COMPUTATION OF ACTIVE EARTH PRESSURE OF COHESIVE BACKFILL ON RETAINING WALL CONSIDERING SEISMIC FORCE

Transcription

1 COMPUTATION OF ACTIVE EARTH PRESSURE OF COHESIVE BACKFILL ON RETAINING WALL CONSIDERING SEISMIC FORCE Feng Zen Wang Na. Scool of Ciil Engineering and Arcitecture Beijing Jiaotong Uniersity Beijing Cina. Institute of Disaster Preention Science and Tecnology SanHe/YanJiao 0650 Cina Abstract: Tis paper based on aing researc conclusion according to te Coulomb s eart pressure teory from te condition of te equilibrium of te force wen te slide wedge was in limit equilibrium tinking about most infaust condition to retaining wall stability during eartquake a formula was deriated for te calculation of actie eart pressure of coesie or non-coesie backfill soils. Tis formula could be used in te calculation of eart pressure wit superimposed load uniformly distributed on any location of ground surface beind retaining wall. Some suggestions were proposed to te calculation of eart pressure in graity retaining wall design in ig frequency seismic region considering seismic force. Key words: Coulomb s teory; graity retaining wall; seismic force; actie eart pressure; uniformly distributed load INTRODUCTION Actie eart pressure computation metod about Graity style retaining wall (CHEN Xize 998; QIAN Jiauan et al. 000) is ery muc but all tis metods ae default. Tere is little error used te Coulomb s eart pressure teory to coesie-less soil; about actie eart pressure of coesie soil reference (GB ) fits for te situation tat uniformly distributed load act from top of retaining wall about te situation tat uniformly distributed load act from a distance to top of retaining wall reference (Feng Zen et al.008) gies a formula tat was deriated for te calculation of actie eart pressure of coesie or non-coesie backfill soils but it can not completely consider seismic force. To te question of retaining wall eart pressure computation reference (MatsuoH 94; MononobeN and H. Matsuo 99; Prakas. S. and B.M.Basanna 969; Prakas. S. and S. Saran 966) do some useful researc; but te conclusion of reference (MatsuoH 94; MononobeN and H. Matsuo 99) only can be used to coesie-less soil; reference (Prakas. S. and B.M.Basanna 969; Prakas. S. and S. Saran 966) do some researc about coesie soil but only fit for uniformly distributed load act from top of retaining wall. About te situation tat uniformly distributed load act from a distance to top of retaining wall considering seismic force (Figure ) tere is no precise simple computation to now. Tis paper based on reference (Feng Zen et al.008; Prakas. S. 984 ) gie a formula of actie eart pressure computation considering seismic force and uniformly distributed load q acting from a distance d to top of retaining wall do some necessary expansion to researces done by Feng Zen et al (008).

2 EARTH PRESSURE ABOUT BACKFILL SURFACE Suppose tere is a retaining wall te angle between wall back and ertical axis is ρ (Figure ) te response of retaining wall to ground moement under seismic force is like figure. Te backfill surface is leel from a distance d to top of retaining wall tere is uniformly distributed load q acting on te eart wedge ABC te forces acting on eart wedge is like figure. Let backfill surface is x axis and troug wall eel ertical line to x axis is y axis. Figure. Force acting on te soil wedge Figure. Response of Retaining wall to ground moement Expression of eart wedge self-weigt: W γ y ( () in wic: γ -eart graity density. If orizontal acceleration of eart wedge is a ertical acceleration of eart wedge is a ten orizontal inertial force is Wa / g ertical inertial force iswa / g in actual eartquake te most infaust condition to actie eart pressure is Wa / g act to wall direction so coose te direction tat can increase eart pressure in actual (Figure ). Now let: a g a α α g were α orizontal eartquake coefficient; α ertical eartquake coefficient.

3 Wen te eart wedge in limit equilibrium condition resistance of retaining wall and static eart to eart wedge is: F ( c y + E tanδ ) () cosρ T cl + N () in wic: δ - friction angle of wall back to eart ϕ- inner friction angle of eart; c - iscous force of wall back to eart c- iscous force of eart. l - lengt of BC. Resistance of retaining wall to wedge F is made of iscous resistance and friction resistance. Tinking about eery kind of factor (for example: decline of wall back coarseness) tis paper let: tan δ η c ηc η- coefficient in 0~. So resistance of retaining wall back is: η F ( cy + E) (4) cos ρ According to situation of eart body standing force x y direction equilibrium formula of force is: y Q + W F cos ρ T cosθ N sin θ E tan ρ ± ( W + Q) α 0 (5) x T sin θ N cosθ ( W + Q) α + E F sin ρ 0 (6) in wic: Q - sum of uniformly distributed load superimposed on wedge surface so Q qy( qd (7) take formula () ( ) ( 4 ) ( 7 ) to equilibrium formula(5) ( 6 ) remoe N get: clean up ten get: so qy( qd + ry ( cy E tan ρ η( cy + E ) E η( cy + E ) tan ρ + cy ± γ y γ y ( + qy( qd α ( + qy( qd α + ( γ y + qy)( ( γ y + qy)( + qd( ) + cy[ + η + tan θ η η tan ρ( + )] ± γ y ( + qy( qd ( tan tan ) α ϕ θ γ y ( + qy( qd α( + ) [( η tan ϕ )( ( + η)( ] E in limit equilibrium condition we get te force acting on retaining wall in direction x is:

4 were: E ωγ y + ωqy ζ qd ψcy ( [ + α ( + ) ± α ( )] ω ( η tan ϕ)( + ( + η)( (8) ζ ψ + α ( + ) ± α ( ) ( η tan ϕ)( + ( + η)( + η + tan θ η η( + ) ( η tan ϕ)( + ( + η)( Differentiate formula(8)to θ and let E θ 0 because denominator can not be 0 numerator must be 0 can get slim craze angle corresponding to most actie pressure. reader can deriate it referring to (Feng Zen et al.008. Let te lengt of AB is Sten y S cos ρ differentiate formula(8)to S ten we get Were: e ----positie pressure intension of x direction. Formula (9)diide cos ρ ten we get Were: σ -----positie pressure intension of x direction troug y axis. e ( ωγ y + ωq ψ c) cos ρ (9) σ ωγ y + ωq ψc (0) wen σ 0 from formula(0)we get te eigt of positie pressure intension equal zero is wen y 0 get te most positie pressure intension is ψ c q y 0 () ψ y γ σ ωq ψc () So get te sum of tension is E y 0 0 σ d y ( ωq ψc) () ω y EARTH PRESSURE OF LEVEL BACKFILL CRACK ZONE THAT BE HOMOGENEOUS REPLACEMENT

5 Te natural condition can gie great effect to soil property and can make fissure on soil surface. Tis paper use uniformly distributed load replacement referring to Feng Zen et al.(008). Look te soil upper intension zero point as uniformly distributed load q0 γ y0 te force acting on soil is like figure. Figure Forces acting on te soil wit uniform load substituted Moe axis x to zero point of positie pressure intension use x to express and let q q + q0 as uniformly distributed load y y y0 take to equilibrium formula(5) ( 6 ) ten E ωγ y + ωq y ζ qd ψ cy ωγ ( y y0 ) + ωq ( y y0 ) ζ qd ψc( y y0 ) (4) were ω ζ ψ same as formula(8). Look formula (4) if differentiate y ten we get: Were: σ -----positie pressure intension of x direction troug y axis. If y 0 ω q ψc ;if y 0 formula(4) (5) can cange to σ ωγ y ωq + ψc (5) E ωγ y ζ qd ωγ ( y y0 ) ζ qd (6) σ ωγ y ) (7) ( y 0 EARTH PRESSURE ABOUT DECLINING BACKFILL SURFACE Suppose tere is angle β between declining backfill surface to leel(look figure 4) still let backfill surface is x axis and troug wall eel ertical line to x axis is y axis according to te forces acting on eart wedge (look figure 4) x y direction equilibrium formula of force is: y ( Q + W ) cos β F cos ρ T cosθ N sinθ E tan ρ ( W + Q) α sin β ± ( Q + W ) α cos β 0 (8) x T sinθ N cosθ + E F sin ρ ( Q + W ) sin β ( W + Q) α cos β m ( Q + W ) α sin β 0 (9) were W T F Q same as formula() ( ) ( 4 ) ( 7 )

6 Figure 4. Forces acting on te soil wedge so in limit equilibrium condition we get te force acting on retaining wall in direction x is: E ωγ y + ωqy ζ qd ψcy in wic: ( [( ± α( ) + α( + ))cos β ω ( η tan ϕ)( + + ( + α( ) ± α( + ))sin β] ( + η)( (0) ζ ψ ( ± α ( ) + α ( + )) cos β + ( η tan ϕ)( + ( + α ( ) ± α ( + )) sin β ( + η)( + η + tan θ η tan ϕ η( + tan ϕ) ( η tan ϕ)( + ( + η)( If β 0 formula(0)cange to formula(8). Let E θ 0 people can get slim craze angle corresponding to most actie eart pressure reader can deriate it referring to Feng Zen et al.(008). pressure. Te eigt upper positie intension zero point computing troug () use aboe formula can sole eart EARTH PRESSURE OF DECLINING SURFACE BACKFILL CRACK ZONE THAT BE HOMOGENEOUS REPLACEMENT As aboe Te natural condition can gie great effect to soil property and can make fissure on soil surface. Tis paper use uniformly distributed load replacement referring to Feng Zen et al.(008). Look te soil upper positie intension zero point as uniformly distributed load q0 γ y0 te force acting on soil is like figure 5.

7 Figure 5. Forces acting on te soil wit uniform load substituted Moe axis x to zero point of positie pressure intension use x to express and let q q + q0 as uniformly distributed load y y y0 take to equilibrium formula(8) ( 9) ten E ωγ y + ωq y ζ qd ψ cy ωγ ( y y0 ) + ωq ( y y0 ) ζ qd ψc( y y0 ) () were ω ζ ψ same as formula(0). Look formula () if differentiate y ten we get: Were: σ -----positie pressure intension of x direction troug y axis. If y 0 ω q ψc ;if y 0 formula() () can cange to σ ωγ y ωq + ψc () E ωγ y ζ qd ωγ ( y y0 ) ζ qd () σ ωγ y ) (4) ( y0 To non-coesie soil let c 0 use aboe formula can sole. Reader can deriate it self. CONCLUSIONS Based on aing researc conclusion according to te Coulomb s eart pressure teory tis paper gets te following results: ()Do some necessary expansion to computation formula of reference (Feng Zen et al.008; Prakas. S. 984); ()Te metod of tis paper mainly fit for coesie soil also fit for non-coesie soil especially to te situation tat uniformly distributed load act from a distance to top of retaining wall considering seismic force use tis paper s metod can make computation of actie eart pressure is feasible and simple; ()Tis paper only can supply a approximate metod to computation of eart pressure because te factor affecting soil property is ery complex; (4)About te question of eart pressure considering layer soil or ground water and inertial force te autor write anoter article to express it.

8 REFERENCES CHEN Xize. (998). Soil Mecanic Ground and foundation. Beijing: Tsingua uniersity Press 69~00 QIAN Jiauan YIN Zong-ze. (000). Geotecnical teory and computing. Beijing: Cina Water Power Press 5~40 GB Code for design of building foundation. Feng Zen Wang Na Lin Wei LI Juwen. (008) Computation of actie eart pressure of coesie backfill on retaining wall considering inertial force. Journal of eartquake engineering and engineering ibration 8(): 5~56. Prakas. S. (984). Soil dynamic. Beijing: Water and Electric Power Press 9~ MatsuoH. (94). Experimental Study on te Distribution of Eart Pressure Acting on a Vertical Wall during Eartquakes. Japanese Society of Ciil Engineers 7() MononobeN and H. Matsuo. (99). On Determination of Eart Pressure During Eartquakes Proc. World Engineering CongressTokyo. Prakas. S. and B.M.Basanna. (969). Eart Pressure Distribution Beind Retaining Walls During Eartquakes Proc. Fourt World Conference on Eartquake Engineering Cileol.~48. Prakas. S. and S. Saran. (966). Static and Dynamic Eart Pressure Beind Retaining Walls Proc. Tird Symposium on Eartquake Engineering Roorkeeol.. 77~88.