Dynamic Earth Pressure Problems and Retaining Walls. Behavior of Retaining Walls During Earthquakes. Soil Dynamics week # 12

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Dulcie Andrews
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1 Dynamic Earth Pressure Problems and Retaining Walls 1/15 Behavior of Retaining Walls During Earthquakes - Permanent displacement = cc ' 2 2 due to one cycle of ground motion

2/15 Hence, questions are : 1 What is the change in earth pressure? 2 Where is its point of application? 3 How much displacement of the wall occurs? (What is the permissible displacement?

2 2/15 Hence, questions are : 1 What is the change in earth pressure? 2 Where is its point of application? 3 How much displacement of the wall occurs? (What is the permissible displacement?) Modification of Coulomb`s Theory - Inertia forces on the trial wedge in horizontal and vertical directions = Wa g and Wa 1 / g respectively 1 h / v ( a : horizontal acceleration, a : vertical acceleration) h v - During the worst conditions for wall stability Wa g acts toward the wall, 1 h / Wa 1 v / g acts downward (or upward)

3 3/15 - a g h α h =, av α v = g horizontal, vertical seismic coefficients - The forces acting on the wedge abc 1 : Weight of the wedge abc 1, W 1, acting at its CG. Earth pressure P 1 inclined at an angle δ to normal to the wall Soil reaction R 1 inclined at an angle φ to normal to the face bc1 Horizontal inertia force Wα 1 h Vertical inertia force Wα 1 v - Constant force polygon to obtain P ( ) 1 = P = P +Δ P total a d - The maximum value of P total is determined by considering other trial surfaces - Analytically, Ptotal 2 2 cos ( φ ψ α)(1 ± αv) = γ H cosψ cos αcos( δ + α + ψ) sin( φ+ δ)sin( φ i ψ) 2 {1 + [ ] } cos( α i) cos( δ + α + ψ) 2

Modified Culmann`s construction 4/15 - bs at an angle φ ψ with the horizontal line - bl = bl - use W ( W (1 ) 1α + W1 + α ) h v Point of Application of the total ( P ) a dyn - at midheight of the

4 Modified Culmann`s construction 4/15 - bs at an angle φ ψ with the horizontal line - bl = bl - use W ( W (1 ) 1α + W1 + α ) h v Point of Application of the total ( P ) a dyn - at midheight of the wall - at the upper third point of the wall Displacement analysis - no information on permissible displacement of retaining wall 1. Draw a dimensional sketch 2. Draw a line bs ' and bl (= bl ') 3. Intercept bd1, equal to the wt. of wedge abc 1, to a convenient scale along 4. Draw a line de 1 1 parallel to bl ( = bl ' ) 5. Trace a Culmann s line 6. Draw a line parallel to bs ' and tangential to the Culmann`s line. 7. Find de P a obtained bs '

5/15 Earthquake Loads on Footings (Pseudostatic method) Effect of moment only -

due to the shaking of structure i.e., horizontal acceleration force (lumped mass at

Effective width, B ' = B 2e Effect of trust only - Inclination Pp + F Pa FS = Q H F

5 5/15 Earthquake Loads on Footings (Pseudostatic method) Effect of moment only - Eccentricity M e = Q v Qv M : moment( = a l ) g Q v : central vertical static load due to the shaking of structure i.e., horizontal acceleration force (lumped mass at CG) B - For e < 6 Q e qmax = (1+ 6 ) A B B - For e > 6 Q 4B qmax = ( ) A 3B 6e - Effective width, B ' = B 2e Effect of trust only - Inclination Pp + F Pa FS = Q H F : Frictional Resistance Pa = kaγ h Pp = kpγ H, take ( 1 ~ ) of Pp

It should be capable of carrying, in tension or compression, a force equal to A a /4of the largest footing or column load ( A a

6 At the present state of practice for earthquake loading 6/15 - Bearing capacity & settlement may be calculated by the pseudostatic method - Interconnecting beams (Tie beams) be provided to tie the foundations. It should be capable of carrying, in tension or compression, a force equal to A a /4of the largest footing or column load ( A a =effective peak acceleration). ATC(1978) Tie beams - transmits the unbalanced shear and moment - reduces the differential settlement - PC pile no use(depends on the building class & earthquake intensity)

7 Dynamic Analysis for Pile Foundations 7/15 - Evaluate the free-vibration characteristics of pile-soil system Calculate the spectral displacement ( y g ) Maximum bending moment ( M ) Computation of soil reaction ( Px ( ) ) max - Preliminaries - Soil properties are known ( kn, h...) - Pile characteristics are known (size, EI, length, type) - Lateral load-deflection of the pile under static conditions - nondimensional frequency factor ( F SL1 ) (based on parametric study) (k varies linearly with depth) F = w W SL1 n1 2 g nh T T =, 5 EI n h w n1 : the first natural angular frequency (rad/sec) W / g : the lumped mass at the pile top k : the soil modulus T : the relative stiffness factor

8 Soil Dynamics week # 12 8/15 - the depth coefficient(z) Z= z (if Z max < 2, rigid body / if Z max > 5, long pile) T - the max. depth coefficient ( Z max ) Z max = D T

9 Soil Dynamics week # 12 9/15 - max. bending moment coefficients (Fig 7.24)

Soil Dynamics week # 12 10/15 Step-by-step procedures ① Estimate the dynamic soil modulus k (or nh ) (modified value from a static lateral load test based on the engineering judgement) ② Compute

10 Soil Dynamics week # 12 10/15 Step-by-step procedures ① Estimate the dynamic soil modulus k (or nh ) (modified value from a static lateral load test based on the engineering judgement) ② Compute the relative stiffness factor, T ③ Calculate the maximum depth factor Z max for a pile ; ( Z max should be > 5) ④ Read the frequency factor FSL1 for the Z max and the pile end condition from Fig 7.22

Soil Dynamics week # 12 11/15 ⑤ Estimate the dead load on the pile top mt = W / g ⑥ Determine the natural frequency wn1 wn1 = FSL1 W gnht 2 ⑦ Compute the time period Tn1 =

11 Soil Dynamics week # 12 11/15 ⑤ Estimate the dead load on the pile top mt = W / g ⑥ Determine the natural frequency wn1 wn1 = FSL1 W gnht 2 ⑦ Compute the time period Tn1 = 2π / wn1 ⑧ From Fig 7.25 determine the spectral displacement S d for assumed damping (for pile-soil system 5% damping may be assumed) maximum displacement of the pile head

reaction Pz = nh z yz(displacement of the pile at z) (refer to table 7.8 & Example 7.

12 9 Estimate the maximum bending moment in the pile section 12/15 M = B n T S (From table 7.7) 3 max me1 h d Pile section needs to be checked against this moment 10 Compute the soil reaction Pz = nh z yz(displacement of the pile at z) (refer to table 7.8 & Example 7.3) Compare this with the allowable Soil reaction : 1+ sinφ P = γ b z ( kg / cm 1 sinφ a ) = K σ b p v

13 Soil Dynamics week # 12 13/15

14 Soil Dynamics week # 12 14/15

15 15/15 11 Check on Design 1. Estimate the fixity of the pile head. In the absence of a realistic estimate, 50 percent fixity may be assumed. 2. Compute displacement. For 50 percent fixity, the displacement under seismic loading condition is = 1.5cm. For any other fixity of the pile head, linear 2 interpolation may be made. 3. Compute the maximum bending moment as for displacements Mmax = 1213 t cm( ) 4. The soil reaction needs to be interpolated at each point and a new diagram obtained

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure.

UNIT V. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. UNIT V 1. Define Active Earth pressure. The active earth pressure occurs when the wall moves away from the earth and reduces pressure. 2. Define Passive Earth pressure. The passive earth pressure occurs