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Transcript of Presentation IQPC Africa
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Seismic Design Aspects of Underground Structures
Asrat Worku (Dr-Ing) Gibb International, Nairobi Kenya (Formerly, Associate Professor at Addis Ababa University, Addis Ababa, Ethiopia)
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Outline 1. Types of UG Structures Addressed 2. Earthquake Effects on UG Structures 3. Performance of UG Structures to Earthquakes 4. Seismic Design Procedures 5. Seismic Hazard Analysis 6. Seismic Design Load Criteria 7. Ground Motion Parameters 8. Response of UG Structures to Ground Shaking 9. Large Ground Deformations 10. Conclusions
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1. Types of UG Structures The presentation focuses on tunnels
Cut-and-cover tunnels Bored tunnels Immersed tunnels
Most issues are applicable to other UG structures including Cut-and-cover structures Portal Structures Deep Chambers Waste Repositories (e.g.: nuclear)
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2. Earthquake Effects on UG Structures
Two major effects 1. Ground Shaking (major concern)
Due to seismic waves 2. Ground Failure
Liquefaction Slope instability Fault Displacement
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2. Earthquake Effects on UG Structures
Severity in both Effects depends on Structure geometry Depth to structure Soil properties Structural properties Ground motion characteristics
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2. Earthquake Effects on UG Structures
On-ground structures Inertia of the structure and resonance are
important
UG structures Inertia of structure (gross11kN/m3) is less than the
inertia of surrounding soil - mostly disregarded
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2. Earthquake Effects on UG Structures
Misguided conception exists due to the small structural inertia
However, seismic design of UG structures is governed by Free-field ground motion, and SSI
(see figures)
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2. Earthquake Effects on UG Structures
(Kawashima 2006)
Significant inertia effect
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2. Earthquake Effects on UG Structures
(Kawashima 2006)
Insignificant inertia effect
Similar frequency content
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3. Observed Performance of UG Structures to EQ Documented case histories of EQ damages to UG
structures exist (ASCE, JSCE, Researchers)
In western US UG structures built as early as 1927 Measured free-field PGA: 0.1g - 0.25g Observed damages to date are insignificant
(including during Loma Prieta and Northridge) However, experts warn: maximum anticipated
seismic events not reached Hashash et al, 2001
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3. Observed Performance of UG Structures to EQ Daikai Subway Station, Japan, exhibited
severest damages so far: Existing Conditions
Cut-and-fill, box-type construction Central columns at 3.5m interval Box: 17m wide by 7.17m high Columns: 0.4m by 1.0m in section and 3.82m high 4.8m overburden No seismic consideration in its design (1962)
Kawashima 2000, 2006
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3. Observed Performance of UG Structures to EQ Daikai Subway Station: Extent of Damage
Severe damage occurred during 1995 Kobe EQ 35 center columns damaged (See figure) Roof slab collapsed Road on the surface settled by 2.5m Columns with light shear r. bars failed Columns with additional zigzag r. bars survived Transverse walls provided at change of station width
were damaged saving the columns
Hashash et al, 2000; Kawashima, 2000, 2006
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3. Observed Performance of UG Structures to EQ Center column failure Mechanism of failure
Kawashima 2000, 2006
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3. Observed Performance of UG Structures in General Less damage than in surface structures
Damages decrease with depth
Cut-and-cover tunnels are more vulnerable than deep bored tunnels
Structures in rocks are safer than in soils
Stabilization of surrounding soil is more
effective than increasing liner thickness
Hashash et al, 2001
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3. Observed Performance of UG Structures to EQ - General
Damage may be related to PGA and PGV
Strong-motion duration is very important to fatigue and excessive deformation
Slope stability is important in portal structures
Damages to lined tunnels are less than in pipelines
Hashash et al, 2001
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4. Seismic Design Procedure
Step 1: Defining the Seismic Environment
Step 2: Evaluation of Ground Response to Shaking
Step 3: Assessment of Structural Behavior
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4. Seismic Design Procedure
Step 1: Defining the Seismic Environment Conducting Seismic Hazard Analysis (SHA)
Establishing Design Criteria
Establishing Design Ground Motion Parameters
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4. Seismic Design Load Procedure
Step 2: Evaluation of Ground Response
It involves evaluating Ground Shaking: the main focus here
Ground Failure
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4. Seismic Design Load Procedure
Step 3: Assessment of Structural Behavior
Establishing Seismic Design Loading Criteria
Determination of Response of UG Structures to Ground Deformation
Any Special considerations
Hashash et al, 2001
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5. Seismic Hazard Analysis
Characterizes potential for strong ground motions for a given region by studying Extent of active faulting, Potential for fault motion, and Recurrence rate
Two approaches available Deterministic seismic hazard analysis (DSHA) probabilistic seismic hazard analysis (PSHA)
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5.1. DSHA Aims at a particular seismic scenario to
summarize hazard at a site and involves 1. Identification of EQ sources: geometry, potential
(M) 2. Source-to-site distance of each 3. Identification of controlling EQ in terms of a
ground motion parameter: attenuation Relations are employed for this purpose
4. Definition of seismic hazard in terms of PGA, PGV, PGD, RS and TH of the design EQ
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5.2 PSHA Accounts for uncertainties in the size, location,
and recurrence rate of EQs probabilistically 1. Identification of EQ sources with probability
distribution of location for each 2. Characterization of seismicity/temporal
distribution 3. Determination of ground motion by all sizes of EQs
with uncertainties considered 4. Combination of uncertainties to establish the
probability that a given ground motion parameter will be exceeded for a given time period
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5.2 PSHA Seismic Hazard Maps (GSHAP)
PGA up to 0.24g in Africa
The EARS has possibly the highest hazard
SA may experience up to 0.16g
PGA for 475-years return period
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5.2 PSHA Seismic Hazard Maps
PGA up to 0.24g In EARS region
Many vulnerable populous cities and towns in EARS region
Capital cities with high hazard: Asmara, Djibouti, Addis Ababa, Juba, Kampala, Bujumbura
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5.2 PSHA Seismic Hazard Maps (GSHAP)
According to SABS 2010, SA may experience up to 0.1g from EQ And up to 0.2g from mining activities
SABS Standards Division, 2010
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5.2 PSHA Generally, site-specific seismic hazard studies are
recommended for major structures in a specific area
A lot has yet to be done in Africa regarding seismic hazard assessment, especially in EARS region
The lack of awareness among policy makers even engineers is quite alarming
In contrast to its relatively low seismic hazard, SA can be cited as a good example in updating seismic codes (e.g. SABS 2010)
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6. Seismic Design Load Criteria
Dual Criteria: 1. MDE: aims at life safety (corresponds to ULS)
In PSHA, 3 5% probability of exceedance in the
life span of the facility (usually 50 years)
Worst combination of DL, LL, EQ to be considered
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6. Seismic Design Load Criteria
Dual Criteria: 2. ODE: minimizes economic risk (corresponds to
SLS) Occurrence: at least once in design life In PSHA, 40 50% probability of exceedance Facility should be operational during and after
event with little or no damage Thus, response must remain elastic
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6. Seismic Design Load Criteria
Load Combinations: 1. MDE
Cut-and-cover tunnels
U=DL+LL+E1+E2+EQ
Bored tunnels U=DL+LL+EX+H+EQ
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6. Seismic Design Load Criteria
Load Combinations: 2. ODE Cut-and-cover tunnels
U=1.05DL+1.3LL+1.05(E1+E2)+1.3EQ
Bored tunnels U=1.05DL+1.3LL+1.5EX+H+1.3EQ
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7. Design Ground Motion Parameters
Maximum/effective A, V and D are employed to define MDE or ODE
Damage to UG structures are better correlated to particle v and u than to a
Most attenuation relations available for A, but also for V and D
In the absence of site-specific data, available relations may be used to estimate PGV and PGD from PGA (see Tables)
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7. Design Ground Motion Parameters (Power et al. 1996)
Mw Ratio: PGV(cm/s)/PGA(g)
Source-to-site distance (km)
0-20 20-50 50-100
Rock (vs>750m/s)
6.5 66 76 86
7.5 97 109 97
Stiff soil (200-750m/s)
6.5 94 102 109
7.5 140 127 155
Soft soil (
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7. Design Ground Motion Parameters (Power et al. 1996)
Mw Ratio: PGD(cm)/PGA(g)
Source-to-site distance (km)
0-20 20-50 50-100
Rock (vs>750m/s)
6.5 18 27 30
7.5 43 56 69
Stiff soil (200-750m/s)
6.5 35 41 48
7.5 89 99 112
Soft soil (
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8. Response of UG Structures
Modes of Response (see Figures)
1. Compression-extension
2. Longitudinal bending
3. Ovaling (for circular shapes)
4. Racking (for rectangular)
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8. Response of Ground Shaking
Hashash et al 2001
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8. Response of Ground Shaking
Hashash et al 2001
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8. Response of Ground Shaking
Hashash et al 2001
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8. Response of UG Structures
MAIN Focus: Response to ground shaking A number of approaches available
1. Free-field deformation Approach 2. SSI Approach 3. Seismic Deformation Method (for soft ground) 4. Numerical Approaches
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8.1 Free-Field Deformation (FFD) Approach FFD describes strains due to elastic plane
waves in the absence of structures It imposes the free-field deformation on the UG
structure Does not account for SSI Provides first-order estimate of structural
response Closed-form relations available FFD is effective tool for small soil deformations
(low-seismic areas, stiff soils)
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8.1 Free-Field Deformation (FFD) Approach Axial and Bending FFD is based on Newmarks (1968) idealization of
elastic waves (see sketch)
St. John and Zahrah (1987) used this to calculate axial and curvature strains analytically due to the three wave types shown schematically (see sketch)
All solutions are available in closed form: longitudinal, normal and shear strains and curvature due to P-, S- and Rayleigh waves
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8.1 Free-Field Deformation (FFD) Approach Axial and Bending
Power et al 1996
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8.1 Free-Field Deformation (FFD) Approach Axial and Bending
Power et al 1996
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8.1 Free-Field Deformation (FFD) Approach Axial and Bending Tunnel modeled as an elastic beam, combined
free-field axial and curvature deformations are obtained as
For P-waves:
For S-waves:
For Rayleigh waves (compression component):
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8.1 Free-Field Deformation (FFD) Approach - Axial and Bending
With increasing r, the curvature contribution increases
However, this component is generally small
Note: the apparent wave velocities, VP and VS, fall in
the range of 4-8km/s and 2-4km/s, respectively These are close to wave velocities in deep rock
than in the shallow soil
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8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation
Ovaling
refers to the distortion of circular tunnels (see Figure)
is caused by waves inducing transverse strains
Is predominantly due to vertically propagating shear waves
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8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation Non-perforated ground Perforated ground
Wang 1993
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8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation
In non-perforated ground (see Figure):
In perforated ground (see Figure):
This is an upper bound
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8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation
The perforated ground scenario
gives 2 to 3 times larger distortion than the non-perforated case
gives an upper bound distortion criterion
Provides a good estimate for thin linings
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8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation
The non-perforated ground scenario gives better estimate for lining stiffness
comparable with the medium
For stiffer linings, distortion can even be less than in the non-perforated case
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8.1 Free-Field Deformation (FFD) Approach Racking Deformation
Racking
refers to the distortion of rectangular tunnels (see Figure)
Associated deformations can be computed from shear strains available in closed form
Alternatively, numerical site response analysis can be used
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8.1 Free-Field Deformation (FFD) Approach Racking Deformation
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8.2 Soil-Structure-Interaction (SSI) Approach
Accounts for soil-structure interaction
Tunnels are modeled as beams on elastic foundation (see Figure)
SSI is accounted for quasi-statically through use of linear springs
No dynamic inertia interaction is considered
The internal forces are as shown (see Figure)
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8.2 Soil-Structure-Interaction (SSI) Approach - Model
(After Kawashima 2000)
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8.2 Soil-Structure-Interaction (SSI) Approach: Internal Forces Sectional forces Circumferential forces
Hashash et al . 2001
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8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending
The maximum axial strain (due to a 45-degrees incident shear wave):
A= free-field displacement response amplitude of idealized sinusoidal shear wave; Q= frictional force; L=Wave length; Ka= longitudinal spring stif
Hashash et al . 2001
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8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending
The maximum bending strain due to a zero-degree incident shear wave:
The maximum shear force:
Kt= transversal spring stiffness; Ic=mom. of inertia
Hashash et al . 2001
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8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending
The spring coefficients:
The wave length:
Where, for an assumed uniform soft soil layer over rock:
Hashash et al . 2001
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8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending
The ground displacement amplitude for a sinusoidal wave:
For free-field axial strains
For free-field bending strains
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8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending
A conservative estimate of the total axial strain is given by
Finally, the structure is designed to sustain these strains
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
The ovaling response of a tunnel is a function of the compressibility and flexibility ratios, C and F defined as:
C: a measure of extensional stiffness F: a measure of flexural stiffness
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
Assuming full slip conditions (for soft soils and severe shaking):
The diametric strain:
Maximum thrust: (see Figure) The maximum b. moment:
Where (See Plots)
K1= Lining response coefficient
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8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling
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8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
For most tunnels, the interface condition is between the full-slip and no-slip cases
The full-slip case may cause significant underestimation of Tmax
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
The no-slip condition can give maximum thrust as given by
Where the lining response coefficient is given by:
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
Variation of K2, and thus of Tmax, against C and F for =0.35 is as plotted (see graph)
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
The normalized lining deflection:
(see Plots)
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
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8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling
Observations from the plots: For F1 (softer lining in stiffer soil): The lining deforms more than the free field
For F: lining deflection equals that of the perforated ground
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking Box-type structures are less efficient to transmit
static loads Thus,
the walls and slabs are thicker and the structure stiffer SSI is more important than in circular tunnels
Besides, ground deformations may be larger due to Site amplification at shallow depth Decreased soil stiffness due to lower overburden
pressure Different nature of backfill
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking
The increased rigidity for statics reduces structural strains
Hence, design based on free-field strains is too conservative
Closed-form solutions are not available due to variable geometric characteristics
The stiffness of the soil in simple shear relative to the structure is the most important factor
(Wang 1993)
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking
It can be easily shown that the soil-to-structure flexibility ratio is given by (see Figure) Where W is the width and S1 is the unit racking
stiffness of the structure given by (see Figure)
(Hashash et al 2001)
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking
(Hashash et al 2001)
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking For simple structures the racking stiffness can be
determined from ordinary frame analysis
Thus, F for a one-barrel frame with moments of inertia, IR=IS and IW, for the slabs and walls is
F can similarly be obtained for other common forms
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8.2 Soil-Structure-Interaction (SSI) Approach - Racking
FE studies showed the following F0: structure is rigid; do not rack regardless of
ground distortion F1: Structure racking is larger than soil F: Nearly Zero stiffness of structure; same
deformation as the perforated ground
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8.2 Seismic Deformation Method
Emerged out of a 5-year research in Japan (1972-1977) for UG structures in soft ground
The modeling accounts for SSI Consists of idealizing the UG structure as
Beam on elastic foundation (for axial and bending deformations) (see Figure)
Spring-mass modeling 2D FE model for in-plane ovaling/racking
(After Kawashima 2006)
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8.2 Seismic Deformation Method Beam on elastic foundation
(Kawashima 2006)
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8.2 Seismic Deformation Method Beam on elastic foundation
The governing DE neglecting inertia Axial deformation:
Bending deformation:
The idealized ground deformation (see sketch):
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8.2 Seismic Deformation Method Beam on elastic foundation
(Kawashima 2006)
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8.2 Seismic Deformation Method Beam on elastic foundation
The wave length based on Guide Specifications: Where
VS and VSB: shear wave velocities of soil (average) and
rock; L1 and L2 are corresponding wave lengths
TS: fundamental natural period
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8.2 Seismic Deformation Method Beam on elastic foundation
The ground surface displacement amplitude: SV: design velocity response spectrum at bedrock
level The surface strains are determined by
differentiating the surface deformation, the amplitudes being
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8.2 Seismic Deformation Method Beam on elastic foundation
The ratio of the strain amplitudes:
For a uniform soil over rock, it can be easily shown that
Thus, for a uniform soil:
The strain ratio varies in the range of
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8.2 Seismic Deformation Method Beam on elastic foundation
The deformation of the structure is determined by solving the DEs
The internal forces for design easily follow from the constitutive laws
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8.2 Seismic Deformation Method Spring-mass system
(Kawashima 2006)
Soil mass is included
3D analysis is possible
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8.2 Seismic Deformation Method In-plane 2D FE model
(Kawashima 2006)
Suitable for ovaling/ racking
Analysis is in 2D
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9. Large Ground Deformations Large ground deformations during EQ are
associated with Liquefaction Fault displacement Slope Instability
Since UG structures are commonly long, They may generally cross soil formations susceptible
to liquefaction Crossing active faults may not be avoidable Certain structures like portals ca be susceptible to
slope instability Hence, considerations for these issues are equally
important as for the ground shaking
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10. Conclusions Knowledge is not as well established as in on-
ground structures
Measured data and studies are fewer
A few state-of-the-art reviews are available
Seismic loadings on UG structures are not as insignificant as commonly perceived
FFD and SSI are very important considerations
In contrast, structure inertia plays a minor role
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10. Conclusions
The FFD Approach is sufficient for anticipated small ground deformations (case in point: Africa?)
The SSI approach and SDM are also easy to use
For the continent: FFD, SSI and SDM approaches are recommendable Complicated numerical modeling do not appear to be
necessary, at least currently
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10. Conclusions
Considerations for large ground deformations are equally important
Adaptation of design guides is not difficult and is recommendable
Regular follow-up of the global state-of-the-art is helpful for improvement
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Thank You
Seismic Design Aspects of Underground StructuresOutline1. Types of UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures2. Earthquake Effects on UG Structures3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures to EQ 3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures to EQ3. Observed Performance of UG Structures in General3. Observed Performance of UG Structures to EQ - General4. Seismic Design Procedure4. Seismic Design Procedure4. Seismic Design Load Procedure4. Seismic Design Load Procedure5. Seismic Hazard Analysis5.1. DSHA5.2 PSHA5.2 PSHA Seismic Hazard Maps (GSHAP)5.2 PSHA Seismic Hazard Maps5.2 PSHA Seismic Hazard Maps (GSHAP)5.2 PSHA6. Seismic Design Load Criteria6. Seismic Design Load Criteria6. Seismic Design Load Criteria6. Seismic Design Load Criteria7. Design Ground Motion Parameters7. Design Ground Motion Parameters(Power et al. 1996)7. Design Ground Motion Parameters(Power et al. 1996)8. Response of UG Structures8. Response of Ground Shaking8. Response of Ground Shaking8. Response of Ground Shaking8. Response of UG Structures8.1 Free-Field Deformation (FFD) Approach8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach Axial and Bending8.1 Free-Field Deformation (FFD) Approach - Axial and Bending8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Ovaling Deformation8.1 Free-Field Deformation (FFD) Approach Racking Deformation8.1 Free-Field Deformation (FFD) Approach Racking Deformation8.2 Soil-Structure-Interaction (SSI) Approach8.2 Soil-Structure-Interaction (SSI) Approach - Model8.2 Soil-Structure-Interaction (SSI) Approach: Internal Forces8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Axial and Bending8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling8.2 Soil-Structure-Interaction (SSI) Approach Forces due to ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Ovaling8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Soil-Structure-Interaction (SSI) Approach - Racking8.2 Seismic Deformation Method8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Beam on elastic foundation8.2 Seismic Deformation Method Spring-mass system8.2 Seismic Deformation Method In-plane 2D FE model9. Large Ground Deformations10. Conclusions10. Conclusions10. ConclusionsThank You