Seismic Analysis of Buried Reinforced Concrete Tunnels

Shawn Carey, P.E. – SRNS, LLCLeslie Sprague, P.E. – SRNS, LLCJay Amin, SRR, LLC

Background• Seismic loads on Buried Tunnels

A) Axial deformationB) CurvatureC) Racking

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C ) Racking

Tunnel Racking Methodologies

• Simplified Frame Analysis (Wang, 1993)– Well known design methodology for new tunnels– Estimate structural racking deformation based on relative flexibility of tunnel and surrounding soil

media– Improvement over conventional design assuming structural displacement equal to free-field soil

displacement which is very conservative for stiff structures in soft soil– Approximates complex SSI problem

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Tunnel Racking Methodologies

• Soil-Structure Interaction Analysis– Best representation of system, but highly complex solution– SASSI is well known example of software

• Frame Analysis on Soil Springs– Assume structure displacement equal to free-field soil displacement and place tunnel on soil

springs– Allows for rigid body rotation of tunnel– Oversimplification of complex problem

without benchmarking

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Case Study at SRS

• A buried, reinforced concrete, ventilation tunnel at SRS has been subject to severe degradation over the decades.– Interior reinforcing exposed in many areas

• Tunnel conveys contaminated airstream from processing facility to sand filter– total length approximately 500-ft– Top of tunnel approximately 15-ft below grade– 9-ft x 12-ft cross section in single tunnel and double tunnel configurations

• Poorly compacted backfill in relatively soft native soil• Tunnel is Safety Class and required to maintain function during and after a

PC-3/SDC-3 seismic event• Determine moments and shears in tunnel using the three methodologies described

previously

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Relative soil displacements

• Relative soil displacement at top of tunnel (compared to bottom) determined using SHAKE

– Overall very small relative displacementsbetween top and bottom of tunnel

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Soil Case Relative Soil Displacements (in)

Upper Bound 0.084

Best Estimate 0.088

Lower Bound 0.122

Racking Loads - Wang

• Based on relative flexibility, free-field displacement is reduced or amplified

• Required forces to yield required relative displacement (UB case controls):

– Tunnel is actually quite stiff, thus requiring large forces even for small displacements

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Soil Case Relative Soil Displacements (in)

Racking Coefficient

Final Relative Structural 

Displacements (in)

Upper Bound 0.084 1.5 0.126

Best Estimate 0.088 1.25 0.110

Lower Bound 0.122 0.6 0.073

16.5 kip3.5 kip/ft

Racking Loads – Soil Springs

• Assume relative lateral displacement of structure is equal to that of soil• Soil spring stiffness based on subgrade modulus of reaction (k1)

– Not reduced for foundation width in order to provide upper bound solution• Model allows rigid body rotation• Required forces to yield required relative displacement (LB case controls):

• Wang vs soil spring – very different loads– Expected result due to lower lateral stiffness of tunnel on soil springs vs. pinned base

with Wang– Obtain structural forces from STAAD model

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2.1 kip0.44 kip/ft

Racking Loads - SASSI

• 2D SASSI Model– Obtain structural forces directly from SASSI

• Analyze tunnel in SASSI and compare structural forces.• Models developed with and without explicit backfill modelling

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SASSI Model (double tunnel) w/ excavated backfill elements

SASSI Model (double tunnel) w/o excavated backfill elements

SASSI Double Tunnel Model - Native Soil Study Results

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• Negligible difference between structural moments in wall between models withand without backfill

SASSI Results

Comparison: Racking Methods

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Analysis Method Seismic D/C of moment on exterior process tunnel wall using LB soil profile

Wang Method / 1.03

Soil Spring Approach

/ 0.31

SASSI / 0.37

Comparable results between the soil spring analysis approach and the SASSI Analysis with LB Soil Profile

Demands from Wang method are much larger

STAAD – soil springs

Moment on exterior wall –double tunnel

Comparison – Triangular vs point racking load

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Single Tunnel Model

• Same approach used for the single tunnel as for the double tunnel model• Large difference between Wang vs soil spring lateral loads

• SASSI Model:

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Structural ElementsSASSI-2D

Beam element SASSI 2-D

STAAD – 2-D Model T-CLC-H-01111

Grade Level

Single Tunnel Analysis: Comparison

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Analysis Method D/C of moment on Single tunnel wall using LB soil profile

Wang Method / 1.14

Soil Spring Approach

/ 0.22

SASSI / 0.37

Comparable results between the soil spring analysis approach and the SASSI Analysis with LB Soil Profile

Demands from Wang method are much larger

STAAD ‐ Soil Spring

SASSI Single Tunnel Analysis Output- Moment on wall

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Comparison of SASSI to Existing Analysis for Single Tunnel- Moment on wall

High StrengthSoil Profile

Maximum D/C using Analysis Method in STAAD Maximum D/C using SASSI

Lower Bound 0.2210.83 ∗

29.4 ∗ 0.37

Best Estimate 0.195.6 ∗

29.4 ∗ 0.17

Upper Bound 0.173.21 ∗

29.4 ∗ 0.11

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Single Tunnel Analysis: Racking - Wang vs. Analysis Approach vs. SASSI

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Analysis Method D/C of Shear on Single tunnel wall using LB soil profile

Wang Racking Method

8.4613.4 0.63

Soil SpringApproach

1.4713.4 0.11

SASSI 3.113.4 0.23

Wall Shear capacity as designed is 13.4

Comparable results between the STAAD soil spring analysis approach and the SASSI Analysis with LB Soil Profile

STAAD ‐ Soil Spring

SASSI Single Tunnel Analysis Output- Shear on wall

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SASSI Single Tunnel Analysis Output- Moment on Roof

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‐4.00

‐3.00

‐2.00

‐1.00

0.00

1.00

2.00

3.00

4.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Mom

ent (k‐ft/ft)

Distance from Left end (feet)

Single Tunnel SASSI & STAAD ANALYSIS  ROOF MOMENTS (BE)

SASSI Roof Moment

STAAD Trapezoidal load

STAAD Concentrated load

SASSI Single Tunnel Analysis Output- Shear on Roof

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Results and Conclusions

• For the SRS case study, seismic demand on the embedded tunnel wall and roof is 2 to 6 times greater using the Wang Racking Method vs. the results obtained from SASSI and a simplified soil spring approach.

• Use of Wang, while appropriate for new design, can yield very conservative results.– SRS case is on edge of applicability of Wang method

• Relatively shallow embedment (depth to height < 1.5)• Structure relatively very stiff

• For the SRS case study , the seismic demand on the wall and roof from SSI analysis are very close to those to the simplified soil spring approach

• Tunnel could not have been qualified using very conservative Wang Racking Method demands

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• EXTRA Slides beyond

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Overall Impact Example – Double Tunnel Moment

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Max D/C at bottom LC 125 to 128

D/C from calculation = 0.73Seismic demand from calculation = 0.31

Seismic demand from SASSI = 0.37

D/C based on SASSI = 0.73 – 0.31 + 0.37 = 0.79 < 1.0

Soil SpringApproach

9 ∗ /29 ∗ / 0.31

SASSI 10.83 ∗ /29 ∗ / 0.37

Overall Impact Example – Single Tunnel Shear

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Max D/C at End of Roof

D/C from calculation = 0.80Seismic demand from calculation = 0.045

Seismic demand from SASSI = 0.103

D/C based on SASSI = 0.80 – 0.045 + 0.103 = 0.86 < 1.0

Study Scope of Work

• The objective of the 2D SASSI analysis is to obtain initial comparison of the horizontal, seismic forces on the walls against the results from the current analysis using UB and LB soil profiles from SHAKE (Figure 3)– Using the simplified soil spring analysis methodology, additional results were obtained

using the UB soil profile for comparison to the results from the SASSI UB soil model (Figures 4 & 5)

• In SASSI, the tunnel is modeled with beam elements and the excavated soil region is modeled with two-dimensional “quadrilateral plane strain” elements (Figure 2)

• SASSI output also includes In-Structure-Response-Spectra (ISRS) at surface, roof and base level of the tunnel (Figure 6) and transfer functions (Figure 7)

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Existing Tunnel Analysis

• In the original calculation using the simplified soil spring approach, the controlling free-field, relative displacement based from the Best Estimate (BE), Upper Bound (UB) and Lower Bound (LB) soil profiles was used to obtain the racking point load and triangular distributed load on the wall (Figure 1)– LB soil profile yielded the controlling case

• If used without a soil spring at the base, the Wang racking methodology yields seismic force which exceeds the capacity on the tunnel without adding any other loads, i.e. lateral soil pressure, soil load on top of the tunnel (Figure 2)

• The original calculation used a racking approach with the addition of a soil spring beneath the base of the tunnel section to determine seismic load

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