE depends on φ and kh* In Figure 4, variation of tan tan αAE with kh* for φ of 15° 40° is shown. Figure 4. Variation of tan αAE with kh* and φ (After Richards et al 1993) Suppose a typical strip foundation is supported on a sandy soil with B = 2 m, and Df = 0.5 m, and γ = 18 KN/m, φ = 34°, and c = 0. The value of kh = 0.3 and kv = 0 and the velocity V induced by the design earthquake is 0.4 m/sec. The static ultimate bearing capacity for this footing for vertical load will be 1,000 KN/m (Eq. 2). The reduced ultimate bearing capacity for vertical load is calculated as 290 KN/m (Eq 1). If the footing is designed using a FS = 3 on the static ultimate bearing capacity (i.e., for an allowable soil pressure of 333 kN/m), the additional settlement GSP 160 Dynamic Response and Soil Properties Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics 5 due to earthquake will be 20.5 mm. This settlement reduces to 7.0 mm if FS of 4 is used. Besides ensuring that the footing soil system does not experience a bearing capacity failure or undergo excessive settlement, the foundations should be tied together using interconnecting beams (Applied Technology Council ,1978) Piles and Pile Groups under Earthquake Loadings Pile foundations are used extensively to support heavy loads. The bulk of loads are static which forms the basis for fixing the section (size), embedded length and configuration (spacing and arrangement) of the piles in the group. Dynamic loads are caused by nature, e.g. earthquakes, winds, waves and by man-made vibrations, e.g. machines, traffic and blasts. Prakash and Sharma (1990) have recommended the following procedures for design of single pile against earthquakes: 1 Estimate the dead load on the pile. The mass at the pile top which may be considered vibrating with the piles is only a fraction of this load. 2. Determine the natural frequency ωn1 and time period in first mode of vibrations. 3. For the above period, determine the spectral displacement Sd for the appropriate damping (radiation + material). 4. Using the pile displacements in (3) above, determine the bending moments and shear forces for structural design of the pile. Analysis of Pile Groups The following steps are involved in analysis of a pile group 1. Determine the stiffness and radiation damping of the single pile 2. Determine the stiffness of the pile group by applying appropriate pile-soil-pile interaction factors. 3. Determine natural frequencies of the pile group. 4. Estimate the response of the pile group for the given input motion. The pile cap displacements (translation and rotation) may be used as input parameters for superstructure analysis. Stiffness and Radiation Damping of Single Piles Stiffness of single piles in horizontal-translation and rotation may be determined as follows: Novak and El-Sharnouby (1983) and Gazetas (1991) have recommended expressions for horizontal sliding stiffness (kxo, rocking stiffness (ko) and cross-coupling stiffness kxo. Corresponding expressions for radiation damping coefficients Cx, Co and Cxo, crossdamping respectively have been developed by both the investigators. Stiffness and Radiation Damping of Pile-Group Gazetas (1991) has recommended pile-soil-pile interaction factors for both the stiffness and radiation damping. Based on experimental studies on piles, following simple expression has been developed for Group Efficiency Factors (e) in horizontal vibrations GSP 160 Dynamic Response and Soil Properties Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics 6 G r o u p s t i f f n e s s ( k ) x g = N X S i n g l e p i l e s t i f f n e s s ( k ) x ∈

On Seismic Design of Retaining Walls

Retaining walls have failed either by sliding away from the backfill or due to combined action of sliding and rocking displacements, during earthquakes. Performance based design of the retaining walls in seismic areas must account for these displacements, in addition to the usual factors of safety against failure in bearing, sliding and overturning. A realistic model for estimating dynamic displacement, which accounts for the combined action of sliding and rocking and takes into consideration, non-linear stiffness of soil and geometric and material damping and coupling effects is now available, Wu and Prakash (2009). This model has been used to calculate the displacement for several combinations of backfill and foundation soil conditions. Based on this study, typical design charts for preliminary design have been proposed.

Foundations for Dynamic Loads

Design of foundations in earthquake prone areas needs special considerations. Shallow foundations may experience a reduction in bearing capacity and increase in settlement and tilt due to seismic loading. The reduction in bearing capacity depends on the nature and type of soil and ground acceleration parameters. In the case of piles, the soil-pile behavior under earthquake loading is generally nonlinear. The nonlinearity must be accounted for by defining soil- pile stiffness in terms of strain dependent soil modulus. A comparison of observed and predicted pile behavior under dynamic loads has attracted the attention of several investigators. The lateral dynamic pile response of single piles predicted by analytical models often yields higher natural frequencies and lower resonant amplitudes compared to those determined from field tests in horizontal vibrations only. This has been found to be due to overestimated shear modulus and radiation damping of the soil. The authors made an investigation to determine a simple method to improve the theoretical predictions of piles embedded in fine soils. Based upon this investigation shear strain dependent reduction factors are proposed for determining the shear modulus and damping for pile response calculations.