Lateral Earth Pressures and Retaining Walls

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Vincent Bruce
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1 Lateral Eart ressures and Retaining Walls Tyes RETINING WLLS are usually built to old bak soil mass Reinforement Reinforement ssistant rof. errak Teymur. Gravity. Semi-Gravity 3. Cantilever Counterfort Streter 5. Crib Wall eaders Filled wit soil 4. Counterfort Fae of wall Design asi soil arameters; Unit weigt of soil ngle of frition Coesion Ten te lateral ressure distribution will be known. Tere are ases in te design of a retaining wall; Te retaining wall is eked for stability: overturning, sliding and bearing aaity failures. Ea omonent of te retaining wall is eked for adequate strengt and te steel reinforement. Emirial relationsis related to te design of walls (ii, )

Counterfort Fae of wall Design asi soil arameters; Unit weigt of soil ngle of frition Coesion Ten te lateral ressure distribution will be known.

2 Lateral Eart ressure t Rest Te total fore: σ v q σ q (q+) + q + were + 3 σ : oeffiient of atrest eart ressure σ v + u / ' /3 sin for normally onsolidated soil If te water table is loated at det <, te at-rest ressure diagram will be as sown. q + q sat GWT q σ (q+ ) (q+ + ) w u sat - w t, σ σ v q t, σ σ v (q+ ) t, σ σ v (q+ +' ) + ( q + ) + ' + ω Rankine tive Eart ressure Relating te rinial stresses for a Mor s irle tat toues te Mor-Coulomb failure enveloe; Wall movement to left x σ v 45+/ σ Rotation of wall about tis oint 45+/ Te Mor-Coulomb failure enveloe is defined by; τ + σ tan Te Mor s irle will tou te Mor-Coulomb failure enveloe reresenting te failure ondition in te soil mass. σ σ a, were σ a is te Rankine ative ressure. σ tan σ tan 45 + σ σ v and σ 3 σ a Tus σ tan v σ a tan 45 + σ a σ v a - a were a tan (45-/); Rankine ative ressure oeffiient owever te ative eart ressure ondition will be reaed only if te wall is allowed to yield suffiiently. Te amount of outward dislaement of te wall neessary is about. to.4 for granular soil bakfills and about. to.4 for oesive bakfills.

q + q sat GWT q σ (q+ ) (q+ + ) w u sat - w t, σ σ v q t, σ σ v (q+ ) t, σ σ v (q+ +' ) + ( q + ) + ' + ω Rankine tive Eart ressure Relating te rinial stresses for a Mor s irle tat toues te

3 Coulomb s tive Eart ressure R a β-δ W θ - β is te angle, te bak fae of te retaining wall makes wit te oriontal. is te angle tat te bakfill makes wit te oriontal. δ is te angle of frition between te soil and te wall. Te ative fore er unit lengt of te wall, a will be inlined at an angle of δ to te normal to te bak fae of te wall. a : eigt of wall a Te value of te wall frition angle, δ is between / and /3. Rankine assive Eart ressure Rankine assive Eart ressure Diretion of wall movement x σ v σ 45-/ Rotation of wall about tis oint Te oriontal stress σ at tis oint is referred to as 45-/ te Rankine assive ressure, σ σ v + were tan (45+/); Rankine assive eart ressure oeffiient Te magnitude of te wall movements, x required to develo failure under assive onditions are; Soil Tye x (for assive ondition) Dense sand.5 Loose sand. Stiff lay. Soft lay.5 3

a : eigt of wall a Te value of te wall frition angle, δ is between / and /3.

4 Coulomb s assive Eart ressure Rankine tive and assive Eart ressure for Inlined Granular akfill sin ( β ) sin( + δ )sin( + ) sin β sin( β + δ ) sin( β + δ )sin( β + ) : Coulomb s assive ressure oeffiient Range of Wall Frition ngle akfill materialδ(º) Gravel 7-3 Coarse sand -8 Fine sand 5-5 Stiff lay 5- Silty lay -6 /3 σ a a a a a os os + os + os σ a a os os os os os os os os os os liation of Lateral Eart ressure Teories to Design Retaining Wall Stability ) Safety gainst Overturning (Rotational stability) : Cantilever Gravity W C /3 W s W C W s /3 W W s V Consider fores W C, W S, V, Take moment w.r.t C (TOE) lokwise : resisting (M R ) (W C, W S, V )a.lokwise :overturning (M O ) ( ) C if not inrease te base ;use iles ;inrease wall dimensions. F s (for oesive bakfill) and.5 (for granular bakfill) 4

of Lateral Eart ressure Teories to Design Retaining Wall Stability ) Safety gainst Overturning (Rotational stability) : Cantilever Gravity W C /3 W s W C W s /3 W W s V Consider fores W C, W S, V,

5 Retaining Wall Stability ) Safety gainst ase Sliding : Driving Fore : Ignore : V Resisting fore :R R + ( ΣV ) tan + + ( ΣV ) tan + Fs os.5 W W s V D If base key : D + D use redued and ( design (,5~,67), design (,5~,67) ) if not inrease ; rovide key ;stronger bakfill (imort soil exansive) ; install tiedown anors Use stronger bakfill Install tiebak anors D,, R,, rovide key Extend eel Install tiedown anors(if large) 3) earing aaity failure. F s 3q u /q max ase ressures : 4) Dee Seated Sear Failure : q all : allowable bearing aaity of foundation soil Sum of vertial W s W V fores ΣM R ΣM D W +W s + v x ΣV ΣV e e x ΣV 6e qmax ( ± ) x min * q min / q max q min > (no tension) q max < q all Weak soil 5) CEC FOR SETTLEMENTS (Conventional) : 6) REINFORCEMENT DESIGN (Strutural Design) : ossible failure surfae CONVENTIONL NLYSIS 5

Install tiebak anors D,, R,, rovide key Extend eel Install tiedown anors(if large) 3) earing aaity failure.

6 Comments Relating to Stability Te lateral fore of te bakfill will deend on (Casagrande, 973); Effet of temerature (freee and taw), Groundwater flutuation, Readjustment of te soil artiles due to ree and rolonged rainfall, Tidal anges, eavy wave ation, Traffi vibration, Eartquakes. Gravity Retaining-Wall Design for Eartquake Conditions Coulomb s ative eart ressure teory an be extended to take into aount te fores aused by an eartquake. ~,6,5 δ ae k W β k v W W k θ tan kv k k v oriontal EQ a. om. a. due to gravity, g vertial EQ a. om. g E ( kv) E sin ( + β θ ) E sin( + δ )sin( θ ) osθ sin β sin( β θ δ ) + sin( β δ θ )sin( + β) Drainage from te akfill of te Retaining Wall Seet ile Walls are widely used for bot large and small waterfront strutures. used for ea erosion rotetion Stabiliing ground sloes Soring walls of trenes and oter exavations and for offerdams. owles, 997 6

Gravity Retaining-Wall Design for Eartquake Conditions Coulomb s ative eart ressure teory an be extended to take into aount te fores aused by an eartquake.

7 Seet ile Walls Seet ile Walls Tyes: Wooden reast onrete Steel Constrution Metods:. akfilled struture. Dredged struture Seet ile onnetions: Seet iles an be ategorised as: a) Cantilever b) nored Cantilever Seet ile Walls -Used for small retaining eigt ( ft 6 m above dredge line) ermanent : sands, gravels Temorary : oter soils -Stability of antilever seet ile wall : due to assive resistane develoed below te lower soil surfae a) Tumb and finger tye b) all and soket tye Cantilever Seet ile Walls nored Seet ile Walls Failure mode Dredge line tive assive tive assive *fixing moment at tive d R assive Design Idealisation dditional suort to seet ile walls an be given by baks (anored) near te to of te wall (Used in dee exavation & water front onstrution ). Tie Rod (steel ables) Net assive Resistane below : given wit R. design : Σ M determine d. Ten d is inreased arbitrarily by % to allow for simlifiation of roedure. (.d : embedment) Σ F determine R ( Cek R / over,d ) d assive tive ending Moment Diagram Note: det of tension rak < det of tie. 7

gravels Temorary : oter soils -Stability of antilever seet ile wall : due to assive resistane develoed below te lower soil surfae a) Tumb and finger tye b) all and soket tye Cantilever Seet ile Walls

8 nored Seet ile Walls Seet iles wit nors Wen tere is a dee exavation DESIGN ROCEDURE: - Calulate tive & assive ressures in terms of (unknown) det of embedment, d. - Usually Fs is alied to assive ressures 3- Take ΣM ; obtain ubi equation in terms of d. Solve for d. Inrease d by % in quay walls. 4- Take ΣF ; solve for T. 5- lot moment diagram & determine maximum bending moment. Determine required ross setion. d tive assive tive nor assive assive tive R Moment Diagram Note: Solved wit equivalent beam metod. Tyes of anor used in seet ile walls are:. nor lates and beams. Tie baks 3. Vertial anor iles 4. nor beams suorted by batter (omression and tension) iles Das, 995 Das, 995 8

5- lot moment diagram & determine maximum bending moment. Determine required ross setion.

9 raed Cuts (raed Exavations) Systems to suort te sides of exavations To suort walls of dee or sallow narrow trenes. Side view struts To view wales Seet iling ERT RESSURES GINST RCING SYSTEMS raed Cuts: Fixed Eart ressure funtion of Wall Dislaement: raing systems Reresented by emirial ressure enveloes CTIVE (Retaining walls) TERZGI & EC (967) EMIRICL RESSURE DIGRMS (sand) u (lay).65 medium to dense SND,5,5 3. to.4 Stiff CLY,5,5,75 4 m soft to medium CLY TERZGI & EC (967) EMIRICL RESSURE DIGRMS ),65 Times Rankine tive ) N:stability number N if N < 4 (elasti equilibrium) 3) N > 4 lasti equilibrium at te bottom ( N/ u > 4) m is usually,, but m,4 for soft NC lays. 4) N > 7 eaving u Strut Loads: INGES to make te system determinant C D C D C raed Cuts Wall onstrution & anorage installation in stages. anor R/C wall + CC +C DD 3 4 5,,C,D Strut Loads REINFORCED ERT Reinfored eart is a onstrution material omrising soil tat as been strengtened by tensile elements su as metal rods and/or stris, nonbiodegradable fabris (geotextiles), geogrids. Te benefiial effets of soil reinforement derive from a) soil s inreased tensile strengt and b) te sear resistane develoed from te frition at te soil-reinforement interfaes. 9

(Retaining walls) TERZGI & EC (967) EMIRICL RESSURE DIGRMS (sand) u (lay).65 medium to

10 REINFORCED ERT REINFORCED ERT Two tyes of geogrids: a) iaxial and b) Uniaxial Geotextiles ave four rimary uses in foundation engineering:. Drainage. Filtration 3. Searation 4. Reinforement inreases te load-bearing aaity of te soil.longitudinal rib.transverse bar 3.Transverse rib 4. Juntion REINFORCED ERT Faing (flexible) Footing Fill Coarse grained soil (drained) Reinforement (tensile stresses) *steel : life years *oter materials; -aluminium alloys -lastis -geotextiles,5 REINFORCED ERT,3 SSIVE Zone CTIVE Zone t-rest RESISTNCE C FCING : *re-ast onrete units (limited relative movement) *U-saed steel setions arranged oriontally COST : *more eonomi tan onrete antilever retaining wall FILURE : *Tensile failure of one element leads to rogressive ollase of te entire struture *Loal sliing leads to redistribution of tensile stress and gradual deformation of struture (not neessarily ollase) L v L e Max. tensile stress urve robable failure surfae Lateral Eart ressure tive

Juntion REINFORCED ERT Faing (flexible) Footing Fill Coarse grained soil (drained) Reinforement (tensile stresses) *steel : life years *oter materials; -aluminium alloys -lastis -geotextiles,5

Module 7 (Lecture 24 to 28) RETAINING WALLS

Module 7 (Lecture 24 to 28) RETAINING WALLS Topics 24.1 INTRODUCTION 24.2 GRAVITY AND CANTILEVER WALLS 24.3 PROPORTIONING RETAINING WALLS 24.4 APPLICATION OF LATERAL EARTH PRESSURE THEORIES TO DESIGN 24.5