Settlements and Damage Caused by Construction Induced Vibrat

8/8/2019 Settlements and Damage Caused by Construction Induced Vibrat

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Massarsch, K. R., 2000. Settlements and damage caused by construction-induced vibrations. Proceedings, Intern. Workshop

Wave 2000, Bochum, Germany 13 15 December 2000, pp. 299 315.1

Settlements and damage caused by construction-induced vibrations

K. Rainer Massarsch

Geo Engineering AB, Bromma, Sweden

1 INTRODUCTION

Most types of construction activities, such as soil and rock excavation, driving of piles and sheetpiles or compaction work, generate vibrations in surrounding soil layers. Construction work isoften carried out in densely populated areas and close to sensitive structures and installations.

This aspect is enhanced by the increasing awareness of the public to environmental issues,vibration-sensitive electronic equipment and machinery. Further, in many countries newenvironmental regulations have been introduced and are stringently enforced. As a consequence,authorities require frequently that a risk analysis be carried out prior to the start of constructionwork. A risk analysis, when properly implemented, can be a complex task, where the impact ofmany factors and the consequences on humans, buildings, and installations need to beconsidered, Figure 1. Therefore, a risk analysis requires that the engineer has extensive practical

experience and a good theoretical knowledge in a number of technical disciplines, such asvibration analysis, geotechnical and construction engineering etc. The risk analysis can haveimportant economic and technical consequences for a project. If unnecessarily conservativeassumptions are made, costs will increase. It may also, limit the choice of construction methodsand delay the project. On the other hand, if important factors are neglected in the risk analysis,

structures may be damaged or authorities stop or interrupt construction work.Most risk analyses deal with the environmental effects of vibrations and noise on human

comfort, assessed primarily according to subjective criteria based on human perception. Codesand regulations provide guidance for the measurement and interpretation of ground vibrationswith respect to environmental effects. Although such environmental consequences can beimportant, they are small compared with damage to structures and installations in the ground. Itis therefore surprising that in most codes, limiting vibration values with respect to damage tostructures are empirical or expressed as rules of thumb, Studer and Ssstrunk (1981), Headand Jardine (1992).

While such rules of thumb may be relevant for the geotechnical and structural conditions

in the particular area where they were developed, their general applicability is limited.

Therefore, such guidelines must be used with great caution. Clearly, representatives of

ABSTRACT:Construction activities can affect structures in different ways. Damage can occuras a result of distortion of the ground support and associated differential settlements. Groundvibrations can also cause settlements in non-cohesive soils as a result of cyclic loading.Dynamic and cyclic laboratory tests indicated that soil stiffness and strength decrease when acritical strain level is exceeded. The magnitude of settlement depends primarily on shear strain

and number of significant vibration cycles. The relationship between strain (vertical and shear)

and ground vibration velocity has been established, based on extensive laboratory studiesperformed for earthquake analysis. The results show that it is possible to estimate critical shearstrain levels at which loss of soil stiffness and strength can occur. A method for quantitative

determination of settlements due to surface vibrations is presented.


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authorities as well as designer and constructors need a better understanding of the mechanism ofdamage caused by ground vibrations.

Figure 1. Factors included in a risk analysis, Holmberg et al. (1984).

2 DAMAGE CAUSED BY CONSTRUCTION ACTIVITIES

Construction work can cause different types of damage to structures and installations in theground, some of which may not be related to, but often are attributed to ground vibrations.Figure 2 identifies four different categories. Category I comprises soil movements, which aredue to static soil displacements, such as heave or lateral movements. In this case, structuraldamage is primarily the result of soil displacement which result in differential settlement; themechanism is well-known and documented in the geotechnical literature. Soil heave occursusually in cohesive soils during installation of displacement piles (either by static or dynamicinstallation methods), e. g. Massarsch and Broms (1989). Lateral soil movements are anadditional cause of structural damage, often due to excavations or slope instability (creepmovements). The extent of the problem may be aggravated by ground vibrations but damage isprimarily caused by static soil movements.

Problems belonging to Category II are less well known but have been discussed in the

geotechnical literature, for instance by Holmberg et al. (1984), Massarsch and Broms (1991),and Massarsch (1993). Horizontally propagating vibrations cause a temporary distortion of the

surface layer to a depth corresponding to approximately one wave length. The magnitude of thedistortion depends on the wave length of the propagating wave (in most cases the surface wave)

and the vibration amplitude (displacement amplitude).


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Figure 2. Different types of building damage observed in connection with constructionactivities.

The propagating waves expose buildings or installations in the ground to repeated distortion

cycles (sagging as well as hogging). This effect is fundamentally a cyclic loading problemand not a dynamic effect. Distortion problems can also occur at very slow distortion rates, forexample in connection with tunnelling work or as a result of seasonal ground water variations(swelling and shrinking of foundation soil). However, in connection with construction activities(for instance soil compaction work or pile driving), the number of distortion cycles can be high.The distortion problem can be analysed using a static approach.

Burland and Wroth ( 1974) have shown that static damage can occur in load-bearing walls

as a result of hogging at a relative deflection d/B > 1.5

10-4

, where d is the vertical deflection(displacement amplitude) and B is the building length. In the case of ground vibration

propagation, distortion is critical when the wave length L becomes shorter than the buildinglength B. This is the case when the surface wave propagation velocity is low, which is typicalfor soft clays and silts below the ground water level. Based on an extensive literature survey,Massarsch (1993) proposed a critical relative deflection d/B > 1.5 10

-5. Assuming sinusoidal

wave motion, a simple relationship can be used to estimate a critical vibration velocity vcr.

vcr= 4.7 10-5

C (1)

where C is the wave propagation velocity (e. g. the surface wave velocity). This simplerelationship is valid if the wave length is smaller than twice the building length B. Massarsch

and Broms (1991) conclude that a large number of cases of vibration damage to structures canbe explained by ground distortion rather than dynamic effects.

I. Differential settlements or heavedue to static soil movements

II. Damage in structure

due to ground distortion

III. Settlement and/or strength loss

due to cyclic effects

IV. Structural damage

due to dynamic effects


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Category III covers permanent settlement (total and differential) and strength loss due tocyclic loading. It resembles at first glance Category II but the problem is fundamentallydifferent. Permanent ground distortion due to settlement occurs mainly in granular soils (cf.Category II, ground distortion creates temporary differential settlements) and is the consequenceof strain-softening soil behaviour. Again, settlement problems are primarily related to cyclicloading effects (degradation of soil strength and stiffness).

Category IV considers the case, where damage is generally caused by dynamic effects dueto ground vibrations. This aspect is discussed extensively in the literature and will not beaddressed in this paper.

During the past three decades, as a result of extensive research in the areas of earthquake and

off-shore engineering, major progress has been made in understanding the static, cyclic anddynamic stress-strain behaviour of soils. While these concepts are now generally accepted in

geotechnical earthquake engineering, they have not yet been applied to other types of vibration problems. Therefore, as a first step in this paper, an introduction to the behaviour of soilssubjected to static, cyclic loading and dynamic loading will be presented. This concept can beapplied to the behaviour of soils subjected to ground vibrations caused by construction

activities. Solutions will be presented for assessing vibration problems quantitatively.

3 STRESS-STRAIN BEHAVIOUR OF SOILS

The stress-strain behaviour of soils can be determined in the laboratory on undisturbed(cohesive soils) and reconstituted (non-cohesive soils) samples. The resonant column test wasinitially developed for studying the response of soils to earthquake loading at small strain levels,

starting at about 10-6

% to about 10-1

%. Such tests are typically performed within a frequencyrange of 10 30 Hz. It should be noted that at a strain level of 10

-6% and a vibration frequency

of 25 Hz, the average strain rate is 0,001 mm/s, which is very low and corresponds to that ofmany static laboratory tests. Figure 3 shows results from a resonant column test on mediumdense sand, performed at a frequency of 30 Hz. The shear modulus is almost constant at a strainlevel lower than 0,001. Once a critical shear strain level has been exceeded, the shear modulusdecreases. At a strain level of 0,1 % the shear modulus has decreased from 75 MPa to 25 MPa .

This corresponds to a reduction by 67 %. Vucetic and Dobry (1990) have reported shearmodulus reduction curves as a function of strain level for a wide range of Plasticity Index (IP)

values and the results are in good agreement with those shown in Figure 3.From the shear modulus G, the shear wave velocity C can be calculated using the following

relationship

C = (G /)0,5

(2)

where is the total soil density. Using equation (2), the variation of shear modulus as a function

of strain level can be shown in Figure 3. It is apparent that also the shear wave velocitydecreases, in the present case from 205 m/s at 10

-4% to 120 m/s at 10

-1%., corresponding to a

decrease by 42 %. It is not generally recognised that also the shear wave velocity is affected bystrain level. The shear wave velocity at a given strain level can be normalised by its maximumvalue and expressed as a shear wave velocity reduction factor, RC. Massarsch (1985) reportedresults of resonant column tests on soil samples with different values of plasticity index, IP,

where the shear modulus is shown as a function of shear strain.Figure 4 presents the results of these tests in a linear diagram, but shown as normalised shear

wave velocities versus shear strain. In the opinion of the author, a linear diagram reflects betterthe engineering properties of soils, compared to the semi-logarithmic presentation, which isnormally used in earthquake engineering.


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20

30

40

50

60

70

80

0,0001 0,001 0,01 0,1 1

Shear Strain ( %)

ShearModulus,

MPa

100

120

140

160

180

200

220

SheaWavVelocity,m/s

Shear Modulus

Shear Wave Velocity

Figure 3. Result of resonant column test on medium dense sand, showing the variation ofshear modulus and shear wave velocity with shear strain (note shear wave velocityright scale).

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

Gulf (IP: 74 %) Vlen (IP: 67 %)

Sk-Edeby (IP: 45 %) Norrkping (IP:36 %)

Bckebol (IP: 28 %) Drammen (IP: 18 %)

Kentucky (IP:12 %)

Velocity

ReductionFactor,RC

Shear Strain, %

Figure 4. Variation of normalised shear wave velocity with shear strain, determined fromresonant column tests, data from Massarsch (1985).


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The most important conclusion from Figure 4 is that the plasticity index, IP has importantinfluence on the reduction of shear wave velocity. The shear wave velocity decreases morerapidly in soils with low plasticity index. Therefore, sands experience a more pronounceddecrease of shear wave velocity even at small strain level than clays with high plasticity index.The author has reviewed results from resonant column tests in different soil types and at varyingstrain levels, as reported by Drringer (1998). Based on a regression analysis of the data, themodulus reduction factor is shown in Figure 5 for different shear strain values. The reduction ofshear wave velocity is most pronounced in soils with low plasticity index and increases withshear strain level.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30 35 40 45 50

Plasticity Index IP, %

ReductionFactor,RC

0,10%

0,25%

0,50%

Shear Strain

Figure 5. Shear wave velocity reduction factor as function of plasticity index and shear strainlevel.

The shear wave velocity can be determined by field and laboratory methods. Hardin (1978) proposed the following, widely used semi-empirical relationship for estimating the shearmodulus at small strains, Gmax for normally consolidated soils

Gmax = 625(0 pa)0,5

/ (0.3+0.7 e2 )

where 0 is the effective confining pressure (1+2+3)/3, pa is a reference stress level (100kPa) and e is the void ratio. Combining equation (3) and (2), the shear wave velocity at smallstrain level, Cmax (elastic wave velocity) can be derived

Cmax = [625 (0 pa)0,5

/(0,3+0.7e2)]

0,5(4)

Figure 6 shows the variation of the shear wave velocity as a function of vertical effective stress

for normally consolidated, dry non-cohesive soils with different void ratio. The calculationassumes a K0-value of 0.57, which corresponds to a sand with a friction angle of 35 degrees.


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50

75

100

125

150

175

200

225

250

275

300

0 25 50 75 100 125 150 175 200 225 250

Vertical Effective Stress, kN/m2

ShearWaveVelocity,m/s

0,3 0,4

0,5 0,6

0,7 0,8

0,9 1

Void Ratio, e

Figure 6. Variation of shear wave velocity with vertical effective stress in dry sand, cf.equation (4).

It is thus possible to estimate, for most practical problems with sufficient accuracy, themaximum shear wave velocity and the effect of wave velocity reduction as a function of shear

strain level. The above data suggest that the shear strain level is an important parameter, which

can not be neglected once it exceeds about 0.001 %. The shear strain level can be determinedfrom the following relationship if the vibration amplitude (particle velocity) v and the shearwave velocity CS are known

= v / CS (5)

For example, if a shear wave velocity (medium dense sand) of 210 m/s, and a particle velocity

of 20 mm/s, are assumed, the shear strain level is about 0.01 % , cf. Figure 3.

4 CYCLIC LOADING EFFECTS ON FRICTION SOILS

One of the most important soil properties governing the behaviour of sand is density. Whensubjected to cyclic loading, loose sands tend to densify until they have reached a criticaldensity or critical void ratio. On the other hand, dense sands dilate when subjected to repeatedcycles of loading until they approach approximately the same critical void ratio. The effect ofcyclic loading has been investigated extensively in the area of earthquake engineering, andespecially with respect to the pore water pressure build-up in loose saturated sands (liquefactionpotential). Design methods for assessing liquefaction by laboratory and field methods have been

published and are now state-of-practice. However, during the past three decades, only fewinvestigations have studied volume change in dry soils during cyclic loading. About thirty years

ago, during the same year three studies were published by eminent researchers, Brumund andLeonards (1972), Seed and Silver (1972) and Youd (1972). These papers present importantinformation regarding the compaction effect during cyclic loading and also describe the

fundamental mechanism which causes soil densification. It is also important to point out that thefindings were obtained independently of each other but are in excellent agreement.


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Many investigators and practitioners have in the past attempted - and still attempt - tocorrelate compaction behaviour of sands with stress fluctuations and with the values ofacceleration and frequency of vibration, associated with the compaction process. This approachhas not and cannot be substantiated by carefully performed laboratory tests but is still widelyused and referred to. The most important conclusions in the above three papers are summarisedbelow.

1. Fundamental concepts and published data show that shear strain is the primary factorcausing compaction of granular material.

2. Compaction (volume change) increases with shear strain amplitude.

3. The parameter that governs the ultimate residual compression is the steady-statetransmitted energy. This is valid for a wide range of frequencies. The residual

settlement cannot be correlated to acceleration.

4. Compaction is not significantly affected by vertical stress (for strain levels exceeding0.05 %).

5. In the 10 cycles/min to 115 cycles/min (0.17 1.9 Hz) range, frequency of straining hasno significant effect on compaction behaviour.

6. No significant behavioural differences were detected between samples tested dry andsimilar samples tested in a saturated, but completely drained, conditions.

7. Even at static loading conditions, evaluations of settlement is subject to considerableerror (+/- 25 50 %). For complex conditions associated with cyclic loading, it isunrealistic to expect that evaluations could be made with even this degree of accuracy.However, an approximate evaluation of possible settlement is adequate for manypurposes.

In order to draw general conclusions of the above test results, the published data have beenredrawn and are below presented in a uniform manner. Youd (1972) performed cyclic sheartests (NGI-type apparatus) on samples of dry and water-saturated Ottawa sand. Tests were performed at different effective stress levels and shear strain was measured at increasingnumber of load cycles, Figure 7. The initial void ratio was approximately eo = 0.545 and therelative density was Dr= 75 79%.

Normalised vertical strain is expressed as vertical strain normalised by strain at the first

loading cycle 1 to demonstrate that the relative settlement (compared to compression after thefirst loading cycle) is largest at low strain level. Settlement does increase almost linearly withthe number of vibration cycles (in a semi-logarithmic diagram). Youd also showed thatsettlement (and thus relative compression) is independent of vertical effective stress and of

frequency (strain rate) at the same strain level. The above findings are important for practical

applications. In order to estimate vertical compression, it is necessary to determine threeparameters: strain level, number of loading cycles, and initial density.Seed and Silver (1972) presented results from important tests, where they correlated shear

strain level to vertical compression. Cyclic load tests were performed on dry silica sand at twodifferent densities, using a shaking table. The vibration frequency was 4 Hz, the maximumnumber of load cycles was 300 and the maximum acceleration was 0.3 g (corresponding to amaximum vibration velocity of 0.7 m/s). The test data for loose sand are shown in Figure 8.

The ratio between vertical strain and shear strain can be calculated from elastic theory for

small strain levels (< 10-4

%) and depends on Poissons ratio, , according to the followingequation

= (1 + )


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Figure 7. Variation of normalised vertical compression as function of shear strain amplitudeand number of loading cycles, after Youd (1972).

Figure 8. Vertical settlement shear strain relationship for silica sand, Seed and Silver (1972).

0

2

4

6

8

10

12

14

16

18

20

1 10 100 1 000

Number of Cycles, N

NormalisedVerticalStrain,

/1

0,115 0,221 2,3

8,35

75% < Dr < 79%

Shear Strain (%)


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The data published by Youd (1972) and Seed and Silver (1972) have been re-analysed in order

to study the relationship between vertical strain and shear strain /as a function of shear strainamplitude and for different numbers of load cycles, Figure 9. In the case of sand with a

Poissons ratio of 0.33 vertical strain should be about 1.33 , which is in good agreement with

the data in Figure 9 at one load cycle and small shear strain level. A shear strain factor f1 = /is defined, which has been plotted against shear strain and as a function of number of loadingcycles. According to Figure 9, vertical compression increases with the number of load cyclesbut decreases with shear strain level. Vertical compression is higher in the case of loose sand,by a factor of about 50% when comparing 45 and 60% relative density.

Figure 9. Shear strain factor f1 as function of shear strain for different values of load cyclesand relative density, data Seed and Silver (1972) and Youd (1972).

The agreement between the two independently performed test series is good. Figure 9 can beused to estimate vertical settlement in sand if the shear strain amplitude and the number of loadcycles are known. One practical problem, however, is to translate field vibration measurements

with irregular cycles into equivalent uniform vibration cycles. A commonly used method inearthquake engineering is to estimate the number of equivalent vibration cycles by visual

inspection of the irregular time history.Seed (1976) proposed a liquefaction curve from which the equivalent number of vibration

cycles can be determined for any given irregular sequence of vibration cycles. Also other moresophisticated methods, such as the cumulative damage approach have been proposed but withsimilar results. Since the settlement mechanism is closely related to the liquefaction problem, itis proposed to use a similar approach when determining equivalent vibration cycles from anirregular record of vibration cycles. Figure 10 shows a relationship between normalisedvibration cycles v/vmax and the normalised number of equivalent vibration cycles, N /Neq.

0,1

1

10

100

0,01 0,1 1 10

SHEAR STRAIN, %

f1=

/

N = 1, DR: 77% N = 30, DR: 77% N = 1000, DR: 77%

N = 2, DR: 45% N = 10, DR: 45% N = 300, DR: 45%

N = 2, DR: 45%, Vert. Str. 17 kPa N = 10, DR: 45%, Vert. Str. 17 kPa N = 300, DR: 45%, Vert. Str. 17,Pa

N = 2, DR: 60% N = 10, DR: 60% N = 300, DR: 60%

N = 2, DR: 60%, Vert. Str. 17 kPa N = 10, DR: 60%, Vert. Str. 17 kPa N = 300, DR: 60%, Vert. Str. 17 kPa

N =2

Dr: 60%

N =10

Dr: 60%

N =300

Dr: 60%

N =2

Dr: 45%

N =10

Dr: 45%

N =300Dr: 45%

100

30

1Elastic

Youd (1972)

Load

cyclesSeed & Silver(1972)


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0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 10 100

N/ Neq

V/Vmax

Figure 10. Determination of equivalent vibration cycles from vibration record with differentnumbers and amplitudes of vibration cycles

From Figure 10 the equivalent number of vibration cycles of an irregular vibration record can bedetermined. For example, one cycle of maximum vibration amplitude, vmax is then equivalent to4,3 vibration cycles at amplitude 0.5

vmax or 10 cycles at 0.4 vmax. Experience from liquefaction

studies has shown that the shape of the correlation curve is not crucial for the outcome of ananalysis, provided that the approach is used consistently.

5 VARIATION OF SHEAR STRAIN WITH DEPTH

An important question in determining settlements caused by the passage of waves is theestimation of shear strain variation with depth. If the vibration source is at a distance greaterthan about 1 2 wave length, most energy will be carried by surface (Rayleigh) waves, which

propagate as a cylindrical wave front. Wave propagation can then be approximated by a planeRayleigh wave, and the variation of shear strain with depth in a linear-elastic isotropic half-

space can be calculated. Mohamed and Dobry (1987) developed charts for assessing thevariation of shear strain in terms of peak particle velocity. An equivalent vibration velocity, v

eq

can be determined at different depths from vibration measurements on the ground surface.Either the horizontal peak particle velocity at the ground surface, vx or the vertical peak particlevelocity vz at the ground surface can be used.

veq = vz mz= vx mx (7)

Figure 11 shows the variation of the shear strain factor mz with dimensionless depth z/L for use

with vertical peak particle velocity, where L is the wave length and is Poissons ratio. A

similar diagram has been developed for the case of horizontal peak particle velocity. The

influence of Poissons ratio is relatively small for non-cohesive soils (0.25


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Figure 11. Shear strain factor mz for use with vertical peak particle velocity, after Mohamed andDobry (1987) with indication of simplified relationship.

For most practical purposes it will be sufficient to use in non-cohesive soils a simplified, linearrelationship according to equation (8) when estimating the value of mz, cf. Figure 11

mz= 0.9 0.6 z/L (8)

The wave length L can be calculated if the wave velocity and the vibration frequency f (or

period of vibration T = 1/f) are known

L = C / f (9)

The relationship given in equation (8) makes it possible to estimate the variation of shear strain

amplitude based on measurement of the vertical vibration amplitude at the ground surface. As afirst approximation, the shear strain factor for a homogeneous soil layer (vertical vibrationmeasurements) can be taken as mz = 0.5. This indicates that the equivalent vibration amplitudein a soil layer corresponds to about half the vertical vibration amplitude measured on the groundsurface.

6 CRITICAL SHEAR STRAINS DUE TO GROUND VIBRATIONS

Clough and Chameau (1980) suggested that the effect of ground vibrations on settlement duringvibratory sheet pile driving in sands can be assessed qualitatively by the shear strain which isgenerated due to wave propagation. Dobry et al. (1982) proposed that the susceptibility of

sands to liquefaction (liquefaction potential) due to earthquakes can be predicted by the strainor stiffness approach. It makes use of the shear wave velocity of the soil deposit to estimate

the maximum cyclic shear strains induced by seismic shaking and then compares these

maximum cyclic shear strains with the threshold strain of the soil, t. The threshold strain is

defined as the value of cyclic shear strain such that the cyclic shear strains less than t will not

cause any densification of dry granular soils, or any pore pressure build-up in water-saturated

granular soil. Mohamed and Dobry (1987) suggest that for most sands, the threshold strain is t

10-2

%.

mz = 0.9 - 0.6 z/L


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Equation (5) makes it possible to estimate the shear strain level if the vibration velocity andthe shear wave velocity at a given strain level are known. The effect of shear strain level onshear wave velocity can be taken into account, cf. Figure 5. The shear wave velocity in normallyconsolidated soils can either be measured in the field or estimated using equation (4) or fromFigure 6. Based on the shear strain factor shown in Figure 11 it is possible to estimate shearstrain variation with depth from vibration measurements on the ground surface. Figure 12 showsthe relationship between vibration velocity (particle velocity) and shear wave velocity for twodifferent levels of shear strain. Based on extensive laboratory tests for different soils it can beassumed that if the shear strain level of 0.001 is not exceeded, the risk of ground settlement orstrength loss is very low. However, if the shear strain level caused by ground vibrations exceeds

0.1 % there is significant risk of settlements or loss of shear strength in cohesive soils. Figure 12does not include the effect of number of load cycles.

Figure 12. Estimation of risk for settlements or strength reduction from vibration velocity asfunction of shear wave velocity for different levels of shear strain, cf. equation (7).

For example, if the shear wave velocity in a very loose sand close to the ground surface is about100 m/s, it can be concluded from Figure 12 that settlements are not likely to occur if theassociated, equivalent vibration velocity veq is lower than 0.5 mm/s. However, the threshold

value, where there is a risk of settlement in loose sand is 6 mm/s. When the shear strain levelexceeds 0.1 % (at a vibratin velocity of approximately 50 mm/s) a significant risk of groundsettlement and loss of shear strength exists. Settlement increases with increasing number ofvibration cycles. However, the risk of settlement decreases with increasing shear wave velocityand increasing plasticity index IP.

7 ESTIMATION OF SETTLEMENT IN LOOSE SAND DUE TO GROUND

VIBRATIONS

The information provided in the previous sections makes it possible to assess quantitatively themagnitude of settlement in free-draining (non-cohesive) soil due to propagation of surface

waves if the thickness of the compressible layer and the vertical strain are known

0,1

1,0

10,0

100,0

10 100 1000

Shear Wave Velocity, m/s

VibrationVelocity,mm/s

Shear Strain: 0,001 %

Litttle Risk for Settlements

or Shear Strength Reduction

Shear Strain: 0,1 %

Risk for Settlements

or Shear Strength ReductionCLAY

IP = 50

CLAY

IP = 50

SAND

IP = 0

SAND

IP = 0

Threshold Shear Strain:

t = 0,01 %


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s = H (10)

where s is the settlement of a layer with thickness H and is vertical stain. The shear strain

level at different depths can be estimated from ground vibration measurements at the ground

surface and taking into account the depth effect using the strain factor mz, cf. Figure 11. Groundvibrations in the far-field from the vibration source (at distance of least 1.5 times the wavelength) are caused primarily by surface waves. The surface wave velocity in sand is onlyslightly (approximately 7 %) lower than that of the shear wave. It can be determined from shearwave velocity either measured or estimated from equation (3), and then be corrected withrespect to strain level. The shear wave velocity reduction for sand and silty sand is shown inFigure 13. Indicated in the figure are the three shear strain levels suggested in Figure 12.

The effect of strain level on shear wave velocity must be determined by iteration, startingwith the small-strain shear wave velocity, then determining the wave reduction factor, Rc fromthe calculated strain level. Already within two or three iteration cycles, a stable value of thevelocity reduction factor is obtained. The irregular number of vibration cycles can be translatedinto an equivalent number of vibration cycles Neq from Figure 10. Finally, the effect of cyclic

loading (number of equivalent shear strain cycles) Neq on vertical strain can be assessedquantitatively by introducing a shear strain factor, f1, cf. Figure 9. The process is expressed inthe following simple relationship

s = f1 mz v H / (Rc Cs )

The calculation of settlements in sand is illustrated by the following example, involving a deeplayer of loose sand subjected to ground vibrations. It is assumed that the shear wave velocity inthe sand is 150 m/s, the vertical peak vibration amplitude at the ground surface (determined byfield measurements) is 15 mm/s and the dominant frequency of vibrations is 20 Hz. Thefollowing vibration cycles are anticipated: two cycles at 10, four cycles at 7, four cycles at 6, sixcycles at 5 mm/s, respectively. The method of calculating the number of equivalent vibration

cycles, based on Figure 10 is shown in Table 1. The number of equivalent vibration cycles,which corresponds to the peak vibration velocity is thus approximately 3,5.

Table 1. Determination of number of equivalent vibration cycles

V (mm/s) v/vmax N N/Neq Neq

15 1.00 1 1 1

10 0.67 2 2 1

7 0.47 4 5 0.8

6 0.40 4 10 0.4

5 0.33 6 27 0.22

N tot: 3.42

The shear wave velocity reduction factor at an initial strain level of (0.015 %) can be estimated

from Figure 13, Rc 0.9. Assuming that the surface velocity is 7 % slower than the shear wave

velocity, a surface wave velocity is 130 m/s is obtained which results in a shear strain level 1.2 10

-2. The wave length L = 6.5 m and therefore, settlements are anticipated to occur down to

a depth corresponding to 9.5 m (1.5 L).The soil layer can now be divided into, say, three layers (2.0 m + 3.0 m + 4.5 m) and

settlement can be estimated for each layer according to equation (11). The calculations areshown in Table 2.


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Figure 13. Variation of shear wave velocity reduction factor for sands and silts, after Vuceticand Dobry (1990).

Table 2. Calculation of settlements in sand deposit divided into three layers

Depth (m) f1 z/L mz v (mm/s) (%) CR*(m/s) s (mm)

0 1.4 0.00 0.90 13.5 0.0104 130 -

1 1.5 0.15 0.81 12.1 0.0093 130 0.28

3.5 1.30 0.54 0.58 8.6 0.0062 140 0.24

7.25 1.30 1.12 0.23 3.5 0.0023 150 0.13

Sum s: 0.65 0.7 mm*)

CR: surface wave velocity

The total settlement in the loose sand deposit caused by short-duration surface wave vibrationswith a vibration amplitude at the ground surface of 15 mm/s will be about 0.7 mm. It should be

noted however, that if the number of vibration cycles increases to, for example 300, then, thesettlement will increase by a factor of 20, resulting in settlements on the order of 6.5 mm. Also,close to the vibration source, other wave types, such as shear and compression waves may

dominate, which can cause larger settlements.

8 SUMMARY

Damage to structures in connection with construction activities can be classified according to

four different categories. Two important factors, which can cause damage to structures inconnection with ground vibrations, are temporary distortion of the ground surface duringpassage of a wave front and differential settlements in compressible soil layers.

The main objective of the paper is to discuss the factors associated with ground vibrations,which can cause settlements in granular soils. Contrary to the general opinion, the rate of

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Shear Strain, %

VelocityReductionFactor,RC

Sand

Sitly Sand

Test data MediumDense Sand


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loading (frequency) and ground acceleration play a negligible role. Instead, two more importantparameters are identified; namely, soil strain (especially shear strain) and cyclic effects (numberof vibration cycles). It can be shown that soil stiffness decreases when a relatively small shearstrain level is exceeded (10

-4%). Carefully performed laboratory tests provide a sound basis for

assessing the effect of shear strain on soil stiffness for different soil types (based on plasticityindex, IP). The shear wave velocity is not a material constant but increases with confiningpressure (depth) and can be estimated with sufficient accuracy by semi-empirical relationships.

Carefully performed cyclic laboratory tests on sand show the importance of the number ofload cycles on settlement. Data published almost 30 years ago have been re-analysed in order toobtain a relationship between shear strain and vertical strain. It can be concluded that vertical

strain increases with shear strain and the number of vibration cycles.In the case of surface waves, shear strain decreases approximately linearly with depth and its

variation can be estimated. Below a depth corresponding to about 1,5 times the wave length,strain levels are very small and thus negligible.

A simple chart is presented for estimating the vibration velocity at different strain levels,based on the shear wave velocity, corrected for strain-effects, cf. Figure 12.

An analytical approach is proposed, which makes it possible to estimate settlement ingranular soils when subjected to ground vibrations at a distance of at least 1,5 times the wavelength (surface waves). It is possible to estimate the vibration velocity (and thus shear strain) atdepth, if the vertical vibration velocity is measured at the ground surface. Similar to a method

used for liquefaction analysis it is possible to translate an irregular number of vibration cyclesinto equivalent number of vibration cycles.

The above elements of stress-strain behaviour of granular soils, when subjected to groundvibrations, have been combined into a method for estimating settlements caused by surfacewave vibrations. The application of the method has been demonstrated by an example.

Finally, it should be pointed out that the proposed method is based on limited laboratory dataand has not yet been verified against field experiments. Therefore, the results should be

interpreted considering the underlying assumptions.

9 ACKNOWLEDGEMENT

Prof. Bengt H. Fellenius, Urkkada Technology Ltd. has reviewed the paper and made many

valuable suggestions for improvement. His support and encouragement is acknowledged withgratitude.

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Clough, G. W. and Chameau, J. 1980. Measured effects of vibratory sheet pile driving. Journalof the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT10, Oct., pp. 1080 - 1099.Dobry, R. Ladd, R. S., Yokel, F. Y., Chung, R. M. and Powell, D. J. 1982. Prediction of pore pressure buildup and liquefaction of sands during earthquakes by the cyclic strain method.Building Science Series 138, U. S. Nat. Bureau of Standards, Washington, D. C, pp.Dring, H. 1997. Verformungseigenschaften von bindigen Bden bei kleinen Deformationen(Deformation properties of cohesive soils at small deformations). Royal Institute of Technology(KTH), Stockholm, Examensarbete 97/8, 54 p.Head, J. M. and Jardine, F. M. 1992. Ground-borne vibrations arising from piling. CIRA

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Massarsch, K. R. and Broms, B. B. 1989. Soil Displacement Caused by Pile Driving in Clay.International Conference on Piling and Deep Foundations, London, 15 - 18 May, 1989,Proceedings, pp 275 - 282.Massarsch, K. R., 1985. Stress-Strain Behaviour of Clays. 11th International Conference on SoilMechanics and Foundation Engineering, San Francisco, Proceedings, Volume 2, pp. 571 - 574.Massarsch, K. R. and Broms, B. B., 1991. Damage Criteria for Small Amplitude GroundVibrations", Second International Conference on Recent Advances in Geotechnical EarthquakeEngineering and Soil Dynamics, St. Louis, Missouri, March 11 - 15, 1991, Vol. 2, pp 1451 -1459.Massarsch, K. R., 1993. Man-made Vibrations and Solutions, State-of-the-Art Lecture, Third

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Mohamed, R. and Dobry, R. 1987. Settlements of cohesionless soils due to pile driving.Proceedings, 9th Southeast Asian Geotechnical Conference, Bangkok, Thailand, pp. 7-23 7-30.Seed, H. B. and Silver, M. L. 1972. Settlements of dry sand during earthquakes. Journal of the

Soil Mechanics and Foundation Division, Proceedings ASCE, Vol. 98, pp. 381 - 396.Seed, H. B. 1976. Evaluation of soil liquefaction effects on level ground during earthquakes.ASCE Annual Convention and Exposition, Liquefaction Problems in Geotechnical Engineering.Philadelphia. pp. 1 104.

Studer, J. and Ssstrunk, A. 1981. Swiss Standard for Vibrational Damage to Buildings, XInternational Conference on Soil Mechanics and Foundation Engineering, Stockholm, Vol. 3,pp. 307 312.Vucetic, M. and Dobry, R. 1990. Effect of soil plasticity on cyclic response. Journal of theGeotechnical Engineering Division, ASCE Vol. 117, No. 1. Jan, pp. 89 107.Youd, T. L. 1972. Compaction of sands by repeated shear straining. Journal of the SoilMechanics and Foundation Division, Proceedings ASCE, Vol. 98, pp. 709 725.

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