Research Needs

1996 .

Ž

If fault movements are small i.e. less than a few .

inches andror distributed over a relatively wide zone, it is possible that the tunnel may be designed to accom-modate the fault displacement by providing articulation of the tunnel liner with ductile joints. This allows the tunnel to distort into an S-shape through the fault zone without rupture. The closer the joint spacing, the better the performance of the liner. Design of a lining to accommodate fault displacement becomes more feasi-ble in soft soils where the tunnel lining can more effectively redistribute the displacements. Again, keep-ing the tunnel watertight is a concern when uskeep-ing joints ŽPower et al., 1996 ..

8.6. Seismic design of high le¨el nuclear waste repositories The methods described in this report can also be used for the analysis of underground openings used in

Ž .

nuclear waste repositories NWR . The main difference is in the seismic hazard analysis, whereby the design seismic event corresponds to return periods that are compatible with the design life of the facility. Stepp Ž1996 presents a report that summarizes many of the. specific issues related to seismic design of NWR.

9. Research Needs

The material presented in this report describes the current state of knowledge for the design of under-ground structures. Many issues require further investi-gation to enhance our understanding of seismic re-sponse of underground structures and improve seismic design procedures. Some of these issues include:

1. Instrumentation of tunnels and underground struc-tures to measure their response during ground shaking. These instruments would include mea-surement of vertical and lateral deformations along the length of the tunnel. This will be useful to understand the effect of spatial incoherency and directivity of the ground motion on tunnel re-sponse. Other instrumentation would be useful to measure differential movement between a tunnel

and a portal structure, and to measure racking of rectangular structures such as subway stations.

2. Improved evaluation of the mechanism of the load transferred from the overburden soil to the ceiling slab of a cut and cover structure. Not all of the inertia force of the overburden soil is transferred to the ceiling slab; however, research into the eval-uation of the soil block that provides inertia force

Ž .

has not yet been undertaken Iida et al., 1996 . 3. Research into the influence of high vertical

accel-erations on the generation of large compressive loads in tunnel linings and subway station columns.

Large vertical forces may have been a factor in the Ž

collapse of the Daikai Subway station Iida et al., .

1996 .

4. Development of improved numerical models to simulate the dynamic soil structure interaction problem of tunnels, as well as portal and subway structures. These models will be useful in studying the effect of high velocity pulses generated near

Ž

fault sources on underground structures Hashash .

et al., 1998 .

5. Evaluation of the significance of ground motion directivity and ‘fling effect’ on tunnel response.

6. Evaluation of the significance of ground motion incoherence on the development of differential

Ž

movement along the length of a tunnel Power et .

al., 1996 . Ground motion incoherence is particu-larly important in soft soils and shallow tunnels where the potential for slippage between the tun-nel and soil is high.

7. Evaluation of the influence of underground struc-tures on the local amplification or attenuation of propagated ground motion.

8. Research into the effects of repeated cyclic loading Ž

on underground tunnels St. John and Zahrah, .

1987 .

9. Research into the application of non-conventional lining, bolting, and water insulation materials that can be used for seismic joints and to enhance the seismic performance of the tunnel.

10. In memoriam

Dr Birger Schmidt has been the main motivating force behind the development of this report. Dr Birger Schmidt, a native of Denmark, passed away on October 2, 2000 after a yearlong fight with cancer. He had a distinguished career in geotechnical engineering span-ning almost four decades. His many contributions in-clude the error-function method for estimating settle-ments due to tunneling as well as over 80 technical publications. He actively contributed to the many

ef-Ž . forts of the International Tunnelling Association ITA Working Group No 2: Research. He maintained his interest and support of this report through the last week of his life and emphasized the need to complete this work.

This report is dedicated to his memory. He has been a friend and a mentor and will be greatly missed.

Youssef Hashash

11. Addendum

Ž .

The reference of Power et al. 1996 has been up-dated and will be issued soon as part of a report by the Multidisciplinary Center for Earthquake Engineering

Ž .

Research MCEER , Buffalo, NY to the U.S. Federal Highway Administration. The update contains many details that are complementary to the material pre-sented in this report and contains revised values for

Ž .

Table 2 based on the work of Sadigh and Egan 1998 .

Acknowledgements

The authors of this report would like to acknowledge the review comments provided by many individuals including members of the International Tunneling As-sociation Working Group no. 2. The authors would also like to thank William Hansmire, Jon Kaneshiro, and Kazutoshi Matsuo for their careful comments. This work made use of Earthquake Engineering Research Centers Shared Facilities supported by the US National Science Foundation under Award no. EEC-9701785.

Appendix A: List of symbols

␣: Coefficient used in calculation of lining᎐soil racking ratio of circular tunnels

␣ⁿ: Coefficient used in calculation of lining᎐soil racking ratio of circular tunnels under nor-mal loading only

␤ :₁ Coefficient used in developing loading crite-ria for ODE

␧^ab: Total axial strain

␧ma x^a : Maximum axial strain caused by a 45⬚ inci-dent shear wave

␧_{ma x}^b : Maximum bending strain caused by a 0 de-gree incident shear wave

␧ :_l Longitudinal strain

␧ :_{l m} Maximum longitudinal strain

␧ :_n Normal strain

␧ :_{n m} Maximum normal strain

␾: Angle of incidence of wave with respect to tunnel axis

␥ :_s Simple shear strain of a soil element

␥: Shear strain

␥ :_m Maximum shear strain

␥ :_{ma x} Maximum free-field shear strain of soil or rock medium

␥ :_t Soil unit weight

␴^ab: Total axial stress

␪: Angular location of the tunnel lining

␳: Radius of curvature

␳ :_m Density of medium

␳_{ma x}: Maximum radius of curvature

␶: Simple shear stress of a soil element

␶ :_{ma x} Maximum shear stress

⌬: Lateral deflection

⌬_structure: Racking deflection of rectangular tunnel cross-section

⌬d_free-field: Free-field diametric deflection in non-perfo-rated ground

⌬d_lining: Lining diametric deflection

⌬dⁿ_lining: Lining diametric deflection under normal loading only

␯ :_l Poisson’s ratio of tunnel lining

␯ :_m Poisson’s ratio of soil or rock medium

⌿: Coefficient used in calculation of flexibility ratio of rectangular tunnels

a :₁ Coefficient used in calculation of flexibility ratio of rectangular tunnels

a :₂ Coefficient used in calculation of flexibility ratio of rectangular tunnels

a :_P Peak particle acceleration associated with P-wave

a :_R Peak particle acceleration associated with Rayleigh wave

a_RP: Peak particle acceleration associated with Rayleigh Wave for compressional compo-nent

a :_RS Peak particle acceleration associated with Rayleigh Wave for shear component a :_S Peak particle acceleration associated with

S-wave

d: Diameter or equivalent diameter of tunnel lining

f : Ultimate friction force between tunnel and surrounding soil

h: Thickness of the soil deposit r: Radius of circular tunnel t: Thickness of tunnel lining

A: Free-field displacement response amplitude of an ideal sinusoidal S-wave

A :_a Same as A, used for axial strain calculation A :_b Same as A, used for bending strain

calcula-tion

A :_c Cross-sectional area of tunnel lining C: Compressibility ratio of tunnel lining

C :_P Apparent velocity of P-wave propagation C :_R Apparent velocity of Rayleigh wave

propaga-tion

C :_S Apparent velocity of S-wave propagation C_sŽR.: Apparent velocity of S-wave propagation in

soil due to presence of the underlying rock C_sŽs.: Apparent velocity of S-wave propagation in

soil only

D: Displacement amplitude of soil

D: Effects due to dead loads of structural com-ponents

E: Plane strain elastic modulus of frame E1: Effects due to vertical loads of earth and

water

E2: Effects due to horizontal loads of earth and water

E :_l Modulus of elasticity of tunnel lining E :_m Modulus of elasticity of soil or rock medium EQ: Effects due to design earthquake motion EX: Effects of static loads due to excavation F: Flexibility ratio of tunnel lining

G :_m Shear modulus of soil or rock medium H: Effects due to hydrostatic water pressure H: Height of tunnel

Ž I: Moment of inertia of the tunnel lining per

.

unit width for circular lining

I :_I Moment of inertia of invert slabs in a rect-angular cut-and-cover structure

I :_c Moment of inertia of tunnel lining section I :_R Moment of inertia of roof slabs in a

rectan-gular cut-and-cover structure

I :_W Moment of inertia of walls in a rectangular cut-and-cover structure

K: Free-field curvature due to body or surface waves

K :_m Free-field maximum curvature due to body or surface waves

K :₁ Full-slip lining response coefficient K :₂ No-slip lining response coefficient

K :_a Longitudinal spring coefficient of soil or rock medium

K :₀ At rest coefficient of earth pressure

K :_t Transverse spring coefficient of soil or rock medium

L: Effects due to live loads

L: Wavelength of ideal sinusoidal shear wave L :_t Total length of tunnel

Ž .

M ␪ : Circumferential bending moment in tunnel lining at angle ␪

M_{ma x}: Maximum bending moment in tunnel cross-section due to shear waves

P: Concentrated force acting on rectangular structure

Q_{ma x}: Maximum axial force in tunnel cross-section due to shear waves

ŽQ_{ma x f}. : Maximum frictional force between lining and surrounding soils

R: Lining-soil racking ratio

Rⁿ: Lining᎐soil racking ratio under normal load-ing only

S :₁ Force required to cause a unit racking de-flection of a rectangular frame structure T : Predominant natural period of a shear wave

in the soil deposit Ž .

T ␪ : Circumferential thrust force in tunnel lining at angle ␪

T_{ma x}: Maximum thrust in tunnel lining U: Required structural strength capacity

Ž .

V ␪ : Circumferential shear force in tunnel lining at angle ␪

V_{ma x}: Maximum shear force in tunnel cross-sec-tion due to shear waves

V :_P Peak particle velocity associated with P-waves

V :_R Peak particle velocity associated with Rayleigh Wave

V_RP: Peak particle velocity associated with Rayleigh Wave for compressional compo-nent

V_{R S}: Peak particle velocity associated with Rayleigh Wave for shear component

V :_S Peak particle velocity associated with S-waves

W: Width of the structure

Y: Distance from neutral axis of cross-section to extreme fiber of tunnel lining

Appendix B: Sample calculations

Design example 1: a linear tunnel in soft ground (after Wang, 1993)

In this example, a tunnel lined with a cast-in-place Ž

circular concrete lining e.g. a permanent second-pass .

support , is assumed to be built in a soft soil site. The geotechnical, structural, and earthquake parameters are listed as follows:

Geotechnical Parameters:

䢇 Apparent velocity of S-wave propagation, Css110 mrs

䢇 Soil unit weight,␥ s17.0 kNrmt ³

Ž .

䢇 Soil Poisson’s ratio,␯ s0.5 saturated soft claym 䢇 Soil deposit thickness over rigid bedrock, hs

30.0 m

Structural Parameters:

䢇 Lining thickness, ts0.30 m

䢇 Lining diameter, ds6.0 mªrs3.0 m

䢇 Length of tunnel, Lts125 m

䢇 Moment of inertia of the tunnel section, I_c

Ž ^{4 4}.

␲ 3.15 y2.85 Ž . 4Ž

s 4 0.5 s12.76 m one half of the full section moment of inertia to account for con-. crete cracking and non-linearity during the MDE

䢇 Lining cross section area, Acs5.65 m²

䢇 Concrete Young’s Modulus, Els24 840 MPa

䢇 Concrete yield strength, fcs30 MPa

䢇 Allowable concrete compression strain under com-bined axial and bending compression, ␧allows0.003 Žduring the MDE.

Ž .

Earthquake parameters for the MDE :

䢇 Peak ground particle acceleration in soil, ass0.6 g

䢇 Peak ground particle velocity in soil, Vss1.0 mrs First, try the simplified equation. The angle of

inci-Ž .

dence ␾ of 40⬚ gives the maximum value for longitu-Ž ^ab.

dinal strain ␧ , the combined maximum axial strain and curvature strain is calculated as:

V_s a r_s

ab 3

␧ s"Cssin␾ cos␾"Cs2cos ␾

1.0 Ž . Ž .

s"2 110Ž .sin 40⬚ cos 40⬚

Ž0.6 9.81 3.0.Ž .Ž . ₃ Ž .

" ₂ cos 45⬚ s"0.0051.

Ž110.

Ž . Eq. 6 The calculated maximum compression strain exceeds

Ž ^ab

the allowable compression strain of concrete i.e.␧ )

␧allows0.003 ..

Now use the tunnel᎐ground interaction procedure.

1. Estimate the predominant natural period of the

Ž .

soil deposit Dobry et al., 1976 : Ž .Ž .

4 h 4 30.0 Ž .

Ts s s1.09s Eq. 16

C_s 110

2. Estimate the idealized wavelength:

Ž . Ž .

LsTC s4hs4 30.0 s120 m_s Eq. 15

3. Estimate the shear modulus of soil: Gms␳ Cm s²

17.0 ₂

Ž .

s9.81 110 s20 968 kPa

4. Derive the equivalent spring coefficients of the soil:

Ž .

16␲G 1y␯m m d KasK st Ž3y4␯m. L

Ž16␲ 20 968 1y0.5.Ž .Ž . 6.0 s ^{Ž3y 4 0.5Ž .Ž ..}

ž /

¹²⁰

s26 349 kNrm Eq. 14Ž .

5. Derive the ground displacement amplitude, A:

The ground displacement amplitude is generally a function of the wavelength, L. A reasonable estimate of the displacement amplitude must consider the site-specific subsurface conditions as well as the character-istics of the input ground motion. In this design exam-ple, however, the ground displacement amplitudes are calculated in such a manner that the ground strains as a result of these displacement amplitudes are compara-ble to the ground strains used in the calculations based on the simplified free-field equations. The purpose of this assumption is to allow a direct and clear evaluation of the effect of tunnel᎐ground interaction. Thus, by assuming a sinusoidal wave with a displacement ampli-tude A and a wavelength L, we can obtain:

For free-field axial strain:

V^ss2␲As V^ssin␾ cos␾«

Cs L CS

Ž120 1.0.Ž .

Ž . Ž .

As 2␲ 110Ž . sin 40⬚ cos 40⬚

s0.085 m. Eq. 17Ž .

Let AasAs0.085 m.

For free-field bending curvature:

2 Ž ².Ž .Ž .

a_{s 3} 4␲ A 120 0.6 9.81

cos ␾s «As

2 2 2Ž 2.

Cs L 4␲ 110

3Ž . Ž .

cos ␾ s0.080 m. Eq. 18 Let AbsAs0.080 m.

6. Calculate the maximum axial strain and the corre-sponding axial force of the tunnel lining:

2␲

ž /

^L

␧ama xs E Al c 2␲ 2Aa

2q

ž /

^Ka

ž /

^L

2␲

ž /

¹²⁰ _{Ž .}

s ₂ 0.085

Ž24, 840, 000 5.65.Ž . 2␲ 2q

ž

^{26, 349}

/ ž /

¹²⁰

s0.00027 Eq. 10Ž .

The axial force is limited by the maximum frictional force between the lining and the surrounding soils.

Estimate the maximum frictional force:

fL _a

Ž .

Qmaxs Qmax fs 4 sE A ␧l c max

Ž .Ž .Ž .

s 24 840 000 5.65 0.00027

s37 893 kN Eq. 10Ž .

7. Calculate the maximum bending strain and the corresponding bending moment of the tunnel lining:

2␲ 2A_b

ž /

^L

␧b_{ma x}s ₄r

E I^{l c} 2␲ 1q ^Kt

ž /

^L

2␲ Ž2 0.080.

ž /

¹²⁰ _{Ž .}

s1qŽ24, 840, 000 12.76^{26, 349}.Ž .

ž /

¹²⁰2␲ 4 3.0 s0.00060 Ž . Eq. 11

E Il c␧^bmax

Mma xs r

Ž24, 840, 000 12.76 0.00060.Ž .Ž .

s 3.0

s63 392 kNym Eq. 12Ž .

8. Compare the combined axial and bending com-pression strains to the allowable:

␧^abs␧^ama xq␧max^b s0.00027q0.00060

s0.00087-␧_{al l o w}s0.003 Eq. 13Ž .

9. Calculate the maximum shear force due to the bending curvature:

2␲ Ž . 2␲

Vma xsMmax

ž /

^L s 63, 391

ž /

¹²⁰ s3319 kN Ž . Eq. 12 10. Calculate the allowable shear strength of con-crete during the MDE:

'

⬘

0.85

ž

f A^{c shear}

/

^Ž0.85.

'

³⁰ _{5.65 Ž .}

␾V s_c ⁶ s ⁶

ž /

² 1000

s2192 kN

Ž . ^⬘

where ␾sshear strength reduction factor 0.85 , f sc

Ž .

yield strength of concrete 30 MPa , and Ashears effective shear areasA r2. Note: Using ␾s0.85 forc

earthquake design may be very conservative.

11. Compare the induced maximum shear force with the allowable shear resistance:

Vma xs3319 kN)␾V s2192 kNc

Although calculations indicate that the induced maxi-mum shear force exceeds the available shear resistance provided by the plain concrete, this problem may not be of major concern in actual design because:

䢇 The nominal reinforcements generally required for other purposes may provide additional shear resis-tance during earthquakes.

䢇 The ground displacement amplitudes, A, used in this example are very conservative. Generally, the spatial variations of ground displacements along a horizontal axis are much smaller than those used in this example, provided that there is no abrupt change in subsurface profiles.

Design example 2: axial and curvature deformation due to S-waves, beam-on-elastic foundation analysis method (after Power et al., 1996)

Earthquake and soil parameters:

䢇 Mws6.5, source-to-site distances10 km

䢇 Peak ground particle acceleration at surface, a_{ma x} s0.5 g

䢇 Apparent velocity of S-wave propagation in soil due to presence of the underlying rock, CsŽ R.s2 kmrs

䢇 Predominant natural period of shear waves, Ts 2 s

䢇 Apparent velocity of S-wave propagation in soil only, CsŽ s.s250 mrs

䢇 Soil density, ␳ s1920 kgrm_m ³, stiff soil

䢇 Soil Poisson’s ratio,␯ s0.3m

Ž

Tunnel Parameters Circular Reinforced Concrete .

Tunnel :

Ž

䢇 ds6 mªrs3.0 m, ts0.3 m, depth below ground .

surface s35 m

䢇 E_ls24.8=10⁶ kPa, ␯ s0.2, A s5.65 m_{l c} ², I_c

Ž ^{4 4}.

␲ 3.15 y2.85 4 Ž

s s25.4 m see tunnel cross

4 .

section in Appendix B

1. Determine the longitudinal and transverse soil spring constants:

2. Determine the maximum axial strain due to S-waves:

Estimate the ground motion at the depth of the tunnel.

3. Determine the maximum bending strain due to S-waves:

4. Determine combined strain:

␧^abs␧^ama xq␧max^b s0.00009q0.00000030

f0.00009 Eq. 13Ž .

If the calculated stress from the beam-on-elastic foundation solution is larger than from the free-field solution, the stress from the free-field solution should be used in design.

Design example 3: ovaling deformation of a circular

( )

tunnel modified from Power et al., 1996 Earthquake and soil parameters:

䢇 Mws7.5, source-to-site distances10 km

䢇 Peak ground particle acceleration at surface, a_{ma x} s0.5 g

䢇 Stiff soil,␳ s1920 kgrmm ³, Cms250 mrs, ␯ s0.3m

Ž

Tunnel parameters circular reinforced concrete tun-.

nel :

䢇 ds6 mªrs3.0 m Ž

䢇 ts0.3 m, depths15 m see tunnel cross-section in .

䢇 Moment of inertia of the tunnel lining per unit

1 _{3 4}

. Ž .Ž .

width , Is12 1 0.3 s0.0023 m rm

Ž .

Use formulations of Penzien 2000 assuming full slip condition.

Note: in the following calculation, more significant figures are kept throughout each step to show that

Ž .

formulations of Penzien 2000 give the same values as

Ž .

Wang 1993 .

Ž ⁿ.

1. Determine the racking ratio R and the displace-ment term ⌬ D_liningⁿ :

Estimate ground motion at depth of tunnel.

Ž .Ž .

a_ss0.9a_maxs 0.9 0.5 g s0.45 g Table 4 Assuming stiff soil,

Ž .Ž .

Vss 140 cmrsrg 0.45 g s63 cmrs

s0.63 mrs Table 2

Vs 0.63

s 2.5735 s0.016213 Eq. 29

2

Ž . 2. Determine the maximum tangential thrust T and

Ž .

moment M due to S-waves:

12 E I⌬dⁿ

Note: maximum T and M occur at ␪s␲r4.

3. Determine combined stress ␴ and strain ␧ from thrust and bending moment:

Ž . Ž . Ž .Ž .

T ␪ M ␪ Y 53.5 160.6 0.15

␴s A_l q I s 0.3 q 0.0023

s178q10474s10 652 kPa

Ž .

Use formulations of Wang 1993 assuming full slip condition.

Ž .

1. Determine the flexibility ratio F and full-slip Ž .

lining response coefficient K :₁ Ž ². ³ 2. Determine the maximum tangential thrust T and

Ž .

moment M due to S-waves:

1 Em

Tma xs K6 1Ž1q␯m.r␥max

Ž .

1 312 000

Ž . Ž .Ž .

s 0.21237 3 0.0021

6 Ž1q0.3.

s 0.21237 3 0.0021

6 Ž1q0.3.

s160.6 kNym Eq. 23Ž .

3. Determine combined stress ␴ and strain ␧ from thrust and bending moment:

Ž .Ž .

T MY 53.5 160.6 0.15

␴sA_lq I s 0.3 q 0.0023 s178q10474s10 652 kPa

The above calculation is repeated for no-slip condi-tion. The results are summarized in the table below:

Ž . Ž .

Wang 1993 Penzien 2000

Full Slip No Slip Full Slip No Slip Ž .

T kN 53.5 870.9 53.5 106.0

Ž . U

M kN-m 160.6 160.6 160.6 158.9

Ž .

␴ kPa 10 652 13 376 10 652 10 716

UAssumed equal to full-slip condition

Note: in the case of full-slip condition, the two formulations give the same values for the force compo-nents. It can be observed that magnitude of the mo-ment has a much stronger influence than thrust over the stresses experienced by the tunnel lining. Calcula-tion also shows that under no-slip assumpCalcula-tion, the

Ž .

formulation of Wang 1993 yields a much higher thrust

Ž .

than the one from Penzien 2000 .

Design example 4: racking deformation of a rectangular

( )

tunnel after Power et al., 1996 Earthquake and Soil Parameters:

䢇 Mws7.5, source-to-site distances10 km

䢇 Peak ground particle acceleration at surface, a_max s0.5 g

䢇 Apparent velocity of S-wave propagation in soil, Cms180 mrs

䢇 Soft soil, soil density,␳ s1920 kgrmm ³

Ž

Tunnel parameters rectangular reinforced concrete .

tunnel :

Ž . Ž .

䢇 Width of tunnel W s10 m, height of tunnel H s4 m, depth to tops5 m

1. Determine the free-field shear deformation

⌬_free-field:

Estimate ground motion at depth of tunnel.

Ž .Ž .

a_ss1.0a_maxs 1.0 0.5 g s0.5 g Table 4 Assuming soft soil,

Ž .Ž .

Vss 208 cmrsrg 0.5 g s104 cmrs

s1.0 mrs Table 2

V_s 1.0

␥_{ma x}s s s0.0056 Table 5

C_m 180

Ž .Ž . Ž .

⌬_freeyfields␥_maxHs 0.0056 4 s0.022 m Eq. 43

2. Determine the flexibility ratio F:

2 1920 Ž 2.

G_ms␳ C s_{m m}

ž /

¹⁰⁰⁰ 180 s62 000 kPa Table 5

G Wm Ž .

Fs Eq. 45

S H1

Through structural analysis, the force required to

Ž .

cause a unit racking deflection 1 m for a unit length Ž1 m of the cross-section was determined to be 310 000. kPa. Note that for the flexibility ratio F to be dimen-sionless, the units of S must be in force per area.

Ž62000 10.Ž . FsŽ310 000 4.Ž .s0.5

For Fs0.5, the racking coefficient R is equal to 0.5.

3. Determine the racking deformation of the struc-ture ⌬_structure:

Ž .Ž .

⌬structuresR⌬freeyfields 0.5 0.022 s0.011 m Ž . Eq. 51 Determine the stresses in the liner by performing a structural analysis with an applied racking deformation of 0.011 m. Both the point load and triangularly dis-tributed load pseudo-lateral force models should be applied to identify the maximum forces in each loca-tion of the liner.

References

American Association of State Highway and Transport Officials ŽAASHTO , 1991. Standard Specifications for Highway Bridges.. ACI 318, 1999. Building Code Requirements for Reinforced

Con-crete, American Concrete Institute

Abramson, L.W., Crawley, J.E., 1995. High-speed rail tunnels in California. Proceedings of the 1995 Rapid Excavation and Tunnel-ing Conference, June 18᎐21, San Francisco, CA, USA.

Abrahamson, N.A., 1985. Estimation of seismic wave coherency, and rupture velocity using theSMART-1 strong motion array recordings.

Abrahamson, N.A., 1985. Estimation of seismic wave coherency, and rupture velocity using theSMART-1 strong motion array recordings.

In document Seismic Design and Analysis of Underground Structures (Page 38-48)