An Overview of Geotechnical Earthquake Engineering

Transcription

1 An Overview of Geotechnical Earthquake Engineering Sudhir K Jain Slide 1 Outline Introduction to Seismic Design Principle Dynamic Soil Properties Site Effects Soil Structure Interaction Issues for Foundation Design Liquefaction Embankment Analysis Slide 2 1

2 Some Remarks on Seismic Design Principles Slide 3 Seismic Design Principle Large earthquakes are infrequent as compared to smaller earthquakes Should a structure meant for 50 years be designed to remain undamaged for an earthquake that may occur once in 500 years? The criteria is: Minor (and frequent) earthquakes should not cause damage Moderate earthquakes should not cause significant structural damage (but could have some nonstructural damage) Major (and infrequent) earthquakes should not cause collapse Slide 4 2

3 Seismic Design Principle A well designed structure can withstand a horizontal force several times the design force due to: Energy dissipation in a variety of ways, e.g., ductility Overstrength Redundancy In many cases, limited deformation may be acceptable, e.g., slopes, retaining walls. Slide 5 Response Reduction Factor Hence, structure is designed for seismic force much less than what is expected under strong shaking if the structure were to remain linear elastic Earlier codes just provided the required design force It gave no direct indication that the real force may be much larger Now, the codes provide for realistic force for elastic structure and then divides that force by some factor. This gives the designer a more realistic picture of the design philosophy. Slide 6 3

4 Increase in Permissible Stresses Applicable for Working Stress Design Permits the designer to increase allowable stresses in materials For instance, 33% - 50% for load cases including seismic loads. Slide 7 Site Specific Design Criteria Seismic design codes meant for ordinary projects For important projects, such as nuclear power plants, dams and major bridges site-specific seismic design criteria are developed These take into account geology, seismicity, geotechnical conditions and nature of project Site specific criteria are developed by experts and usually reviewed by independent peers A good reference to read on this: Housner and Jennings, Seismic Design Criteria, Earthquake Engineering Research Institute, USA, Slide 8 4

5 Shaking is not the only issue! Ground shaking can affect the safety of structure in a number of ways: Shaking induces inertia force Soil may liquefy Sliding failure of founding strata may take place Fire or flood may be caused as secondary effect of the earthquake. Fault rupture may pass through the structure Slide 9 Direction of Ground Motion During earthquake shaking, ground shakes in all possible directions. Direction of resultant shaking changes from instant to instant. Structure must withstand maximum ground motion occurring in any direction. Peak ground acceleration may not occur at the same instant in two perpendicular directions. Hence for design, maximum seismic force is not applied in the two horizontal directions simultaneously. Slide 10 5

6 Direction of Ground Motion On average, peak vertical acceleration is onehalf to two-thirds of the peak horizontal acceleration. Structures experience vertical acceleration equal to gravity (g) at all times. Vertical acceleration is a concern for: Stability issues (e.g., slopes) Large span structures Cantilever members Prestressed horizontal members Slide 11 Load Combination 0.9DL 1.5EL Horizontal loads are reversible in direction. In many situations, design is governed by effect of horizontal load minus effect of gravity loads. In such situations, a load factor higher than 1.0 on gravity loads will be unconservative. Hence, a load factor of 0.9 specified on gravity loads. Many designs of footings, columns, and positive steel in beams at the ends in frame structures are governed by this load combination Slide 12 6

7 Dynamic Soil Properties Slide 13 Dynamic Soil Properties Behaviour of soil complex under static loads. Even more complex under dynamic loads Need for simple methods to characterize complex behaviour Analysis techniques: Equivalent linear models Cyclic non-linear models Advanced constitutive models Slide 14 7

8 Shear Modulus Soil stiffness depends on strain amplitude, void ratio, mean principal effective stress, plasticity index, over consolidation ratio, and number of loading cycles Shear Modulus Tangent modulus Secant modulus Shear modulus varies with strain level. It is high at low strains Slide 15 Shear Modulus Figure: Hysteretic stress-strain response of soil subjected to cyclic loading Slide 16 8

9 Dynamic Properties Shear modulus decreases with strain increase Damping increases with strain increase Slide 17 Maximum Shear Modulus (G max ) Can be obtained in a number of ways: shear wave velocity, laboratory tests, and empirical relationships Shear wave velocity obtained from geophysical tests at strains lower than about 3x10-4 % G max = ρv s 2 Slide 18 9

10 Depth (m) 3/3/2013 Soil Properties Exploration data converted to shear modulus: G max = 65N [Seed, and Idris 1983] G max = 1000[35(N 60 ) 0.34 ] (σ ) 0.4 [Seed,Wong,and Idris, 1986] G max = 1000[20(N 1,60 ) 0.33 ] (σ ) 0.5 [Seed,Wong,and Idris, 1986] G max = 325(N 60 ) 0.68 [Imai, and Tonouchi, 1982] G max = K (N 60 ) 0.66 [PWRI, 1998] Where, N 60 = SPT value, uncorrected for over-burden pressure N 1,60 = SPT value, corrected for over-burden pressure Slide 19 σ = Effective soil pressure Soil Properties Small strain Shear Modulus (G max ) Tends to vary significantly, depending on which relationship is used Small-strain Shear Modulus(G max ) (kn/m 2 ) 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 6.E+05 7.E+05 8.E Eqn (1) 100 Eqn (5) Eqn (2) Eqn (4) Eqn (3) 300 G max (Eqn 2) G max (Eqn 3) G max (Eqn 5) Gmax (Eqn 1) G max (Eqn 4) Slide 20 10

11 Ground Motion Along Depth Peak amplitude of underground motion is smaller than that at the surface Variation of amplitude depends on Earthquake characteristics Frequency content Type of soil and its distribution along depth Slide 21 Ground Motions Along Depth Vertical distribution PGD Vertical distribution PGV Vertical distribution PGA Figure: Distribution of peak amplitude of ground motion along depth, (Kanade, 2000) Slide 22 11

12 Spectral Acceleration (g) 3/3/2013 Ground Motions Along Depth Time perios (s) Artificially generated time history [SIMQKE -1] Functional - Target response spectrum Safety - Target response spectrum Functional - Generated response spectrum Safety - Generated response spectrum Known Spectrum Back calculated time history [SHAKE 2000] Slide 23 Ground Motions Along Depth Response time history [SHAKE 2000] Response time history [SHAKE 2000] Response time history [SHAKE 2000] Assumed earthquake Corresponding Artificially generated response time history [SIMQKE-1] spectrum [SMSIM] Figure: Schematic representation of procedure used for artificially generated time histories for earthquake motion Slide 24 12

13 Underground Structures When seismic waves hit the ground surface, these are reflected back into ground The reflection mechanics is such that the amplitude of vibration at the free surface is much higher (almost double) than that under the ground Codes allow the design spectrum to be one-half if the structure is at depth of 30m or below. Linear interpolation for structures and foundations if depth is less than 30m. Slide 25 Site Effects Slide 26 13

14 Site Effects Motion at the base rock different from that at the top of soil. Local amplification of the earthquake motion due to the soil profile at the site. Site Effect. Slide 27 Mexico Earthquake of 1985 Earthquake occurred 400 km from Mexico City Great variation in damages in Mexico City Some parts had very strong shaking In some parts of city, motion was hardly felt Ground motion records from two sites: UNAM site: Foothill Zone with 3-5m of basaltic rock underlain by softer strata SCT site: soft soils of the Lake Zone Slide 28 14

15 Mexico Earthquake of 1985 PGA at SCT site about 5 times higher than that at UNAM site Epicentral distance is same at both locations Time (sec) Figure from Kramer, 1996 Slide 29 Mexico Earthquake of 1985 Extremely soft soils in Lake Zone amplified weak long-period waves Natural period of soft clay layers happened to be close to the dominant period of incident seismic waves This lead to resonance-like conditions Buildings between 7 and 18 storeys suffered extensive damage Natural period of such buildings close to the period of seismic waves. Slide 30 15

16 Site Response Amplification Depends on: Soil properties (shear modulus, damping) Soil depth Contrast in soil properties More amplification if greater contrast Intensity of ground motion Soil is elastic at low strains Shear modulus decreases and damping increases as soil strain increases More amplification for weak motion Slide 31 Site Response Amplification Figure: Relationship between maximum acceleration on rock and on soft sites (Idriss, 1990, 1991). Slide 32 16

17 Site Response Amplification Slide 33 Site Response Amplification Figure: Procedure for modifying ground motion parameters from a seismic hazard analysis to account for the effects of local site conditions Slide 34 17

18 Site Response Amplification Figure: Two hypothetical soil deposit overlying rigid bedrock: (a) site A; (b) site B. Soils are identical, except the s- wave velocity of the soil at site B is four times greater than that at site A. Slide 35 Site Response Amplification Figure: Amplification functions for sites A and B. Note that the softer soil at site A will amplify low-frequency input motions much more strongly than will the stiffer soils of site B. At higher frequencies, the opposite behaviour would be expected. Slide 36 18

19 Spectral Acceleration Coefficient (S a /g) 3/3/2013 Soil Effect Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996 Period (sec) Slide 37 Soil Effect This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites. Fig. from IS: Period (s) Slide 38 19

20 Soil Effect Modern Codes (e.g., IBC) classify the soil type based on weighted average (in top 30m) of: Soil Shear Wave Velocity, or Standard Penetration Resistance, or Soil Undrained Shear Strength Slide 39 Shape of Design Spectrum The three curves in IS1893 have been drawn based on general trends of average response spectra shapes. In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected. Slide 40 20

21 Soil Structure Interaction Slide 41 Soil Structure Interaction If there is no structure, motion of the ground surface is termed as Free Field Ground Motion Normal practice is to apply the free field motion to the structure base assuming that the base is fixed. This is valid for structures located on rock sites. For soft soil sites, this may not always be a good assumption. Slide 42 21

22 Soil Structure Interaction Presence of structure modifies the free field motion since the soil and the structure interact. Hence, foundation of the structure experiences a motion different from the free field ground motion. The difference between the two motions is accounted for by Soil Structure Interaction (SSI) SSI is not the same as Site Effects Site Effect refers to the fact that free field motion at a site due to a given earthquake depends on the properties and geological features of the subsurface soils also. Slide 43 Soil Structure Interaction Consideration of SSI generally Decreases lateral seismic forces on the structure Increases lateral displacements Increases secondary forces associated with P- delta effect. For ordinary structures, one usually ignores SSI. Slide 44 22

23 Radiation Damping Radiation of energy to infinity Also called geometric damping or geometric attenuation Ground Surface Structure Scattering Wave Transmitted Wave Reflected Wave Artificial Boundary Infinite Soil Medium Analytical Region Slide 45 Issues for Foundation Design Slide 46 23

24 Foundations Lessons from Past Earthquakes: Seismic damage, particularly to low height bridges, often caused by foundation failures. Foundation failures could be due to: Excessive ground deformation Loss of stability Bearing capacity problem Large foundation displacements may cause: Relative shifting of and damage to the superstructures, Damage to the bearings Backfills cause large forces on abutments. Slide 47 Foundations Wing walls may break loose from the abutments due to excessive backfill forces. Poor soils (soft soil and a high water table) contributed to a lot of damage to bridges in the past earthquakes. Examples: Nigata earthquake of 1964 Alaska earthquake of Slide 48 24

25 Modes of Foundations Failure Slide 49 Modes of Failure for Spread Footings Slide 50 25

26 Modes of Failure for Pile Footings Slide 51 Shallow Foundations in Clay Cyclic loading during earthquake Generally, clay does not loose much strength during cyclic undrained loading There may be some settlement, lateral movement or rotation, depending on Factor of safety under static condition Generally, good seismic performance due to adequate factor of safety in static loading Concern: site effects Slide 52 26

27 Shallow Foundations in Dry Sand Under cyclic shear, dry sand reduces in volume Settlement of ground (and hence the foundation) during earthquake motion Settlement more significant for loose sand than for dense sand Structure: part on shallow footing and part on end bearing piles: Part on footing may undergo settlement relative to the other part Slide 53 Shallow Foundation in Saturated Sand Liquefaction is a major concern Liquefaction Geologically young sand Saturated sand Loose sand Right particle size distribution Liquefaction can occur at the same site in subsequent earthquakes Slide 54 27

28 Shallow Foundations (Contd ) Lateral flow (lateral spreading) of liquefied sand can occur Liquefaction leads to surface settlement after the water pressure dissipates Liquefaction occurs first adjacent to the spread footing and then under it Liquefaction may occur after the earthquake motion has stopped Slide 55 Deep Foundations in Clay Gapping may occur near the ground surface Pile foundation failures in buildings in the Mexico 1985 earthquake Due to low factors of safety Development of a gap adjacent to a pile subject to cyclic lateral load in clay (after Swane and Poulos, 1984). Slide 56 28

29 Deep Foundations in Sand Bridge performance in Alaska (1964) earthquake (Ross et al 1969) shows: Large foundation displacements for foundations in saturated sands Foundations in gravel and gravelly sands have much less damage Foundations on rock not damaged Foundations by piling through sands to bedrock have minor damage Slide 57 Foundations on Raked Piles Particularly vulnerable to severe damage during earthquakes Slide 58 29

30 Liquefaction Slide 59 Liquefaction In case of loose or medium dense saturated soils, liquefaction may take place. Sites vulnerable to liquefaction require Liquefaction potential analysis. Remedial measures to prevent liquefaction. Else, deep piles are designed assuming that soil layers liable to liquefy will not provide lateral support to the pile during ground shaking. Slide 60 30

31 Liquefaction Analysis Difficult to obtain undisturbed samples Approach based on in-situ tests preferred SPT and CPT based procedures are popular Simplified procedure of Seed and Idriss used with SPT values Slide 61 Liquefaction Analysis (Example) North Bank: Rail and Road : At Center of Embankment : Water Level 1.0 m below GL amax/g 0.60 h w 1.00 g w 0.98 h emb g emb 1.85 g sub 0.85 M 7.00 D Rng Depth %Fine g sat s v u 0 s v ' Avg.N C N C 60 (N l ) 60 r d K m K a K s CSR eq CSR 7.5 CSR L FS liq CSR eql % e D V (N l ) 60 Greater than 30 hence soil is Non - Liquefiable rd is calculated at the center of depth range below top of embankment TOTAL D 0.23 Units : Tons & Meters Slide 62 31

32 Liquefaction Analysis (Example) S.No. Details Depth of Liquefaction Functional Evaluation Motion (0.1g) Soil Settlement 1. North Embankment (Rail & Road) South Rail Embankment South Road Embankment - - Safety Evaluation Motion (0.6g) 4. North Embankment (Rail & Road) South Rail Embankment South Road Embankment Slide 63 Embankment Analysis Slide 64 32

33 Issues for Embankments Slope failure due to Inertial loading, and/or Softening of material strength or liquefaction Fault displacement under the foundation Not being addressed here Slide 65 Two Methods Pseudo-static slope stability analysis Factor of safety concept Permanent deformation analysis as per Newmark s sliding block approach Slide 66 33

34 Pseudo-Static Analysis Complex ground shaking replaced by a single constant unidirectional pseudo-static acceleration Ensure adequate factor of safety against sliding How to choose seismic coefficient and factor of safety? Slide 67 Newmark s Sliding Block Model Developed originally for evaluation of seismic slope stability Motivated by concerns about realistic ground motions that are much higher than the traditional design based on pseudo-static stability analysis If FOS slid < 1.0 What will happen? Will the structure collapse? Not, if the permanent deformation is within an acceptable limit Slide 68 34

35 Newmark s Sliding Block Model W θ N T Time (s) Figure: Development of permanent displacement for actual earthquake ground motion Slide 69 Newmark s Sliding Block Model Deformations accumulate when the rigid body acceleration exceeds the yield acceleration. Slide 70 35

36 Embankment Analysis (Example) Slide 71 Embankment Analysis (Example) Assuming No Liquefaction Static load (only self weight): FOS=1.99 Pseudo-static: Yield coeff (FOS=1.0) is 0.275g FOS Approach by: Terzaghi (1950): Yield coeff. should be >0.20g Mercuson (1981): Yield coeff. > 0.2g-0.3g Hynes and Franklin (1984): Yield coeff of 0.1g will give permanent deformation less than 1m. Slide 72 36

37 Embankment Analysis (Example) Permanent Deformation by Newmark s Sliding Block Concept Makdisi and Seed (1978) approach: 5-15 mm Ambraseys and Menu (1988): 39 mm Yegian et al. (1991): 30mm Permanent deformation of about 40mm quite acceptable. Slide 73 Liquefaction of Sub-Soil Liquefied soil layers may not transmit significant amount of shear waves. Will the embankment be stable under its own weight? Liquefied soil layers will loose considerable amount of strength. Slide 74 37

38 Embankment Analysis (Example) Residual strength of liquefiable soil strata considered as per Seed and Harder (1990) FOS against self weight: 1.39 for North Embankment 1.18 for South Rail Embankment 1.31 for South Road Embankment Embankment will be stable due to its own weight after foundation soils have liquefied Slide 75 Liquefaction of Sub-Soil Figure: Relationship between Corrected Clean Sand Blow Count (N 1 ) 60 and Undrained Residual Strength (S r ) (Seed and Harder, 1990) Slide 76 38

39 Embankment Analysis (Example) Conservative Assumptions: Liquefaction occurs early during shaking Base of embankment still sustains PGA of 0.60g Deformations computed for 0.60g but with residual strength of liquefiable soils Slide 77 Embankment Analysis (Example) Analysis Using Residual Strength Details FOS for Static Case (No earthquake) Yield Acceleration (for FOS = 1.0) North Bank Embankment South Bank Embankment Rail Road g 0.048g 0.08g Permanent Displacement Considering PGA = 0.6g (in mm) Ambraseys and Menu (1998) Yegian et al. (1991) Makdisi and Seed (1978) Slide 78 39

40 Embankment Analysis (Example) Deformation of 500mm: acceptable. Deformation of 1300mm: on the higher side; but can be handled as an emergency measure in a relatively short time These deformations are for maximum embankment height and with conservative assumptions Remedial measures not recommended. Slide 79 Slide 80 40