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The challenge of earthquake design of foundations

Report on the BGA-Society for Earthquake and Civil Engineering Dynamics Touring Lecture 2004, by Dr Robert May, Atkins, and Ziggy Lubkowski, Arup.

The BGA's 2004 Touring Lecture, co-hosted with the Society for Earthquake and Civil Engineering Dynamics, was presented by Professor Alain Pecker at the Universities of Southampton, Manchester and Newcastle in November.

Pecker described the challenge of earthquake design of foundations, including theoretical frameworks, practical implementation and codes, charted the historical development of the subject, the current state of the art and pointed the way ahead.

Pecker is the prÚsident directeur gÚnÚral of his consultancy GÚodynamique et Structure. He holds professorships at Ecole Nationale des Ponts et ChaussÚes and UniversitÓ di Pavia and he is director of research at Ecole Polytechnique de Paris. He provided advice to the drafting committee of Eurocode 8: Design of structures for earthquake resistance.

Seismic design of shallow foundations The understanding of shallow foundation performance under earthquake loading developed in the opposite direction to static foundation design.

Seismic foundation design started with development of methods for elastic response analysis. In contrast, the earliest problems to be solved for statically loaded foundations were those of ultimate capacity.

The Mexico earthquake of 1985 provided many examples of seismically induced foundation failure. This and foundation failures from more recent earthquakes have spurred on the development of seismic bearing capacity theory.

The passage of earthquake waves from bedrock through a layered soil profile to the surface is complex to analyse. The incident body waves, shear and p-waves are refracted and refl ected as they pass through the soil strata, possibly resulting in surface Rayleigh and Love waves in a free field situation.

For cases where a structure and its foundation are also involved, the situation becomes even more complex. Foundation construction and the subsequent changes in soil loading may have locally modified the soil properties and foundation elements will generate more reflections of seismic waves.

The excitation of the structure generates inertia forces that are imposed on the foundation. Also, the deformation of the soil relative to the foundation generates kinematic forces.

Seismic design of a foundation must consider both the inertia and the kinematic interactions. Various Tapproaches have been developed to address this problem.

Typical approaches include spring and dashpot models of varying complexity, the linear elastic substructure superposition method and direct interaction analyses by fi nite element or finite difference methods.

The simplest soil-structure interaction (SSI) models show the major change occurring in the fundamental frequency of the structure as the foundation stiffness reduces (Figure 1).

Associated with these changes in fundamental frequency are changes in system damping and foundation input displacement amplitude. A significant consequence is that the direct application of a free field seismic motion to a fi xed base structural model can be quite unrealistic for structures founded on soils.

Models consisting of springs, dashpots and masses can be used to evaluate the inertial aspects of seismic SSI, provided certain implicit assumptions are reasonably valid.

These assumptions include system linearity, neglect of kinematic interaction and availability of dynamic impedances.

Non-linear soil stiffness effects can be incorporated into such models using global stiffness modifi ation factors. Uniquely among seismic codes, Eurocode 8 provides suggested factors for the small strain stiffnesses for such analyses.

The neglect of kinematic interaction between the soil and the foundation may be conservative or unconservative with respect to the amplitude of structural motions.

Unfortunately kinematic interactions cannot readily be estimated without specific analysis. Dynamic impedances are complicated because with limited depths of soil they may be strongly frequency dependent. It is normally possible to correct for such effects by adding additional masses to the model with associated springs and dashpots.

Most seismic codes neglect the potential effects of soil-structure interaction. However, Eurocode 8 specifi es various cases where SSI is mandatory. These include cases of massive or deep foundations (eg piles), slender tall structures, structures that could suffer signifi cant P-d effects and structures founded on soft soils (ie V s less than 100m/s).

In other cases Eurocode 8 implicitly permits SSI to be neglected - although there may be benefits in performing such analyses for some of these cases. Figure 2 shows a potential effect of ignoring SSI.

The two buildings were affected by the 1985 Mexico earthquake. The foundation soils have a shear wave velocity of around 50-70m/s.

Both structures were 11 storeys high, but earthquake-induced rocking led to pounding between the structures and the collapse of several intermediate storeys of the one on the left. Had appropriate seismic SSI been undertaken at the design stage, the separation between the structures would undoubtedly have been increased.

The theoretical understanding of the seismic bearing capacity of shallow foundations has developed significantly in the last 15 years.

Annex F of Eurocode 8 Part 5 provides a formulation that accounts for normal and shear forces, moments and the (instantaneous) soil inertia force. This allows investigation of the effect of the soil inertia force on the bearing capacity - for high vertical loads and low static safety factors, an appreciable reduction in normalised vertical capacity occurs as soil inertia force increases.

This provides an explanation for the observed bearing capacity failures of raft foundations in Mexico City (Figure 3) and at Adapazari in the Kocaeli earthquake where many raft foundations were built with slim static factors of safety.

The seismic design of shallow foundations is likely to develop in the direction of displacement based approaches.

Formulations for such analyses are usually based on a Newmark approach which provides an approximate uncoupled analysis (ie soil inertia forces do not affect capacity).

However, recent numerical analysis techniques using macro elements are making fully coupled displacement analyses practical. This technique was used in the pier foundation design for the recently opened Rion-Antirion Bridge (see box).

Seismic design of piled foundations The understanding of the seismic behaviour of piles and pile groups is not as advanced as the understanding of shallow foundations. Design methods often involve significant simplifiations and important factors are diffi cult to include in available forms of analysis.

It has been recognised for some time that kinematic interaction between piles and the soil can generate major pile loadings, particularly in the vicinity of strata boundaries which involve signifi cant changes of soil stiffness.

Eurocode 8 requires kinematic effects on piles to be considered for soft soil sites, for moderate or high levels of seismicity and for important structures.

Standard practice considers such effects for two pile diameters either side of the strata boundary and within the uppermost 2.5 diameters of the pile. The seismic design of raked piles is subject to particular uncertainty.

In cohesive soils gapping may develop around the upper section of pile shafts. Under some circumstances gapping may extend to six pile diameters or more below the pile head leading to substantial changes in lateral stiffness as the earthquake proceeds.

Typically gapping may increase lateral defl ctions and pile head rotations by a factor of two. Analytical beam on Winkler non-linear spring models incorporating dashpot dampers are available for the analysis of the non-linear lateral (and vertical) behaviour of single piles.

Cyclic loading can significantly reduce the vertical capacity of fl ating piles, particularly where complete load reversals from compression to tension and back occur during the earthquake. Figure 4 shows an example of a piled structure affected by the 1985 Mexico earthquake. The post-earthquake tilt of the structure greatly exceeds serviceability limits due to loss of vertical capacity during the shaking.

One of the most complex issues facing the designer of piled foundations for earthquake resistance is the assessment of the dynamic pile group interaction. In the static condition the effect of any given pile on its neighbours decreases fairly rapidly with increasing distance. But when the pile group is subjected to earthquake loading each pile shaft generates stress waves which affect all of the other piles in the group.

Solutions for dynamic pile group interaction factors have been produced by Gazetas and various coworkers. However, the commonly used solutions involve signifi cant simplifi tions including imposition of the free fi eld soil motion at the pile location, assuming the pile vibrates in phase along its length (creating a cylindrical wave front) and the imposition of an infi nitely stiff pile cap.

The designer must fi nd alternative means to account for effects such as the development of gapping, or pore pressure increases on the pile group behaviour, as the earthquake event proceeds.

Conclusions Seismic design of foundations is complex and solutions are better developed for shallow foundations than for their piled counterparts.

Codes such as Eurocode 8 are beginning to recognise that soil structure interaction cannot be ignored for certain classes of structure-foundation systems and some of these detailing requirements are now appearing in these codes.

Also, kinematic interaction between piles and soil strata may be critical in certain cases. But, observation of the behaviour of foundations loaded by actual large earthquakes shows that there is still have some way to go before the subject is fully understood.

Pecker emphasised that appropriate seismic detailing of structures is essential to achieve adequate performance.

Detailing requirements for reinforced concrete beams and columns have become better understood in recent years but detailing of foundations is just as important in many cases. Some of these detailing requirements, which are now beginning to appear in seismic codes, include:

Faults. Foundations must be located clear of active faults and the potential for damaging movement on secondary faults must be considered.

Homogeneous foundations. Foundation elements should be of a similar size and type beneath a structure to minimise differential movements between elements.

Liquefaction and seismic settlement. Where foundation soils may be subject to signifi cant pore pressure increases or liquefaction, appropriate mitigation measures must be implemented. These may typically use vibro-compaction with stone columns.

Tie beams. Shallow pad foundations should be connected with appropriately detailed tie beams.

This detail restrains foundation spreading which, if it occurs, will frequently lead to structural collapse.

Pile reinforcement. Piles designed for seismic loading should be reinforced over their full depth. Eurocode 8 permits plastic design at the pile head. The designer should allow for the effects of gapping which may extend to a depth of six pile diameters or more in clay soils.

Raked piles. Inclined piles should only be used with considerable caution. Under earthquake loading they attract major lateral loads from the supported structures. They may also be prone to damage from seismically induced settlements. In most seismic foundation design situations raked piles are best avoided.

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