foundations for seismic loads

8/13/2019 Foundations for Seismic Loads

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FOUNDATIONS FOR SEISMIC LOADS

Vijay K. Puri 1 and Shamsher Prakash 2

1Professor, Civil Engineering, Southern Illinois University, Carbondale, IL 62901USA

2Professor Emeritus, University of Missouri – Rolla, Rolla, MO 65409 USA

Abstract

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 soil- pile 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 andload 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 instrength 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 andIzmit earthquake (1999) in Turkey (Day, 2002).Prasad et al (2004) made anexperimental 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 groupefficiency 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

right ASCE 2007 Geo Denver 2007: New Peaks in Ge Dynamic Response and Soil Properties



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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 theultimate bearing capacity is accordingly estimated. To account for the effect of

dynamic nature of the load, the bearing capacity factors are determined by usingdynamic 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 BuildingCode (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 hasadequate 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 friablerock, 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 withliquefaction 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 1shows the assumed failure surfaces. The seismic bearing capacity (quE) is given by

Eq. 1:

quE = cNcE + qNqE + ½ BNE (1)where, = Unit weight of soil

q= Df and Df = Depth of the foundation

NcE, NqE, and NE = Seismic bearing capacity factors which are functions of andtan = k h / (1-k v)

k h and k v are the horizontal and vertical coefficients of acceleration due to earthquake.

For static case, k h = k v, = 0 and Eq. (1) becomes

qu = cNc + qNq + ½ BN (2)





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in which Nc, Nq and N are the static bearing capacity factors. Figure 2 shows plots of NE /N, NqE /Nq and NcE /Nc with tan and .

tan = k h / (1-k v), tan = k h / (1-k v), tan = k h / (1-k v),

Figure 2. Variation of N qE /Nq , NE /N and NcE /Nc with and tan (After Richardset al 1993)

Figure 3. Critical acceleration *

hk (After Richards et al, 1993)





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Seismic Settlement of Foundations

Bearing capacity-related seismic settlement takes place when the ratio k h /(1 - k v)

reaches a critical value (k h /1 – k v)*. If k v = 0, then (k h /1 - k v)* becomes equal to k h*

Figure 3 shows the variation of k h*

(for k v = c = 0; granular soil) with the static factor

of safety (FS) applied to the ultimate bearing capacity Eq, (2), for = 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) as42

*( ) 0 . 1 7 4 t a n

k V hS m E q A E

A g A

= (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/sec2).

tan AE depends on and k h*

In Figure 4, variation of tan tan AE with k h* for of 15° - 40° is shown.

Figure 4. Variation of tan AE with k h* and (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 = 18 KN/m3, = 34°, and c = 0. The value of k h = 0.3 and k v =

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/m2

(Eq.

2). The reduced ultimate bearing capacity for vertical load is calculated as 290 KN/m2

(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/m2), the additional settlement





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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 bearingcapacity 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 n1 and time period in first mode of vibrations.

3. For the above period, determine the spectral displacement Sd for the appropriatedamping (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 pile2. 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 (k xø, rocking stiffness (k ø)and cross-coupling stiffness k xø. Corresponding expressions for radiation damping

coefficients Cx, Cø and Cxø, cross- damping 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, followingsimple expression has been developed for Group Efficiency Factors () in horizontal

vibrations





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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

1 / 222 2

4 2

22 3

k C C C k k k k x x x x x

m M m M m M m M m M m m m m m

k C k k k C C C x x x x x

m M m M m M M mm m m m

+ + +

+ + +

3 1 152 21 s 1

= < 12 d N

(4)

Group Efficiency Factor () is defined as:

(5)

where s = Center to center spacing of pilesd = Diameter or width of pile

N = Number of piles in group

Similarly group radiation damping in sliding (Cxg) is given by Eq. 6.,

)(

)(

x

xg

C damping pileSingle X N

C dampingGroup (6)

The above equation follows from the recommendations for pile group effects by

Novak (1974).The pile cap stiffness and damping needs be added to the k xg, k g and Cxg and Cg

computed above (Prakash and Sharma, 1990).

Pile Group Natural Frequencies

The next step is to determine natural frequencies of the system, which may bedetermined from the following equation (Kumar and Prakash, 1995)

(7)

Pile Group Response

The response of the pile group may be determined by any standard structuraldynamic method of analysis. A detailed time history solution for a given ground

motion may be obtained and the maximum response values be selected for design.

The above response may be used as input motion for analysis of the superstructure.

Alternatively, a spectral response method be used.

Non-Linear Analysis

Various relationship between soil shear modulus (G) and normalized shear modulus

(G/Gmax) with strain have been developed (Vucetic and. Dobry, 1991). The strains in

soils during earthquakes may be of the order of 10-4

to 10-2

. Non-linear analysis may





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be performed by using step- by- step linear approach and repeating the process until

convergence between predicted and assumed strains has been obtained

Strain-Displacement Relationships

Shear strain and displacement relationship is not well defined. In manypractical problems reasonable expressions must be assumed and used as the basis for

evaluating the shear strain in each particular case; Prakash and Puri (1981)

recommended for vertically vibrating footings as:

foundationof widthAverage

vibrationfoundationof Amplitude= (8)

Kagawa and Kraft (1980) used the following relationship between shear strain ( x )

and horizontal displacement (x);

x ( ) D

X

5.2

1 += (9)

Where, = Poisson’s ratioX = horizontal displacement in x-directionD = diameter of pile

Rafnsson (1992) recommended that the shear strain due to rocking can be

reasonably determined as

3

= (10)

Where, = rotation of foundation about y axis

The shear strain-displacement relationship for couple sliding and rocking can bedetermined as:

( )35.2

1 +

+=

D

X (11)

Solution Technique for Displacement Dependent K’s and C’s1. OBTAIN Unit weight, shear wave velocity, poisson’s ratio, initial shear modulus;

shear modulus degradation curve as function of soil shear strain

2. OBTAIN Pile length, pile diameter, elastic modulus of pile, shear wave velocity





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3. SELECT relationship for half space stiffness and damping parameters as function

of soil parameters, pile dimensions, and piles arrangements.4. DETERMINE Strain-Displacement Relationship

5. DETERMINE Stiffness and damping factor for single pile at selected

displacements

6. CALCULATE Group efficiency factor7. CALCULATE Group piles stiffness and damping factors

8. REPEAT Steps 5-7 for all desired displacements and plot stiffness (k) anddamping (c) parameters versus displacement functions

Figure 5 k xg , k y

g , k zg versus, non-dimensional displacement ( /D)

Figure 5 shows a plot of k’s versus non dimensional displacement of a typical pilegroup (Munaf and Prakash (2002)

These and similar relationships were used in the analysis of bridge structures at two

locations (Anderson, Prakash et al 2001, Luna et al 2001).

Conclusions

1. A method to estimate seismic bearing capacity and settlements of strip foundations

has been reviewed. Analytical solution need validation on model, full scale and/or

centrifuge tests.





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2. Further research on model and field tests on settlement and tilt of shallow

foundations and their analysis are needed to develop reasonable design procedures forearthquake resistant design.

3. A procedure to determine non-linear response of soil-pile systems using stiffness

based on strain- dependent soil modulus and damping is presented.

References

Anderson, N, Prakash, S. et al (2001) “Earthquake Hazard Assessment Along

Designated Emergency Vehicle Priority Access Routes,” Final report RDT MO R

198-043 T-Missouri Department of Transportation

ATC (1978) Tentative Provisions for the Development of Seismic Regulations for

Buildings, Applied Technology Council (ATC) Document ATC 3-06.

Bruneau, M. (1999), ‘Structural Damage: Koceali , Turkey Earthquake , August 17,1999’,on the internet.

Das, B.M.(1992). Principles of Soil Dynamics, PWS Kent

Day, Robert W. (2002). Geotechnical Earthquake Engineering Handbook, McGraw

Hill

Day, Robert W. (2006). Foundation engineering Handbook, McGraw Hill.

Gazetas, G. (1991), Foundation vibrations, Ch 15 in Handbook of Foundation Engg.by F.Y. Fang (Second Edition) Van Nostrand, NY.

Kumar, S. and Prakash, S. (1995), Couple horizontal and rocking vibration of block foundations, Proc. III Intern. Conf. on Recent Advances in Geot. Earthquake Eng and

Soil Dyn. April, St. Louis, MO Vol. III, pp 1369-1373.

Kagawa, T., and Kraft, L. M., Jr. (1980), “Lateral Load-Deflection Relationships for

Piles Subjected to Dynamics Loading, “Soil Foundations, Japanese Society of Soil

Mechanics and Foundation Engineering, Vol. 20, NO. 4, pp 19-36.

Luna, R., Prakash….et al (2001), “Earthquake Assessment of Critical Structures for

Route 66 Missouri, Paper No. 8-13 Proc. 4th

International Conf. Recent Advances in

Geot. Earthquake Energy Soil Dynamics, San Diego, CA, CD-ROM (March).

Munaf, Y.and Prakash, S. (2002),”Displacement Dependent Spring and DampingFactors of Soil Pile Systems,” Proc. 12th ECEE, London Paper No. 763

Novak, M. (1974), Dynamic stiffness and damping of piles, Con. Geot. J. Vol. II No4, pp. 574-598.





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Novak, M. and ElSharnouby, E.B. (1983), Stiffness and damping constrants for single

piles, J. Geot. Engg. Dn. ASCE, Vol. 109 No 7, pp 961-974.

Pecker, A. (1996). Seismic Bearing Capacity of Shallow Foundations, 11th

World

Conference on earthquake engineering, Acapulco, Mexico.

Prakash, S., (1981), Soil dynamics, McGraw Hill, New York.

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under earthquake loadings, Proc. 11th WCEE, Acapulco, June .

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Wiley and Sons, NY.

Prasad, S.K., Chandrahara, G.P., Nanjundaswamy, P. and Revansiddappa, K.(2004).Seismic Bearing Capacity of Ground from Shake Table Tests, IGC -2004, Vol. 1,

Warrangal

Rafnsson, E.A., (1991), “Displacement-Based Design of Rigid Retaining Walls

Subjected to Dynamic Loads Considering Soil Non-linearity, “PhD Dissertation,

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Settlement of Foundations, Journal of Geotechnical Engineering Division, ASCE,

Vol. 119, No. 4, April, pp 662-674.

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loading, J. Soil Mech. Found. Dn. ASCE, Vol. 88 No SM 2 pp 99-132.


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