地震波分析论文

211. Seismic Topics in Geotechnical Engineering

211.1. Seismic Stress Waves

There are two primary kinds of seismic waves: body waves and surfacewaves. The faster body waves move through the earth. Slower surface wavestravel along the surface of the earth.

There are two kinds of body waves: (1) compressional waves, also calledprimary waves (P-waves) and (2) shear waves, also called secondary waves (S-waves). P-waves apply longitudinal (push-pull) stresses. S-waves apply lateral(side-to-side) stresses. P-waves can travel through solids, liquids, or gases,but shear waves can pass only through solids. P-waves are the fastestseismic waves, and they arrive first at a point distant from the epicenter.Body waves travel faster deep within earth than near the surface. For

example, at depths of less than 16 miles, P-waves travel at about 4.2 miles persecond, and S-waves travel at 2.4 miles per second. At a depth of 620 miles,the waves travel more than 1.5 times that speed.

There are two kinds of surface waves: (1) Love waves have a horizontalmotion that is transverse to the direction of propagation and (2) Rayleighwaves have a retrograde, elliptical motion at the Earth's surface. These arethe slowest, but often the largest and most destructive, of the wave typescaused by an earthquake. They are usually felt as a rolling or rocking motionand in the case of major earthquakes, can be seen as they approach.

A detector located on the surface first detects the P-waves, then the S-waves,and finally the Rayleigh waves. An approximate depiction of vertical ground

disturbance due to these types of waves is shown in Fig. 211.1. Note that theground displacement caused by Rayleigh waves is significantly greater thanthat caused by P- and S-waves.Figure 211.1. Ground motion induced by seismic waves.The amplitude of body waves (P-waves and S-waves) is inversely proportionalto the distance (1/r) from the rupture point, whereas the amplitude ofRayleigh waves is proportional to r−0.5. Transmission velocities of P- and S-waves have been derived from analysis of an elastic half-space and are shownbelow. Transmission velocity of compression (P) waves is given by(211.1)where the parameter λ is given by(211.2)where μ = Poisson's ratio of soilρ = density of soilγ = unit weight of soilTransmission velocity of shear (S) waves is given by(211.3)

The shear modulus G is related to the modulus of elasticity E according to

(211.4)

Example 211.1

The arrivals of P-waves and S-waves at a seismograph from a remote seismicevent are separated by 25 min. Given the following properties for the soil,calculate the distance to the epicenter.

Solution

Velocity of P-wavesVelocity of S-wavesIf distance to epicenter is d, the difference in travel times can be written as

211.2. Liquefaction

Liquefaction occurs in medium- to fine-grained cohesionless soils due to lossof shear strength. Earthquakes usually create loads characterized by a highstrain rate. In fine-grained granular soils, this rapid loading does not permittimely dissipation of pore pressures, effectively creating an undrained

condition, thereby raising pore water pressure. The sudden increase in thepore water pressure causes a sudden decrease in the effective stress. Sincethe shear strength of a cohesionless soil is solely dependent on the effectivestress (little or no cohesion), this causes a sudden decrease in the shearstrength, causing the soil to liquefy (behave like a fluid, zero shear strength).Thus, the primary risk factors for liquefaction are1. Fine-grained soil with little to no cohesion2. Low relative density3. Rapid loading4. Absence of high magnitude loads in loading historySand deposits with void ratio greater than a critical void ratio tend todecrease in volume due to seismic load, thus showing susceptibility toliquefaction.211.2.1. Shear Stress in Soil Due to Ground AccelerationConsider a rigid block of soil extending from the ground surface to thestratum of interest, as shown in Fig. 211.2. If the peak ground acceleration isamax, then the resulting shear stress at depth h (assuming the soil behavesas a rigid block) is given by(211.5)Figure 211.2. Block of soil subject to shear forces from groundacceleration.Accounting for flexibility of the soil column, the maximum shear stress atdepth h is calculated as(211.6)where γh = total vertical stress at depth hCD = stress reduction factor (related to flexibility of soil column)The shear stress reduction factor CD is given by Seed and Idriss[1] andreproduced in Fig. 211.3. The shaded area shows approximate range ofvalues at various depths. The maximum shear stress τmax is then converted toan equivalent average shear stress according to Seed and Idriss.(211.7)(211.8)Click to loadinteractive graph

Figure 211.3. Shear stress reduction factor (Seed and Idriss).where τh,field = cyclic peak shear stress required to cause initialliquefaction in the field

τave = average cyclic shear stress caused by ground acceleration

The shear stress at liquefaction is dependent on the relative density of thesoil, and any measured values in the laboratory can be converted toappropriate values in the field according to

(211.9)

where τh,field = cyclic peak shear stress required to cause initialliquefaction in the field

τh,lab = cyclic peak shear stress which causes initial liquefaction in thelaboratory

RRD,field = relative density of the soil in the fieldD,lab = relative density of the soil in the laboratory

Example 211.2

Determine the factor of safety against liquefaction at a depth of 30 ft for a 15-

ft-deep fine-sand layer (γ = 122.4 pcf) overlaid by a 15-ft-deep clay layer (γ =115 pcf). The ground water table is a depth of 15 ft. Use the design

earthquake of magnitude 7.0, with a peak ground acceleration of 0.85 g. Letthe peak cyclic shear stress required to cause liquefaction be 25 psi.Solution At z = 30 ft, the total stress = γh = 15 × 115 + 15 × 122.4 = 3561psf. At depth = 30 ft, CD ≈ 0.92.

211.3. Bearing Capacity under Dynamic Loading

For saturated clays, cohesion is calculated from an unconsolidated, orundrained triaxial test. The cohesion obtained under dynamic conditions ishigher than that obtained under static conditions. Typically

(211.10)

On dense sands subject to dynamic loads, the ultimate bearing capacity canbe found by replacing the ϕ value as in Eq. (211.16).

211.4. Cyclic Stress Ratio

The cyclic stress ratio is defined as the ratio of the average cyclic shearstress produced in a soil (due to rapid loading) to the effective vertical stress.

(211.11)

Thus, if the cyclic stress ratio is specified, it can be used to estimate theaverage cyclic shear stress due to a particular earthquake event. This shearstress can then be used to calculate the factor of safety given by

(211.12)where τh,field = cyclic peak shear stress required to cause initial liquefactionin the field.211.5. Glossary of Earthquake-Related TermsDeep focus earthquake: One whose focal depth is greater than about 300 km(200 miles).Epicenter: The point on the ground directly above the focus or hypocenter.Epicentric distance: The horizontal distance (measured along the ground)from the epicenter to a particular site.Focus (hypocenter): The point below the ground surface where the rupture ofa fault first occurs.Focal depth: The vertical distance from the ground surface to the focus.Intermediate focus earthquake: One whose focal depth is between 70 and 300km (40–200 miles).Magnitude: According to Richter, the magnitude of an earthquake is basedon the amplitude of generated stress waves. It is given by log10 E = 11.8 +1.5M where E is the energy released (ergs) and M is the Richter magnitude.Shallow focus earthquake: One whose focal depth is less than 70 km (40miles).[1]Seed, H. B. and Idriss, I. M. (1971), \"Simplified Procedure for Evaluating SoilLiquefaction Potential,\" Journal of the Soil Mechanics and FoundationsDivision, American Society of Civil Engineers, Vol. 97, SM9, 1249–1273.CitationEXPORTIndranil Goswami: Civil Engineering All-In-One PE Exam Guide: Breadth and Depth,Second Edition. Seismic Topics in Geotechnical Engineering, Chapter (McGraw-HillProfessional, 2012), AccessEngineeringCopyright © McGraw-Hill Global Education Holdings, LLC. All rights reserved. Any use is subject to the Terms of Use. Privacy Notice and copyright information.For further information about this site, contact us.Designed and built using Scolaris by Semantico.This product incorporates part of the open source Protégé system. Protégé isavailable at http://protege.stanford.edu//