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Chapter 3

GROUND MOTION

3.1 GENERAL

3.1.1 Scope. All structures shall be designed for the earthquake ground motions prescribed in this chapter. If the alternate design procedure of Alternative Simplified Chapter 4 is used, the values of Fa, SMS, and SDS shall be as determined in that Alternate Chapter, and values for Fv, SM1, and SD1 need not be determined.

3.1.2 References. The following documents shall be used as specified in this chapter.

ASTM D 1586 Standard Test Method for Penetration Test and Split-barrel Sampling of Soils (D 1586-99), American Society for Testing and Materials, 2003.

ASTM D 2166 Standard Test Method for Unconfined Compressive Strength of Cohesive Soil (D 2166-00), American Society for Testing and Materials, 2003.

ASTM D 2216 Standard Test Method for Laboratory Determination of Water (Moisture) Content of Soil and Rock by Mass (D 2216-98), American Society for Testing and Materials, 2003.

ASTM D 2850 Standard Test Method for Unconsolidated-Undrained Triaxial Compression Test on Cohesive Soils in (D 2850-03), American Society for Testing and Materials, 2003.

ASTM D 4318 Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils (D 4318-00), American Society for Testing and Materials, 2003.

3.1.3 Definitions

Active fault: A fault for which there is an average historic slip rate of 1 mm per year or more and geographic evidence of seismic activity within Holocene times (past 11,000 years).

Characteristic earthquake: An earthquake assessed for an active fault having a magnitude equal to the best-estimate of the maximum magnitude capable of occurring on the fault, but not less than the largest magnitude that has occurred historically on the fault.

Design earthquake ground motion: See Sec. 1.1.4.

Maximum considered earthquake ground motion: The most severe earthquake effects considered by these Provisions as defined in this chapter.

Seismic Design Category: See Sec. 1.1.4.

Site Class: A classification assigned to a site based on the types of soils present and their properties as defined in Sec. 3.5.1.

Site coefficients: The values of Fa and Fv indicated in Tables 3.3-1 and 3.3-2, respectively.

Structure: See Sec. 1.1.4.

3.1.4 Notation

dc The total thickness of cohesive soil layers in the top 100 ft (30 m); see Sec. 3.5.1.

di The thickness of any soil or rock layer i (between 0 and 100 ft [30 m]); see Sec. 3.5.1.

ds The total thickness of cohesionless soil layers in the top 100 ft (30 m); see Sec. 3.5.1.

Fa Short-period site coefficient (at 0.2 sec period); see Sec. 3.3.2.

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Fv Long-period site coefficient (at 1.0 second period); see Sec. 3.3.2.

H Thickness of soil.

N Standard penetration resistance, ASTM D1586-99.

Ni Standard penetration resistance of any soil or rock layer i (between 0 and 100 ft (30m); see Sec.3.5.1.

N Average standard penetration resistance for the top 100 ft (30 m); see Sec. 3.5.1.

chN Average standard penetration resistance of cohesionless soil layers for the top 100 ft (30 m); see Sec. 3.5.1.

PI Plasticity index, ASTM D4318.

S1 The mapped, maximum considered earthquake, 5-percent-damped, spectral response acceleration parameter at a period of one second as determined in Sec. 3.3.1.

Sa The design spectral response acceleration at any period as defined in this chapter.

SaM The maximum considered earthquake spectral response acceleration at any period as defined in this chapter.

SD1 The design, 5-percent-damped, spectral response acceleration parameter at a period of one second as defined in Sec. 3.3.3.

SDS The design, 5-percent-damped, spectral response acceleration parameter at short periods as defined in Sec. 3.3.3.

SM1 The maximum considered earthquake, 5-percent-damped, spectral response acceleration parameter at a period of one second adjusted for site class effects as defined in Sec. 3.3.2.

SMS The maximum considered earthquake, 5-percent-damped, spectral response acceleration parameter at short periods adjusted for site class effects as defined in Sec. 3.3.2.

SS The mapped, maximum considered earthquake, 5-percent-damped, spectral response acceleration parameter at short periods as determined in Sec. 3.3.1.

su Undrained shear strength, ASTM D2166 or ASTM D2850.

sui Undrained shear strength of any cohesive soil layer i (between 0 and 100 ft (30 m); see Sec. 3.5.1.

us Average undrained shear strength in top 100 ft. (30 m); see Sec. 3.5.1.

T See Sec. 4.1.4.

T0 0.2SD1/SDS

TL Long-period transition period as defined in Sec. 3.3.4.

TS SDI/SDS.

vs The shear wave velocity at small shear strains (equal to 10-3 percent strain or less).

vsi The shear wave velocity of any soil or rock layer i (between 0 and 100 ft (30m); see Sec. 3.5.1.

sv The average shear wave velocity at small shear strains in the top 100 ft (30 m); see Sec. 3.5.1.

w Moisture content (in percent), ASTM D2216.

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3.2 GENERAL REQUIREMENTS

As used in these Provisions, spectral acceleration parameters are coefficients corresponding to spectral accelerations in terms of g, the acceleration due to gravity.

3.2.1 Site Class. For all structures, the site shall be classified in accordance with Sec. 3.5.

3.2.2 Procedure selection

Ground motions, represented by response spectra and parameters associated with those spectra, shall be determined in accordance with the general procedure of Sec. 3.3 or the site-specific procedure of Sec. 3.4. Ground motions for structures on class F sites and for seismically isolated structures on sites with S1 greater than 0.6 shall be determined using the site-specific procedure of Sec. 3.4.

3.3 GENERAL PROCEDURE

3.3.1 Mapped acceleration parameters. The parameters SS and S1 shall be determined from the respective 0.2 sec and 1.0 sec spectral response accelerations shown on Figures 3.3-1 through Figures 3.3-14.

3.3.2 Site coefficients and adjusted acceleration parameters. The maximum considered earthquake (MCE) spectral response acceleration parameters SMS and SM1, adjusted for site class effects, shall be determined using Eq. 3.3-1 and 3.3-2, respectively:

MS a SS F S= (3.3-1)

and

M1 v 1S F S= (3.3-2)

where Fa and Fv are defined in Tables 3.3-1 and 3.3-2, respectively.

Table 3.3-1 Values of Site Coefficient Fa Mapped MCE Spectral Response Acceleration Parameter at 0.2 Second

Period a

Site Class

SS ≤ 0.25

SS = 0.50

SS = 0.75

SS = 1.00

SS ≥ 1.25

A

0.8

0.8

0.8

0.8

0.8

B

1.0

1.0

1.0

1.0

1.0

C

1.2

1.2

1.1

1.0

1.0

D

1.6

1.4

1.2

1.1

1.0

E

2.5

1.7

1.2

0.9

0.9

F

___b

___b

___b

___b

___b a Use straight line interpolation for intermediate values of SS. b Site-specific geotechnical investigation and dynamic site response analyses shall be performed.

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Table 3.3-2 Values of Site Coefficient Fv

Mapped MCE Spectral Response Acceleration Parameter at 1 Second Period a

Site Class

S1 ≤ 0.1

S1 = 0.2

S1 = 0.3

S1 = 0.4

S1 ≥ 0.5

A

0.8

0.8

0.8

0.8

0.8

B

1.0

1.0

1.0

1.0

1.0

C

1.7

1.6

1.5

1.4

1.3

D

2.4

2.0

1.8

1.6

1.5

E

3.5

3.2

2.8

2.4

2.4

F

___b

___b

___b

___b

___b

a Use straight line interpolation for intermediate values of S1. b Site-specific geotechnical investigation and dynamic site response analyses shall be performed.

3.3.3 Design acceleration parameters. The parameters SDS and SD1 shall be determined from Eq. 3.3-3 and 3.3-4, respectively:

23DS MSS S=

(3.3-3) and

23D1 M1S S=

(3.3-4) 3.3.4 Design response spectrum. Where a design response spectrum is required by these Provisions and site-specific procedures are not used, the design response spectrum shall be developed as indicated in Figure 3.3-15 and as follows: 1. For periods less than or equal to T0, Sa shall be taken as given by Eq. 3.3-5:

0

0.6 0.4DSa DS

SS T ST

= + (3.3-5)

2. For periods greater than or equal to T0 and less than or equal to TS, Sa shall be taken as equal to SDS. 3. For periods greater than TS and less then or equal to TL, Sa shall be taken as given by Eq. 3.3-6:

1Da

SST

= (3.3-6)

4. For periods greater than TL , Sa shall be taken as given by Eq. 3.3-7.

12

LDa

S TST

= (3.3-7)

where:

SDS = the design spectral response acceleration parameter at short periods

SD1 = the design spectral response acceleration parameter at 1 second period

T = the fundamental period of the structure (sec)

T0 = 0.2SD1/SDS

TS = SD1/SDS

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TL = Long-period transition period shown in Figure 3.3-16 (conterminous U.S. except California), Figure 3.3-17 (California), Figure 3.3-18 (Alaska), Figure 3.3-19 (Hawaii), Figure 3.3-20 (Puerto Rico), and Figure 3.3-21 (Guam and Tutuila).

1.0

0

1

0 1

Period, T (sec)

Spec

tral R

espo

nse

Acc

eler

atio

n, S

a (g

)

DSS

D1S

D1a

SST

=

T L

21

TTSS LD

a⋅

=

T 0 T S

Figure 3.3-15 Long-Period transition Period.

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3.4 SITE-SPECIFIC PROCEDURE A site-specific study shall account for the regional tectonic setting, geology, and seismicity, the expected recurrence rates and maximum magnitudes of earthquakes on known faults and source zones, the characteristics of ground motion attenuation, near-fault effects if any on ground motions, and the effects of subsurface site conditions on ground motions. The study shall incorporate current scientific interpretations, including uncertainties, for models and parameter values for seismic sources and ground motions. The study shall be documented in a report.

3.4.1 Probabilistic maximum considered earthquake. Where site-specific procedures are utilized, the probabilistic maximum considered earthquake ground motion shall be taken as that motion represented by a 5-percent-damped acceleration response spectrum having a 2 percent probability of exceedance in a 50 year period.

3.4.2 Deterministic maximum considered earthquake. The deterministic maximum considered earthquake spectral response acceleration at each period shall be taken as 150 percent of the largest median 5-percent-damped spectral response acceleration computed at that period for characteristic earthquakes on all known active faults within the region. For the purposes of these Provisions, the ordinates of the deterministic maximum considered earthquake ground motion response spectrum shall not be taken lower than the corresponding ordinates of the response spectrum determined in accordance with Figure 3.4-1, where Fa and Fv are determined using Tables 3.3-1 and 3.3-2, with the value of SS taken as 1.5 and the value of S1 taken as 0.6.

Figure 3.4-1 Deterministic Lower Limit on Maximum Considered Earthquake

3.4.3 Site-specific maximum considered earthquake. The site-specific maximum considered earthquake spectral response acceleration at any period, SaM, shall be taken as the lesser of the spectral response accelerations from the probabilistic maximum considered earthquake ground motion of Sec. 3.4.1 and the deterministic maximum considered earthquake ground motion of Sec. 3.4.2.

3.4.4 Design response spectrum. Where site-specific procedures are used to determine the maximum considered earthquake ground motion, the design spectral response acceleration at any period shall be determined from Eq. 3.4-1:

0

1

0 1Period, T (sec)

Spec

tral R

espo

nse

Acc

eler

atio

n, S

a (g

)

0.6 vaM

FST

=

1.5aM aS F=

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23a aMS S= (3.4-1)

and shall be greater than or equal to 80 percent of Sa determined in accordance with Sec. 3.3.4. For sites classified as Site Class F requiring site-specific evaluations (Note b to Tables 3.3-1 and 3.3-2 and Sec. 3.5.1), the design spectral response acceleration at any period shall be greater than or equal to 80 percent of Sa determined for Site Class E in accordance with Sec. 3.3.4.

3.4.5 Design acceleration parameters. Where the site-specific procedure is used to determine the design response spectrum in accordance with Section 3.4.4, the parameter SDS shall be taken as the spectral acceleration, Sa , obtained from the site-specific spectrum at a period of 0.2 second, except that it shall not be taken as less than 90 percent of the peak spectral acceleration, Sa , at any period larger than 0.2 second. The parameter SD1 shall be taken as the greater of the spectral acceleration, Sa , at a period of 1 second or two times the spectral acceleration, Sa , at a period 2 seconds. The parameters SMS and SM1 shall be taken as 1.5 times SDS and SD1, respectively. The values so obtained shall not be taken as less than 80 percent of the values obtained from the general procedure of Section 3.3.

3.5 SITE CLASSIFICATION FOR SEISMIC DESIGN Where the soil properties are not known in sufficient detail to determine the Site Class in accordance with Sec. 3.5.1, it shall be permitted to assume Site Class D unless the authority having jurisdiction determines that Site Class E or F could apply at the site or in the event that Site Class E or F is established by geotechnical data.

3.5.1 Site Class definitions. The Site Classes are defined as follows:

A Hard rock with measured shear wave velocity, v̄s > 5,000 ft/sec (1500 m/s)

B Rock with 2,500 ft/sec < v̄s ≤ 5,000 ft/sec (760 m/s < v̄s ≤ 1500 m/s)

C Very dense soil and soft rock with 1,200 ft/sec < v̄s ≤ 2,500 ft/sec (360 m/s < v̄s ≤ 760 m/s) or with either N > 50 or s̄u > 2,000 psf (100 kPa)

D Stiff soil with 600 ft/sec ≤ v̄s ≤ 1,200 ft/sec (180 m/s ≤ v̄s ≤ 360 m/s) or with either 15 ≤ N ≤ 50 or 1,000 psf ≤ s̄u ≤ 2,000 psf (50 kPa ≤ s̄u ≤ 100 kPa)

E A soil profile with v̄s < 600 ft/sec (180 m/s) or with either

N < 15, s̄u < 1,000 psf, or any profile with more than 10 ft (3 m) of soft clay defined as soil with PI > 20, w ≥ 40 percent, and su < 500 psf (25 kPa)

F Soils requiring site-specific evaluations:

1. Soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils, quick and highly sensitive clays, collapsible weakly cemented soils.

Exception: For structures having fundamental periods of vibration less than or equal to 0.5 second, site-specific evaluations are not required to determine spectral accelerations for liquefiable soils. Rather, the Site Class may be determined in accordance with Sec. 3.5.2, assuming liquefaction does not occur, and the corresponding values of Fa and Fv determined from Tables 3.3-1 and 3.3-2.

2. Peat and/or highly organic clays (H > 10 ft [3 m] of peat and/or highly organic clay, where H = thickness of soil)

3. Very high plasticity clays (H > 25 ft [8 m] with PI > 75)

4. Very thick, soft/medium stiff clays (H > 120 ft [36 m]) with su < 1,000 psf (50 kPa)

The parameters used to define the Site Class are based on the upper 100 ft (30 m) of the site profile. Profiles containing distinctly different soil and rock layers shall be subdivided into those layers

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designated by a number that ranges from 1 to n at the bottom where there are a total of n distinct layers in the upper 100 ft (30 m). The symbol i then refers to any one of the layers between 1 and n.

where:

vsi = the shear wave velocity in ft/sec (m/s).

di = the thickness of any layer (between 0 and 100 ft [30 m]).

1

1

n

ii

s ni

i si

dv

dv

=

=

=∑

∑ (3.5-1)

where 1

n

ii

d=∑ is equal to 100 ft (30 m).

Ni = the Standard Penetration Resistance determined in accordance with ASTM D 1586, as directly measured in the field without corrections, and shall not be taken greater than 100 blows/ft. Where refusal is met for a rock layer, Ni shall be taken as 100 blows/ft.

1

1

n

iin

i

i i

dN

dN

=

=

=∑

∑ (3.5-2)

where Ni and di in Eq. 3.5-2 are for cohesionless soil, cohesive soil, and rock layers.

1

sch m

i

i i

dNdN=

=

∑ (3.5-3)

where Ni and di in Eq. 3.5-3 are for cohesionless soil layers only,

and 1

m

i si

d d=

=∑

ds = the total thickness of cohesionless soil layers in the top 100 ft (30 m).

sui = the undrained shear strength in psf (kPa), determined in accordance with ASTM D 2166 or D 2850, and shall not be taken greater than 5,000 psf (250 kPa).

1

cu k

i

i ui

dsds=

=

∑ (3.5-4)

where 1

k

i ci

d d=

=∑ .

dc = the total thickness of cohesive soil layers in the top 100 ft (30 m).

PI = the plasticity index, determined in accordance with ASTM D 4318.

w = the moisture content in percent, determined in accordance with ASTM D 2216.

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3.5.2 Steps for classifying a site

Step 1: Check for the four categories of Site Class F requiring site-specific evaluation. If the site corresponds to any of these categories, classify the site as Site Class F and conduct a site-specific evaluation.

Step 2: Check for the existence of a total thickness of soft clay > 10 ft (3 m) where a soft clay layer is defined by: su < 500 psf (25 kPa), w ≥ 40 percent, and PI > 20. If these criteria are satisfied, classify the site as Site Class E.

Step 3: Categorize the site using one of the following three methods with v̄s, N and s̄u computed in all cases as specified in Sec. 3.5.1:

a. v̄s for the top 100 ft (30 m) (v̄s method)

b. N for the top 100 ft (30 m) ( N method)

c. chN for cohesionless soil layers (PI < 20) in the top 100 ft (30 m) and average s̄u for cohesive soil layers (PI > 20) in the top 100 ft (30 m) (s̄u method)

Table 3.5-1 Site Classification

Site Class

v̄s

N or chN

s̄u

a

E

< 600 fps ( < 180 m/s)

< 15

< 1,000 psf ( < 50 kPa)

D

600 to 1,200 fps (180 to 360 m/s)

15 to 50

1,000 to 2,000 psf

(50 to 100 kPa)

C

> 1,200 to 2,500 fps (360 to 760 m/s)

> 50

> 2,000

( > 100 kPa) a If the s̄u method is used and the chN and s̄u criteria differ, select the category with the softer soils (for example, use Site Class E instead of D).

Assignment of Site Class B shall be based on the shear wave velocity for rock. For competent rock with moderate fracturing and weathering, estimation of this shear wave velocity shall be permitted. For more highly fractured and weathered rock, the shear wave velocity shall be directly measured or the site shall be assigned to Site Class C.

Assignment of Site Class A shall be supported by either shear wave velocity measurements on site or shear wave velocity measurements on profiles of the same rock type in the same formation with an equal or greater degree of weathering and fracturing. Where hard rock conditions are known to be continuous to a depth of 100 ft (30 m), surficial shear wave velocity measurements may be extrapolated to assess v̄s.

Site Classes A and B shall not be used where there is more than 10 ft (3 m) of soil between the rock surface and the bottom of the spread footing or mat foundation.

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