soil structure interaction

Ammar Motorwala Modelling Soil-Structure Interaction for Non-linear Dynamic Analysis of Framed structures with Pile Foundation

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Modelling Soil-Structure Interaction for Non-linear Dynamic

Analysis of Framed structures with Pile Foundation

An earthquake is a phenomenon which basically takes place to dissipate the strain energy

accumulated over time at the fault surface and this dissipation of energy takes place in terms

of emission of the shock waves. So, basically the ground motion which is felt at the surface of

the earth is due to these shock waves. One of the important characteristics of any earthquake

ground motion is its frequency content and dominant frequency along with other parameters

like time history records, peak ground acceleration and duration of ground motion.

Local site conditions are defined in terms of the materials that lie directly beneath the site.

The preferred definition is in terms of shear-wave velocity and the depth of sediment beneath

the site. These two parameters define the natural frequency of the site material and as

observed in Mexico City, (1985) Earthquake and Loma Prieta, (1989) Earthquake, if the

dominant frequency of the earthquake waves is near the fundamental frequency of the site

material, disasters can happen. From these studies it is evident that the dynamic response of

a structure to an earthquake depends on the nature of the surrounding soil along with

characteristics of the ground motion and the physical properties of the structure itself.

Soil-structure interaction analysis evaluates the collective response of the structure,

foundation and the soil under and surrounding the foundation to a specified ground motion.

In usual practice, when a structure is to be designed for seismic loads, standard procedures in

chapter 11 and 12 of ASCE 7-10 Minimum Design Loads for Buildings and Other Structures

(ASCE, 2010) are followed and the ground motion characteristics scaled based on the

probabilistic models are used. The influence of local site class is taken into account through

modification factors. Thus, a crude and more probabilistically conservative form of SSI is

considered and hence, the structural designer inputs “free field” response spectra or ground

motions directly to an analysis of the structure without any consideration of interaction and

then designs the foundations for the resulting forces. The term “free-field” refers to motions

that are not affected by structural vibrations or the scattering of waves at, and around, the

foundation.


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In most cases ignoring soil-structure interaction is conservative, provided the design response

spectra and ground motions adequately envelope the kinematic effect of the foundation

structure and its effect on site response. This may be difficult to do in cases such as the

following, where soil-structure interaction analysis is advisable to reduce risk:

The foundation system alters the soil properties (e.g., a pile foundation in soft soils).

Buildings with a deep basement or pile foundation system where it is difficult to

determine the effective ground excitation and where the structural inertia forces are

dependent on the foundation reaction with the soil. This issue is compounded for sites

where the soil properties vary significantly with depth.

Where the site conditions are susceptible to large ground deformations, e.g., lateral

spreading or ground fault rupture, or soil liquefaction.

Soil-structure interaction analysis is also undertaken to realize substantial construction cost

savings by reducing the conservatisms in the conventional approach. This is typically

worthwhile on sites with relatively soft soils where:

The flexibility of the soil-foundation system significantly elongates the effective natural

periods of the structure and increases the damping, leading to reduced earthquake

design forces.

Where the structure is massive and its inertia forces significantly increase the strain

levels in the soil relative to the free field response.

If a decision is made to incorporate SSI in the design of a structure, it should be kept in mind

that modeling of SSI is dominated by the issues associated with the soil being an infinite

medium, making it difficult to model the transmission of earthquake induced stress and strain

waves through the boundaries of the soil model. The behavior of soils is also significantly

nonlinear under strong ground shaking, and soil materials display strain softening, energy

dissipation through material hysteresis and radiation damping, and strain rate dependency.

Even if a detailed geotechnical investigation is available, a high degree of uncertainty in

behavior of the soils will remain. For this reason, a great caution should be exercised and it is

recommended that analyses are undertaken using upper and lower bounds of soil properties.


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The upper bound soil stiffness and strength is usually more critical for the demands on the

structure itself, and lower bound properties may be critical for the design of the foundation.

The three main effects of SSI which need to be addressed in any SSI model are categorized as

inertial interaction effects, kinematic interaction effects, and soil-foundation flexibility effects

and these effects can be related to structural analysis in terms of:

Foundation stiffness and damping. As compared to the normal assumption of rigid

foundation, the inertial forces (base shear, moment and torsion) generates lateral

displacement and rotation at the foundation level. This effects introduces flexibility in the

structure and leads to period elongation. Moreover, these displacements give rise to energy

dissipation via radiation damping and hysteretic soil damping, which can significantly affect

overall system damping. Since these effects are rooted in structural inertia, they are referred

to as inertial interaction effects.

Variations between foundation input motions and free-field ground motions.

Comparatively stiffer foundation elements, placed at or below the ground surface composed

of comparatively flexible material, cause foundation motions to deviate from free-field

motions due to base slab averaging, wave scattering, and embedment effects in the absence of

structure and foundation inertia. This effect is called kinematic interaction effect as it does not

involve any inertial forces.

Foundation Deformations. Flexural, axial, and shear deformations of structural foundation

elements occur as a result of forces and displacements applied by the superstructure and the

soil medium. These represent the seismic demands for which foundation components should

be designed, and they could be significant, especially for flexible foundations such as rafts and

piles.

To address these effects, there are two generic approaches for practical nonlinear soil-structure

interaction analysis:


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(i) Direct Analysis Approach

As schematically depicted in the figure, the soil is often represented as a continuum

(e.g., finite elements) along with foundation and structural elements, transmitting

boundaries at the limits of the soil mesh, and interface elements at the edges of the

foundation. The ground motions (including spatial variability, when significant)

are applied at transmitting boundaries at the base and sides of the model, and the

kinematic interaction is modeled directly.

Though direct solution of the

SSI problem is quite intuitive,

it is very difficult from a

computational standpoint,

especially when the system is

geometrically complex or

contains significant non-

linearities in the soil or

structural materials. Hence, it

is seldomly used in practice

and has been more limited to research applications.

(ii) Indirect (Sub-structure) Approach

Proper consideration of SSI effects in a substructure approach requires:

o an evaluation of free-field soil motions and corresponding soil material

properties;

o an evaluation of transfer functions to convert free-field motions to foundation

input motions;

o incorporation of springs and dashpots (or more complex nonlinear elements)

to represent the stiffness and damping at the soil-foundation interface; and

o a response analysis of the combined structure-spring/dashpot system with the

foundation input motion applied.


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The superposition inherent in a substructure approach requires an assumption of

linear soil and structure behavior, although in practice this requirement is often

followed only in an equivalent-linear sense. The steps in a substructure approach

are as follows:

o Defining foundation input motion (FIM), which is the motion of the

base-slab that accounts for the stiffness and geometry of the foundation. The

foundation input motions are expressed by a transfer function that represents

the ratio of foundation/free-field motion in the frequency domain. Since

inertial effects are neglected, the transfer function represents the effects of

kinematic interaction only. An essential first step in defining the FIM is to

evaluate the free-field response of the site, which is the spatial and temporal

variation of ground motion in the absence of the structure and foundation.

Having established the free-field motion, wave-propagation analyses are

performed to estimate the foundation input motion along the planned soil-

foundation interface. Equivalent linear properties for the soil (e.g., shear

modulus, material damping) can be evaluated as part of this analysis.

o The stiffness and damping characteristics of the soil-foundation interaction are

characterized using relatively simple impedance function models or a series of

distributed springs and dashpots. Impedance functions represent the frequency

dependent stiffness and damping

characteristics of soil-foundation

interaction.

As shown in the figure, the stiffness

and damping due to SSI are

represented using either single

spring and dash-pot for each

degree of freedom or a series of

springs and dash-pots distributed

over the foundation. The latter

case of distributed springs and


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dashpots is needed when foundation elements are non-rigid, or when internal

demands (e.g., moments, shears, deformations) are required outcomes of the

analysis.

o The superstructure is modeled above the foundation and the system is excited

through the foundation by displacing the ends of the springs and dashpots using

the rocking and translational components of the FIM. It should be noted that

FIM varies with depth. In the case of the distributed spring and dashpot model,

differential ground displacements should be applied over the depth of

embedment. This application of spatially variable displacements introduces a

rotational component to the FIM, which is why a rotational spring is not

required in such model.

Pile-supported footings or mat are normally used for building structures founded on soft soils,

especially when the foundation is not embedded. A single pile can be quite conveniently

represented by springs and dash-pots in numerical models of pile-supported foundations. The

dynamic stiffness of a single pile for a particular vibration mode 𝑘𝑗𝑝 can be represented as a

product of static stiffness 𝐾𝑗𝑝 and a dynamic modifier 𝛼𝑗

𝑝. Subscript j represents the vibration

mode, which is taken as x (horizontal) and z (vertical).

𝑘𝑗𝑝

= 𝐾𝑗𝑝

× 𝛼𝑗𝑝

Where,

Here, j is a dimensionless constant for vibration mode j; d is pile diameter; Es and Ep are the

Young’s moduli for soil and pile materials, respectively; s and p are the mass densities for

soil and pile materials, respectively; is the Poisson’s ratio of the soil; wpj, wsj, and wbj

represent weight factors that together sum to unity for pile, soil, and pile tip stiffness

contributions, respectively, for vibration mode j; and a0p is a dimensionless frequency for piles.


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A fundamental aspect of pile response to lateral head loading is that

a long pile does not deflect over its entire length, but only to a

certain depth, termed the active pile length, La. The active pile

length is on the order of 10 to 20 pile diameters, depending on pile-

soil stiffness contrast, soil non-homogeneity, and fixity conditions

at the pile head. It is found that active lengths tend to be greater for

dynamic loading than for static loading, due to the ability of elastic

waves to travel further down the pile than a static stress field and

also axially loaded piles tend to respond to much greater depths. Approximate values of active

pile lengths, La, are 10d to 20d for lateral loading, and the actual pile length, Lp, for axial

loading.

Once an appropriate active length, La, is selected, an average effective profile velocity between

the ground surface and depth, La, can be computed, using which small strain shear modulus

G0 can be evaluated using 𝐺0 = 𝜌𝑠𝑉𝑠2. Then based on Table 19.2-1 in chapter 19 of ASCE 7-

10 Minimum Design Loads for Buildings and Other Structures (ASCE, 2010) soil shear modulus,

G, should be reduced relative to G0 for large strain effects. These are more kind of

approximations and further research is needed to produce better estimates of Vs. From G,

Young’s modulus for soil can be calculated:

Weight factors in the above equation for stiffness (wpj, wsj, and wbj) represent the relative

contributions of the pile structural stiffness, pile-soil interaction through side-load transfer,

and pile-soil interaction through toe resistance for vibration mode j. These weight factors

always sum to unity (i.e., wpj + wsj + wbj = 1.0).

Using this information and the recommendations provided by various researchers, the

empirical formula as tabulated in the Table 2-4a and Table 2-4b of NIST GCR 12-917-21 Soil-

Structure Interaction For Building Structures (NEHRP Consultants Joint Venture, 2012), the


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stiffness of the springs and the damping ratio of the dash-pots can be calculated and

impedance of piles can be modeled.

Usually, for building foundation system, if piles are used, then they are configured in groups

to support a mat or discrete pile caps, and seldom used as a single a pile. The impedance of

a pile group cannot be determined by simple addition of individual pile impedances because

grouped piles interact through the soil by “pushing” or “pulling” each other through waves

emitted from their periphery. This is called a group effect, and it can significantly affect the

impedance of a pile group as well as the distribution of head loads among individual piles in

the group. Group effects depend primarily on pile spacing, frequency, and number of piles.

The ratio of the pile group impedance in any oscillation mode, 𝑘𝑗𝐺, to the sum of the individual

static pile impedances in the same oscillation mode, 𝑁𝑝𝑖𝑙𝑒𝑠 × 𝑘𝑗,𝑠𝑡𝑎𝑡𝑖𝑐𝑃 , is the efficiency factor of

the pile group. Efficiency factors are generally less than unity for low frequencies, but can

increase significantly at higher frequencies under low strain conditions.

There are lots of known as well as unknown sources of non-linearity and capturing all of them

in the analysis models is kind of impossible. Most of the research performed on nonlinear SSI

has been related to structural yielding with linear, or equivalent-linear, soil or soil

yielding/gapping with a linear structure.

If structural yielding develops at relatively low intensity input motions, or if the

foundation is over-designed, significant material nonlinearities in the foundation and

soil may not occur. This justifies the use of equivalent-linear representations of

subsurface material properties in the analyses. Hence, because of difficulties associated

with modeling the constitutive behavior of soil in three dimensions and wave

propagation in a finite volume of geologic material under the structure, without

spurious wave reflections at fictitious model boundaries, most studies focus on

nonlinearities in the superstructure.

Mounting analytical and experimental evidence proving that material and geometric

nonlinearities in the soil may be beneficial to the seismic response of a structure has

initiated revision of the foundation design philosophy by allowing significant yielding


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in the soil close to the foundation, or the foundation itself, to dissipate energy and

protect the superstructure. This requires control of settlement and tilting of the

structure. Hence, the analysis and design process considering soil nonlinearity involves

optimization of the trade-offs between the potentially beneficial effects of soil yielding

(especially with regard to energy dissipation) and the detrimental effects of settlement

or residual tilt. Soil-structure interaction studies with nonlinear soil and foundation

behavior can be classified into three approaches:

1) Continuum models

2) Beam-on-Nonlinear Winkler Foundation (BNWF) Models

3) Plasticity Based Macro-Element (PBM) Models

Models for kinematic interaction effects are expressed as frequency dependent ratios of the

Fourier amplitudes (i.e., transfer functions) of foundation input motion (FIM) to free-field

motion. The FIM is the theoretical motion of the base slab if the near-surface foundation

elements (i.e., base slabs, basement walls) and the structure had no mass, and is used for

seismic response analysis in the substructure approach.

When building foundations are pile-supported, the kinematic interaction problem is

complicated by the influence of the piles on wave propagation below the foundation, and also

by the potential for the soil to settle away from the pile-supported base of the structure,

forming a gap. This is a complex kinematic soil-structure interaction problem for which there

are no well-calibrated engineering models. There are few suggestions made by researchers

about the use Transfer functions applied for shallow foundations with some small

modifications, but no definite scientifically proven method exists.

Hence, to accurately estimate the response of structure, the effect of soil structure interaction

is needed to be considered under the influence of both static and dynamic loading. Though,

SSI as an area of research is quite dynamic and good amount of literature is already available,

still a detailed analysis considering the nonlinear soil model and gap separation between pile

and soil has not been addressed.


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References

Fundamentals of Seismic Loading on Structures [Book] / auth. Sen Tapan K.. - West Sussex, U.K. : John

Wiley & Sons Ltd., 2009.

Improvement of Nonlinear Static Seismic Analysis Procedures FEMA 440 [Report] / auth. FEMA. -

Washington D.C. : Applied Technology Council (ATC-55 Project), 2005.

Minimum Design Loads for Buildings and Other Structures ASCE/SEI 7-10 [Book] / auth. ASCE. - Reston

Virginia : American Society of Civil Engineers, 2010.

NEHRP Recommended Seismic Provisions for New Buildings and Other Structures FEMA P-750

[Report] / auth. FEMA. - Washington D. C. : Building Seismic Safety Council, 2009.

Soil-Structure Interaction For Building Structures (NIST GCR 12-917-21) [Report] / auth. NEHRP

Consultants Joint Venture. - Gaithersburg, MD : National Institute of Standards and Technology, 2012.

SSI Analysis of Framed Structures Supported on Pile Foundations : A Review [Journal] / auth. Pulikanti

Shushma and Ramancharla Pradeep Kumar. - [s.l.] : Frontier in Geotechnical Engineering (FGE), 2013. -

2 : Vol. 2.


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Appendix – A Impact of Soil-Structure Interaction on Seismic Analysis of China Basin Landing,

185 Berry Street, San Francisco, CA

For the given project assignment, an investigation is being made for refining the modelling

assumptions for the non-linear dynamic analysis of a 3 story reinforced concrete moment

frame structure which is to be added with two more stories atop.

Based on the research done so far on the important soil-interaction parameters to be

included in the non-linear dynamic analysis, the expected impact the final designs can be

summarized as:

Time Period Elongation:

The consideration of the flexible base accounting for deformity both in the

foundation elements and soil leads to the considerable reduction in the stiffness of the

overall structure and hence the fundamental time period of the structure increases as

compared to the period of the same structure designed with rigid base assumption.

Where,

T = period of structure with rigid base assumption

= period of the structure with flexible base

k = lateral stiffness of the structure with rigid base

kx = effective lateral stiffness of the foundation-soil system

kyy =effective rotational stiffness of the foundation-soil system

h = the height of the center of mass for the first-mode shape

≈ 2/3rd of the overall structure height

Period lengthening increases markedly with structure-to-soil stiffness ratio, which is the most

important parameter controlling inertial SSI effects. As the geotechnical investigations have

revealed that the surrounding soil at the foundation of given structure is liquefiable, this

indicates there will definitely be high structure-to-soil stiffness ratio and hence there will be

considerable increase in the fundamental time period of the structure.


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Damping:

In addition to period lengthening, system behavior is also affected by damping associated with

soil-foundation interaction, referred to as foundation damping, f. This damping is composed

of two parts: (1) contributions from soil hysteresis (hysteretic damping); and (2) radiation of

energy away, in the form of stress waves, from the foundation (radiation damping).

Foundation damping is a direct contributor to the flexible-base system damping, 0:

Where, i is the structural damping in the superstructure assuming a fixed base, which is

generally taken as 5% for typical structural systems. Observations have shown that f ranges

from approximately 0% to 25%. The exponent, n, on the period lengthening term in the above

equation is taken as 3 for linearly viscous structural damping, and 2 otherwise (e.g., for

hysteretic damping) and as was the case for period lengthening, foundation damping f also

increases strongly with structure-to-soil-stiffness ratio

The effect of these two modifications on the demand (Base shear) are illustrated as below:

Thus, When the period is lengthened on the descending branch of the spectrum (i.e., T/Tp >

1), the seismic demand is reduced, regardless of whether the structure yields or not. Where Tp

is the predominant time period of the ground motion.

In the case of long-period input motions that potentially place the structure on the ascending

branch of the spectrum (i.e., T/Tp < 1), SSI-induced period lengthening may lead to an

increase in ductility demand. This can be viewed as progressive resonance, when the effective

fundamental period of the yielding structure, T, approaches the predominant period of the


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foundation input motion, Tp. This is the most extreme case scenario and is rare by disastrous

(as observed in Mexico City earthquake, 1985).

Basically with the period of a 5-story building being typically near 2 sec, it can be estimated

from this plot that there will be reduction in the demands (base shear, moments, torsion) to

be resisted by the structural elements. Hence, this would also have a considerable impact on

the design of the connections between the new and old construction and also the design of the

base isolators will be impacted.

soil structure interaction

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