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Chapter 4 Analysis of Soils and Soil-Structure Interaction | Earthquakes | Mechanics
Chapter 4 Analysis of Soils and Soil-Structure Int...
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4 Analysis of soils and soil–structure interaction
‘Seismic loading is unique in that the medium (i.e. the soil) which imposes the loading on a structure also provides it with support.’
Soil properties for seismic design Liquefaction: prediction and countermeasures Site ampliﬁcation eﬀects Topographical eﬀects Slope stability Fault breaks Soil–structure interaction analysis
The designer of earthquake-resistant structures needs some understanding of how soils respond during an earthquake; not only is this important for the foundation design itself, but the nature of soil overlaying bedrock may have a crucial modifying inﬂuence on the overall seismic response of the site. This chapter gives a fairly brief overview of soil properties under seismic excitation, and also reviews site response and soil–structure interaction eﬀects. For a more detailed discussion of these issues, the reader is referred to Pappin (1991).
4.2 Soil properties for seismic design 4.2.1 Introduction
The response of soils to earthquake excitation is highly complex and depends on a large range of factors, many of which cannot be established with any certainty. The discussion that follows is intended to highlight the important features that apply to most standard cases; often, specialist geotechnical expertise will be needed to resolve design issues encountered in practice.
Soil properties for a dynamic analysis
In common with any structural system, dynamic response of soil systems depends on inertia, stiﬀness and damping. These three properties are now discussed in turn.
the behaviour in compression. This is because the bulk stiﬀness of saturated materials is very high. which dominates response to horizontal seismic motion. therefore. the soil therefore acts in an essentially rigid manner with little modiﬁcation due to dynamic eﬀects. for example. which may. the transmission of P or seismic compression waves.1 Idealised stress–strain behaviour of a soil sample in one-dimensional shear . is less important. the area contained within the hysteresis loop formed by the stress–strain curve increases with shear strain. There are exceptions. Therefore. Mexico City clay has a bulk density of only 1250 kg/m3 . the shear behaviour of soils will be of most concern. Further discussion here is conﬁned to shear behaviour. There are three important features to note when comparing the small with large shear strain response. As explained in Chapter 3.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 81 (a) Inertia This can easily be determined from the soil’s bulk density. being approximately equal to that of water divided by the soil porosity. decreases with shear strain. which for most clays and sands is in the range 1700–2100 kg/m3 . need consideration. characterised by the bulk stiﬀness. First.1 shows a typical cyclic response of a soil sample under variableamplitude shear excitation. It is important to note Fig. Second. Soils with signiﬁcant proportions of air may have much lower bulk stiﬀness. this area is directly related to the level of hysteretic damping. determined from the slope of the stress–strain curve. For compression eﬀects (for example. (b) Stiﬀness and material damping Generally. 4. Figure 4. soil damping increases with strain level. however. important for vertical motions). as more energy is dissipated hysteretically. the stiﬀness.
A ﬁnal feature to notice is that after a large shear strain excursion.82 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS that the dissipated energy is generally much more dependent on amplitude than rate of loading.01%. Fig. that is. but there is considerable scatter in the data.1. despite the intervening loop 2.1 is similar in shape to loop 1.2. G 0 .1). G 0 can be measured directly on site from measurements of shear wave velocity (see Pappin 1991) or from more conventional measurements. using empirical relationships. cu . where the damping resistance depends upon speed. For clays. For sands. loop 3 in Fig.5. typical correlations between G 0 (in MPa) and blow count used in Japanese practice (Imai and Tonouchi 1982) are G 0 ¼ 7N and G 0 ¼ 14:4N 0:68 . as shown in Table 4. which has important consequences for analytical modelling (see subsection 4.3 Stiﬀness of sands and clays Figure 4. 4. the stiﬀness is expressed as a ratio of secant shear stiﬀness at the shear strain of interest.2 shows typical relationships between shear strain amplitude and shear stiﬀness. It can be seen that the stiﬀness of clays becomes similar to that of sands as the plasticity index (PI) approaches zero. 4. 4. This is in contrast with viscous damping. not absolute shear strain. In Fig. Therefore. No such reduction to zero occurs in soils. G 0 can be determined as a ratio of the undrained shear strength. both stiﬀness and damping under cyclic loading are functions primarily of shear strain amplitude. to the small strain stiﬀness. 4. and so for example reduces to zero for very slow rates of cycling. Soil damping is thus essentially hysteretic in nature.2 Relationship between normalised shear stiﬀness G s =G 0 and cyclic shear strain . The values for clays are for overconsolidation ratios (OCRs) of 1–15. G s . Note the very large reduction in stiﬀness for shear strains exceeding 0. the hysteresis loop reverts to its original shape for a small cyclic excitation. these relate G 0 to the blow count N for 300 mm penetration in the Standard Penetration Test (SPT).2.
2. The cyclic loading imposed on soils during an earthquake may seriously aﬀect soil strength. 4.2. the values for clay approach those for sand as the PI reduces.1 G 0 =cu values (from Weiler 1988) Plasticity Index. PI: % 1 Overconsolidation ratio (OCR) 2 G 0 =cu 15–20 20–25 26–45 1100 700 450 900 600 380 600 500 300 3 4. Granular materials. (1986) advise that the lower bound of the damping values shown for sands on the ﬁgure may be generally appropriate.2.6 Stiﬀness and damping properties of silts Strength of granular soils Silts have properties equivalent to clays with a PI of about 15% (Khilnani et al. Note the marked increase in damping as shear strains rise above 0.5 4. 1982).2. such as sands and gravels. rely for their strength on Fig. Stokoe et al.3 shows typical values of damping ratio.001%.2. once again. caused by the hysteretic energy dissipation discussed in subsection 4.4 Material damping of sands and clays Figure 4.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 83 Table 4.3 Relationship between material damping ratio and cyclic shear strain . 4.
7 Strength of cohesive soils Clay particles are weakly bonded and are not subject to densiﬁcation under cyclic loading. Ten cycles of extreme loading is a very conservative estimate except in very large magnitude earthquakes.2.84 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS interparticulate friction.4) (i.3 Liquefaction 4. Strength reduction under cyclic loading is progressive with a number of cycles. Rate eﬀects may give rise to strength increases of up to 25% in soft clays under seismic loading conditions.3. since this relies on interparticulate friction. the pressure will release and the strength will be restored. It is highly dependent on the overconsolidation ratio (OCR). the eﬀective stress drops to zero).e.3. At this point. until the porewater pressure overcomes the forces between soil particles (Fig. Clays with high OCR are much more sensitive to cyclic loading. is not aﬀected by cyclic loading. Although the angle of friction. they are unlikely to liquefy. uncemented granular soils lose their shear strength. is aﬀected both by the rate of loading and by the number of cycles of loading. the porewater will ﬁnd drainage paths. this drops to ten cycles at about 75% cu for a clay with OCR of 4 and to ten cycles at about 60% cu for OCR of 10.1 Assessing the liquefaction potential of soils Liquefaction is a phenomenon which occurs in loose. and in order for it to occur. . and their strengths revert to normally consolidated values with increasing numbers of load cycles. unlike that due to porewater pressure increase in sands.23). 0 . A rise in porewater pressure will occur if a loose granular material tries to densify under the action of earthquake shaking and the pressure has not had time to dissipate. 4. Under such loading. 4. although the increase is less for ﬁrm clays and very stiﬀ clays are insensitive to rate eﬀects. the eﬀective stress between particles will be reduced in saturated soils if porewater pressures rise during an earthquake. This may however take a few minutes to occur. 1. This is the phenomenon of liquefaction. The strength of granular soils is scarcely aﬀected by the rate of loading. and dramatic failures can arise in the meantime (for example Fig. 4. Only certain types of soil are susceptible to liquefaction. porewater pressure between the soil particles builds up as the soil tries to densify. A normally consolidated clay (OCR ¼ 1) can sustain ten cycles of 90% of the undrained static shear strength cu . The short-term undrained shear strength cu however. compared with static strength. Therefore. The reduction in eﬀective stress in turn reduces the shear strength. all the following features must be present (a) a soil which tends to densify under cyclic shearing (b) the presence of water between the soil particles (c) a soil which derives at least some of its shear strength from friction between the soil particles (d ) restrictions on the drainage of water from the soil. In time. which is discussed more fully in section 4. saturated. granular soils under cyclic loading. The strength loss is permanent.
Conversely. The main risk of liquefaction therefore occurs in sands. the overall risk of it actually occurring must be related to the seismic hazard at the site. the resistance to porewater drainage increases.2 Analytical methods of assessing liquefaction Having established that a soil poses a potential liquefaction risk.3 shows criteria developed by Seed and Idriss (1982) which are often used for a preliminary and usually conservative assessment of liquefaction. land reclaimed by pumped dredged material is highly susceptible. although liquefaction is very unlikely where the water table depth is deeper than 15 m (Youd 1998). (a) The eﬀective shear stress e occurring in the soil during a design earthquake must ﬁrst be calculated. As grain size decreases. because any potential build-up of porewater pressure is usually dissipated rapidly by the free drainage available. Table 4. . but oﬀsetting this is an increase in cementation between particles. water-saturated. Condition (b) necessitates that the soil is below the water table. common examples are naturally deposited soils that are geologically young (Holocene deposits younger than 10 000 years) or man-made hydraulic ﬁlls. Condition (d) means that large-grained soils such as gravels are unlikely to liquefy. Condition (c) means that granular soils are the most likely to liquefy. silts may still liquefy. although silts still have some potential for liquefaction. and so older deposits are less susceptible to liquefaction.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 85 Fig. unless suitable measures are undertaken. 1994) Condition (a) implies a loose soil. the greater the risk. Table 4. 4.3. moisture content and liquid limit. 4. clearly the more intense the motions. However. e corresponds to constant amplitude cyclic loading. Densiﬁcation and also cementation between particles (see condition (c)) tend to increase with age.4 Shearing of a loose. granular soil in the process of liquefying (modiﬁed version from EERI.2 provides a more detailed list of the susceptibility of soils. while coarse sands can liquefy if they are contained as lenses in larger areas of clay which inhibit dissipation of excess porewater pressures. based on a soil’s grading. The most common method of calculation involves the following steps.
005 mm) <15% .86 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS Table 4.2 Estimated susceptibility of sedimentary deposits to liquefaction (Youd 1998) Type of deposit <500 years Age of deposit Holocene Pleistocene Pre-Pleistocene Likelihood that cohesionless sediments. Clay fraction (per cent ﬁner than 0. Moisture content (MC) >0. would be susceptible to liquefaction (a) Continental deposits: River channel Floodplain Alluvial fan and plain Marine terraces and plains Delta and fan-delta Lacustrine and playa Colluvium Talus Dunes Loess Glacial till Volcanic tuﬀ Volcanic tephra Residual soils Sebka Very high High Moderate — High High High Low High High Low Low High Low High High Moderate Low Low Moderate Moderate Moderate Low Moderate High Low Low High Low Moderate High Moderate Low Moderate Moderate Moderate — — Low Low Low Low Low Low Low Very low Low High Very low Very low ? Very low Low Low Low Very low Low Low Low — — Very low Very low Very low Very low Very low Very low Very low Very low Very low Unknown Very low Very low ? Very low Very low Very low Very low Very low Very low Very low Very low — — (b) Coastal zone – delta and estuarine: Delta Very high Estuarine High (c) Coastal zone – beach: High wave energy Low wave energy Lagoonal Foreshore (d ) Artiﬁcial ﬁll: Uncompacted ﬁll Compacted ﬁll Moderate High High High Very high Low Table 4.3 Criteria for assessing liqueﬁability of ﬁne-grained soils (based on Seed and Idriss 1982) Criteria required for liquefaction of ﬁne-grained soils (all three criteria must be met for soil to be liqueﬁable) .9 LL . when saturated. Liquid limit (LL) <35% .
Equation (4. g is the acceleration due to gravity (¼ 9:81 m/s2 ).1) assumes that the peak shear stress at the level of interest is (ag vo =g). The equivalent shear stress e can then be taken as 65% of the peak value. and the way the test borehole is drilled and backﬁlled. after allowing for soil ampliﬁcation eﬀects (m/s2 ).5 Liquefaction potential for magnitude 7. for example using SHAKE (1991).5 earthquakes. as discussed in the subsection on site ampliﬁcation eﬀects (4.e. and vo is the vertical total stress at the level of interest (i. overburden stress less porewater pressure without allowance for liquefaction eﬀects). the type of soil and a soil property such as SPT (standard penetration test) value.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 87 Fig. to calculate the ‘cyclic shear stress ratio’. based on SPT values (Eurocode 8. It should be remembered that SPT is a relatively crude test. which is calculated as explained in (d ) to ( f ) below. e =0vo . Part 5. Figure 4. (c) The liquefaction potential is then assessed as a function of the cyclic shear stress ratio. since the peak occurs only once. In fact.5 shows the charts provided by Eurocode 8 Part 5 (CEN 2004). this is generally rather conservative. A preliminary estimate of e can be made from e ¼ 0:65ag vo =g ð4:1Þ where ag is the peak acceleration at ground level. the total gravity overburden pressure). . including the test equipment and its operators. and a more rigorous analysis would use a simple one-dimensional shear beam model of the soil to estimate the peak cyclic shear stress on the soil at any depth.4. (b) e is divided by the vertical eﬀective stress 0vo at the level of interest (i. which allows for the fact that the peak occurs only once during the earthquake. CEN 2004) and is generally taken as 65% of the peak value occurring during seismic loading.e. 4. These are based on the corrected value of SPT blowcount in the soil N60 . which depends on many things. as discussed above.1).
30 1.30 1. noise. Larger magnitude earthquakes tend to give rise to more cycles of loading.67 Idriss (1999) Liquefaction unlikely 1.14 1. including the diameter and means of drilling the test boreholes. rod vibration and so on). (h) Eurocode 8 Part 5 suggests that the critical cyclic stress ratio from Fig. at which the onset of liquefaction is expected.86 2.00 0. 4. heat.88 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS Table 4. (e) NSPT is further corrected for energy ratio.5 6. the 475-year return period event for most building structures). 4. In particular.5.g.48 1. and Table 4.0 6. 4. the SPT is a somewhat crude test.00 0. Therefore. which suggest a lower dependence on earthquake magnitude.5 7. EC8 advises that the correction factor should lie between the values 0.5. and measured SPT values depend on the details of the testing method. 4.0 EC8 Part 5 Liquefaction unlikely 2. irrespective of the peak shear values arising.69 1. .4 Correction factors on critical value of shear stress ratio from Eurocode 8 Part 5 (CEN 2004) and Idriss (1999) Correction factor for cyclic shear stress ratio Surface wave magnitude: Ms 5.0 7. These empirical correlations between SPT values and liquefaction potential suﬀer from the drawbacks of all empirical relationships. should be at least 25% greater than that estimated for the design earthquake (e. ASTM (1986) gives a method for quantifying ER.5. by multiplying by (ER=60) where ER is the percentage of the potential energy from the hammer drop which gets delivered to driving the SPT probe (the rest being lost in friction.5 relates to earthquakes of magnitude 7. The boundary value of cyclic shear stress ratio e =0vo at which liquefaction can be expected is calculated for other earthquake magnitudes by multiplying the Fig.5 is therefore given by the following equation N1 ð60Þ ¼ NSPT ð100=0vo Þ1=2 ðER=60Þ ð 4: 2Þ (g) Figure 4.20 1. where 0vo is the eﬀective vertical stress in kPa in the soil at the level of interest.4 allows for this. the reliability of empirical predictions of liquefaction depends on the testing methods employed being similar to those used to derive the data shown in Fig.69 1. Idriss (1999) proposes diﬀerent values for these corrections factors.5 and 2. and further discussion is provided by Abou-Matar and Goble (1997).88 (d ) The SPT blowcount per 300 mm NSPT is corrected to a standard value of eﬀective vertical stress of 100 kPa by multiplying NSPT by ð100=0vo Þ1=2 .0 5.5 values by the correction factors in Table 4. ( f ) N1 (60) in Fig.5 8.4.
which may cause structural distress. 4.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 89 More sophisticated methods of assessing liquefaction risk have also been developed.3 Consequences of liquefaction Having established that the soils around a structure may liquefy.1 and 1. Retaining walls are particularly at risk because they suﬀer not only from loss of bearing support but also from greatly increased lateral pressures. the consequences must be evaluated.6 Liquefaction-induced lateral spreading. 4. These models are still under development. when an area 2 km long by 300 m wide slid by up to 30 m (Fig. in which large surface blocks of soil move as a result of the liquefaction of underlying soil strata.23). and should always be supplemented by the more empirical measures described above. Lateral spreading usually takes place on shallow slopes less than 38. whereby constitutive models of soil including porewater pressure generators are used in dynamic ﬁnite-element analysis. The minimum consequence is that the densiﬁcation associated with liquefaction gives rise to small local settlements. showing destruction of a road and housing . and are accompanied by breaking up of the displaced surface soil. Fig. occurred during the Anchorage Alaska earthquake of 1964. Alaska 1964. if the retained soil liqueﬁes. 4.6).3. which destroyed 70 houses. A dramatic example. The movements are usually towards a free surface such as a river bank. A much more serious consequence occurs where the reduction in shear strength caused by the liquefaction leads to a bearing failure (see for example Figs 1. Lateral spreading can also occur.
which can give rise to displacements of large masses of soil over distances of tens of metres. 4. SHAKE (1991) is a wellknown example. more sophisticated allowance should be made. Thus. at sites where soft clay layers are present which are deeper than 10 m and have a plasticity index PI > 40. These eﬀects are not currently addressed in codes of practice. Design measures in the presence of liqueﬁable soils are discussed in section 7. Eurocode 8 requires a site-speciﬁc calculation of the modiﬁcation they cause in surface motions. . The ﬂows may be comprised either of completely liqueﬁed soil. These frequency-dependent ampliﬁcation factors can then be used to modify design spectra appropriate for rock sites. it is usually suﬃcient to make this modiﬁcation on the basis of simple one-dimensional shear beam models of the soil. Movements can reach tens of kilometres. It should be noted that ampliﬁcation tends to reduce with increased intensity of ground motions because of the increase in soil damping and reduction in soil stiﬀness with shear strain amplitude (Figs 4. and since the former changes less than the latter (particularly in saturated soils) when the earthquake waves pass from rock into the overlying soil. little ampliﬁcation occurs.6.1 Site ampliﬁcation eﬀects The tendency of soft soils overlaying bedrock to amplify earthquake motions has already been discussed in Chapter 2. or of blocks of intact material riding on liqueﬁed material (EERI 1994). and velocities can exceed 10 km/h. A range of bedrock motions appropriate to the site and to the depth of soil overlaying bedrock should be input to the base of the shear beam soil model and the ratio of surface to bedrock motion should be calculated at a range of frequencies. The discussion so far has been on ampliﬁcation of horizontal motions. particularly at the basin edges (Faccioli 2002). section 2.8. A number of standard computer programs exist to perform this calculation. IBC: 2003 (ICC 2003) allows for this but Eurocode 8 (CEN 2004) does not.and three-dimensional eﬀects are at work.2. In cases where very soft materials are present. In many cases. using the soil properties discussed in section 4.90 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS The most catastrophic failure is a ﬂow failure of soils on steep slopes (usually greater than 38).1–4. adequate allowance for these eﬀects can be made by simple ampliﬁcation factors provided in codes of practice. and even complex ﬁnite-element modelling does not appear to yield reliable results (Adams and Jaramillo 2002). they depend mainly on the bulk rather than the shear modulus of the soil.3). One-dimensional shear beam models may not be adequate to describe site eﬀects in alluvial basins where there is increasing evidence that more complex two.4 Site-speciﬁc seismic hazards The next subsections consider how the seismic hazard at a site may be aﬀected by the local geology and how knowledge of the soil properties discussed in the previous sections can allow these hazards to be estimated. The techniques are fully discussed by Pappin (1991).4. and this may be unconservative for soil sites where the peak ground acceleration is less than around 15%. 4. For horizontal motions. Vertical motions are much less aﬀected.
Eurocode 8 Part 5 provides for ampliﬁcations of up to 40% at the ridge of slopes greater than 158 forming part of a signiﬁcant two-dimensional feature. Even without liquefaction. . the width at risk should be taken as several hundred metres. Structural damage from fault breaks arises not only from the consequences of straddling the fault (Fig. the design issues are clear: building structures should be sited away from them.4.4.3 Slope stability Slope failures connected with soil liquefaction were discussed in subsection 4. i. tension or compression) also aﬀects whether the fault reaches the surface. 1. Faccioli (2002) provides further information. where the instantaneous safety factor drops below 0. For major active faults such as the San Andreas fault in California or the Northern Anatolian fault in Turkey which have a well-recorded history of movement. The underlying fault movement (i. both at the ridge-top positions. and at the ridge base. Even for large earthquakes. a surface expression of the fault does not necessarily occur if large depths of soil overlay bedrock. where damage had been greatest. he found that at certain frequencies the former motions were over ten times greater than the latter.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 91 4.5. Relationships between instantaneous safety factor and slope displacement were originally developed by Newmark (1965) and form the basis for many current methods both of slope design and also for checking the seismic stability of retaining structures.e.4 Fault breaks Large earthquakes are almost always associated with rupture along fault lines. Celebi (1987) measured ground motions during aftershocks of this event. 4. the horizontal (and vertically upward) accelerations caused by an earthquake can dramatically reduce the factor of safety against movement of the slope.e.3. this rupture initiates at a depth of many kilometres and will rarely extend to the surface if the earthquake magnitude is 6 or less. An example was seen at a housing estate in Vina del Mar after the 1985 Chilean earthquake. these reductions in factor of safety are instantaneous and only lead to large soil movements if the peak forces tending to displace the slope exceed the restraining strength of the soil by a factor of at least 2. The seismic hazard maps for the USA provided in IBC (ICC 2003) allow for increases in ground motion of up to a factor of 2 in the vicinity of faults. However.2) but also the high pulses of ground motion (‘seismic ﬂings’) that may arise in their vicinity (Bolt 1995). 1991). whether it consists of shear.2 Topographical eﬀects Damage to structures is often observed to be greater on the tops of hills or ridges than at their base. However. Generally.3. However. further investigation may be needed (Mallard et al. 4. allowing for the uncertainty in where the fault may appear at the surface in future earthquakes. the potential activity of other faults may be much harder to establish and not all potentially active faults have been mapped.4. For extended structures and systems such as pipelines or for very high-risk structures. and linear structures such as roads or pipelines should be designed to cope with possible fault movements.
(b) Structures with massive or deep-seated foundations.5 Soil–structure interaction Most of the previous discussion has been based on response of soils in the ‘free ﬁeld’ without man-made structures. tending to reduce its motion. The following subsections discuss brieﬂy how to account for the interaction between a structure and its supporting soil. An additional point is that even where none of these factors apply. the cyclic movement of the soils in contact with the structure’s foundations causes energy to be radiated away from the structure.92 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS 4. 4. (c) Tall and slender structures such as towers and chimneys. such as bridge piers. it is conservative to ignore these soil–structure interaction (SSI) eﬀects. Usually. structural deﬂections may well increase due to foundation ﬂexibility. This assumption may be seriously in error. provided the site eﬀects discussed in section 4.5. Generally. Eurocode 8 Part 5 lists the following instances where SSI should be allowed for. The conservatism is not always present. (e) The eﬀect of the interaction between piles and the surrounding soils during earthquakes needs to be considered when the piles pass through interfaces between very soft soils and much stiﬀer soils. and (b) reduction in radiation damping with thin soil strata .7 Radiation damping: (a) waves radiating away from an oscillating building.7). 4. P –delta eﬀects and Fig.4 have been accounted for. This is known as radiation damping (Fig. however. therefore. 4.1 Foundation ﬂexibility Structures founded on bedrock can be analysed assuming that their base is ﬁxed.2. where the translational and rotational restraint oﬀered to the structure by the soil is less than rigid. Moreover. (d ) Structures supported on very soft soils. the eﬀect of soil ﬂexibility is to increase the fundamental period of the structure which often takes it away from resonance with the earthquake motions. caissons and silos. however. (a) Structures where P – eﬀects (subsection 3.8) play a signiﬁcant role.
(1997). may be satisfactory in many cases. The analysis is not straightforward. The material damping associated with the soil spring is also strain-dependent (Fig. VA. ASCE.7(b)). These may be satisfactory where the soil depth is uniform over a depth much greater than the greatest foundation dimension.6 References Abou-Matar H. which may be signiﬁcant.2. A rigorous treatment of SSI eﬀects using soil springs requires the use of springs whose stiﬀness and damping properties are frequency-dependent. the soil spring stiﬀness can be found from simple formulae. (2002). a safe value for material damping of 5% is often taken. A number of analytical techniques to investigate SSI are possible. embedment of foundations and other complexities. A two-dimensional study on the weak-motion seismic response of the Aburra Valley. The simplest method is to represent the soil ﬂexibility by discrete springs connected to the foundation.2). This type of analysis. October. Reston. ASCE 4-98 provides values of equivalent viscous damping for uniform soils. 35. & Goble G. the damping levels due to material and radiation damping will apply only to the modes of vibration involving foundation movement.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 93 potential impact between structures may be adversely aﬀected even if structural forces reduce. and in this case special analysis is required. To this may be added the radiation damping. Colombia. 4. VA. as shown in Fig. . pp. 4. Finite-element modelling of soils is an alternative to the use of soil springs. However. Eurocode 8 Part 5 provides formulae for the eﬀective stiﬀness of soil–pile systems. In a response spectrum analysis. a series of iterative analyses is therefore required to ﬁnd a suitable shear stiﬀness consistent with the computed shear strain. however. which. & Jaramillo J. but is theoretically not correct. American Society of Civil Engineers Standard: Seismic analysis for safety-related nuclear structures. so the damping level used should depend solely on the superstructure. albeit modiﬁed in stiﬀness to allow for shear strain. Journal of Geotechnical and Geoenvironmental Engineering. assuming conventional linear springs. SPT dynamic analysis and measurements. ASCE 4-98 (ASCE 1998) provides standard formulae for circular and rectangular bases. Adams B. 17–41. Vol. pp. 441–462. and there are special problems in treating boundaries of the portion of soil modelled in the analysis. ASCE (1998). Medellin. 4. For shallow foundations on deep uniform soils. American Society of Civil Engineers. Issue 1. depends on the shear strain amplitude. for which suitably reduced spectral accelerations can be assumed. D. This type of analysis is discussed by Pappin (1991) and is not treated further here. Where linear elastic analysis is performed. M. Reston. Higher modes of vibration are unlikely to involve the foundation soils. and may be required to account for sloping or non-uniform soil strata. These require a knowledge of the shear stiﬀness of the soil. Bulletin of the New Zealand Society for Earthquake Engineering. Similarly. March. Such an analysis can be relatively straightforward if frequency domain techniques are used. ASCE 4-98. 4. the presence of harder layers reﬂecting back radiated energy may signiﬁcantly reduce radiation damping (Fig.
Earthquake Engineering Research Institute. ‘Complex’ site eﬀects in earthquake strong motion. (1982).2/64. M.buﬀulo-edu/publications/workshop/99-SP04. & Yeung K. Stroud M. ASCE Journal of Geotechnical Engineering. pp. An update on the Seed–Idriss simpliﬁed procedure for evaluating liquefaction potential. (1991). Sykora D. Keynote address. retaining structures and geotechnical aspects. (1986). & Tokimatsu K. Part 5: Foundations. 89–109. USA. Report No. Davis. 12th European Conference on Earthquake Engineering. International Code Council. Muirwood R. Earthquake basics: liquefaction – what it is and what to do about it. D4633-86. & Wood R. Idriss I. Celebi M. TRB [Transportation Research Board] Workshop on New Approaches to Liquefaction Analysis. Birmingham. Khilnani K. 117. B. Kim J. (eds) Cyclic Loading of Soils. University of California at Berkeley. J. Seismic stability of the Revelstoke earthﬁll dam. 6–8 July. Elsevier. In: Civil Engineering in the Nuclear Industry. 29–49. 24–27. American Society for Testing and Materials. pp. B. & Idriss I. pp. VA.. CA. Pappin J. In: Proceedings. Idriss I... Proceedings of the 2nd European Symposium on Penetration Testing. International Building Code. W. pp. F. CA. (1982). Bolt B. From earthquake acceleration to seismic displacement. Correlations of N value with S-wave velocity and shear modulus. W. The Fifth MalletMilne Lecture. Seed H. M. Imai T. 77. Vol. E. Byrne P. Institution of Civil Engineers. Issue 1. including topography. A. Available as Special Report Number MCEER-99-SP04 on: http://mceer.94 EARTHQUAKE DESIGN PRACTICE FOR BUILDINGS ASTM (1986). (1965). Wong R. 19. UK. K.. (1984). P. London. . CEN (2004). Ladd R. Brussels. SHAKE (1991). London. 631–652. Moduli and Damping Factors for Dynamic Analysis of Cohesionless Soils. Higginbottom I. Newmark N. M. (2002). Blackie. European Committee for Standardisation. EN1998-5: 2004. Wiley. Stokoe K. (1982). Issue 4. UCB/EERC-84/14. Field and laboratory investigations of three sands subjected to the 1979 Imperial Valley earthquake. Faccioli E. The standard penetration test: its application and interpretation. pp. Ground Motions and Soil Liquefaction During Earthquakes. S. Vol. Canadian Geotechnical Journal. Lisbon. M. & Dobry R. T. Oakland. Falls Church. Bulletin of the Seismological Society of America. 1147–1167. Earthquake Engineering Research Institute. 306–366. pp. American Society of Civil Engineers. (1988). Eﬀect of soil plasticity on cyclic response. EERI (1994)... 63–75. Mallard D. Center for Geotechnical Modeling. Philadelphia. 5. M.. Oakland. Vol. In: O’Reilly M. Proceedings of the Conference on Penetration Testing in the UK. Recent developments in the methodology of seismic hazard assessment. (1987). Topographical and geological ampliﬁcations determined from strongmotion and aftershock records of the 3rd March 1985 Chile earthquake..2/57–5. H. (1995). Proceedings of the 8th European Conference on Earthquake Engineering. May. Design of foundation and soil structures for seismic loading. Selected papers. & Tonouchi K. Vol. ICC (2003). Chichester. 1976. CA. 2. New York. Standard test method for stress wave energy measurement for dynamic penetrometer testing systems. University of California. A computer program for conducting equivalent linear seismic response analysis of horizontally layered soil deposits. S. Seed H. Design of structures for earthquake resistance. Institution of Civil Engineers. 8–12 September. CA. Vucetic M. pp. 75–94. pp. (1991). O. pp. & Brown S. IBC: 2003. M. Amsterdam. & Dobry R. College of Engineering. Eﬀects of earthquakes on dams and embankments. Oxford. (1999).. Skipp B. (1991).
20. ASCE Geotechnical Special Publication No. Technical Report MCEER-98-0005. Screening guide for rapid assessment of liquefaction hazard at highway bridge sites. NY.ANALYSIS OF SOILS AND SOIL–STRUCTURE INTERACTION 95 Weiler W. Buﬀalo. . Earthquake Engineering and Soil Dynamics II – Recent Advances in Ground Motion Evaluation. (1998). L. (1988). National Center for Earthquake Engineering Research. A. 331–345. Youd T. Small-strain shear modulus of clay. pp.
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