Lateral Earth Pressures and Retaining Walls
RETAINING WALLS Lateral Earth Pressures and are usually built to hold back soil mass Retaining Walls Types
Reinforcement Reinforcement
Assistant Prof. Berrak Teymur 1. Gravity 2. Semi-Gravity 3. Cantilever
Headers Filled with soil Strectcher Counterfort 5. Crib Wall
4. Counterfort Face of wall
Design
Basic soil parameters; Unit weight of soil Angle of friction Cohesion Then the lateral pressure distribution will be known. There are 2 phases in the design of a retaining wall; The retaining wall is checked for stability: overturning, sliding and bearing capacity failures. Each component of the retaining wall is checked for adequate strength and the steel reinforcement.
Empirical relationships related to the design of walls (Azizi, 2000)
1 If the water table is located at depth z K0 (q+γH) 1 2 K0 (q+γH1+γγH2) γwH2 The total force: P0 = P1 + P2 = qK0H + H K0γ K =1− sinφ 2 where 0 H H for normally 1 1 γ 1 P + P 2 2 2 1 2 2 3 consolidated soil P0 = K0qH1 + K0 H1 + K0 (q + H1 )H 2 + K0 H 2 '+ γ ω H 2 z ′ = 2 2 2 P 0 Relatingσ the principal stresses for a Mohr’s circle that Rankine Active Earth Pressure touches theσ Mohr-Coulomb failure envelope; φ Wall movement to left σ σ ∆x 45+φ/2 45+φ/2 2 φ 1 = 3 tan 45 + + φ2c tan45 + 2 2 γ σ σ1=σv and σ3=σa z v z c φ φ 2 H Thus v = a tan 45 + + 2c tan45 + σh 2 2 σa=σvKa-2c Ka The Mohr’s circle will touch the 2 Rotation of wall Mohr-Coulomb failure envelope where Ka=tan (45-φ/2); Rankine active pressure coefficient about this point representing the failure condition in However the active earth pressure condition will be reached only if the wall is the soil mass. σh=σa, where σa is the allowed to ‘yield’ sufficiently. Rankine active pressure. The amount of outward displacement of the wall necessary is about 0.001H to The Mohr-Coulomb failure envelope is defined by; 0.004H for granular soil backfills and about 0.01H to 0.04H for cohesive τ = c + σ tanφ backfills. 2 The active force per unit length of the wall, Pa will be Coulomb’s Active Earth Pressure inclined at an angle of δ to the normal to the back face of the wall. β is the angle, the back face of the 1 2 retaining wall Pa = K a γH makes with the 2 horizontal. α is the angle that the backfill makes β-δ with the Pa horizontal. δ is the angle of W friction between R the soil and the H: height of wall θ -φ wall. 1 The value of the wall friction angle, δ is between φ/2 and 2φ/3. Rankine Passive Earth Pressure Rankine Passive Earth Pressure Direction of wall movement ∆x The horizontal stress σ at 45-φ/2 h this point is referred to as the Rankine passive γ 45-φ/2 σv z pressure, z c The magnitude of the wall φ σ =σ K +2c movements, ∆x required Soil Type ∆x (for passive condition) H σh p v p Kp to develop failure under Dense sand 0.005H where K =tan2(45+φ/2); Loose sand 0.01H p passive conditions are; Rankine passive earth Stiff clay 0.01H pressure coefficient Soft clay 0.05H Rotation of wall about this point 3 Rankine Active and Passive Earth Pressure for Coulomb’s Passive Earth Pressure β β Inclined Granular Backfill β φ δ 2 sin ( −φ ) δ α 1 2 K p = 2 P = γH K β φ α p p 2 sin( +δ )sin( + ) 2 sin sin( + )1− β γ sin( + )sin( +α) 1α 2 c=0 P = γH K σ = γzK a 2 a α a a K : Coulomb’s passive pressure z φ α p φ coefficient 2 2 σa cos − cos α− cos Pa K = cosα α a 2 2 φ Range of Wall H cos + cos − cos Friction Angle Backfill materialδ(º) α 1 2 H/3 α Pp = γH K p Gravel 27-30 α2 α Coarse sand 20-28 φ 2 2 Fine sand 15-25 cos + cos α− cos K p = φcosα Stiff clay 15-20 cos − cos2 − cos2 Silty clay 12-16 Retaining Wall Stability Application of Lateral Earth Pressure Theories 1) Safety Against Overturning (Rotational stability) : to Design Cantilever α α Gravity Consider forces WC, WS, PV, PH Ws Ws PV Take moment w.r.t ‘C’ (TOE) Ws Wc PA H H’ H H’ W PA W PA C C clockwise : resisting (MR) (WC, PH H/3 α H/3 α WS, PV)a.clockwise :overturning (MO) (PH) C B if not increase the base ‘B’ ;use piles ;increase wall dimensions. Fs=2 (for cohesive backfill) and 1.5 (for granular backfill) 4 Retaining Wall Stability 2) Safety Against Base Sliding : 1 If base key : P = γ D 2 K + 2c D K p 2 2 1 p 2 1 p use reduced c2 and φ2 (φdesign=(0,5~0,67) φ2 , cdesign= =(0,5~0,67) c2) Driving Force : PH if not increase B ; provide key ;stronger backfill (import soil ∴ Ignore : PV expansive) ; install tiedown anchors Resisting force :R Ws Install tieback anchors PV R = c2 B + (ΣV ) tan φ2 + Pp Wc PA Use stronger α backfill c2 B + (ΣV ) tanφ 2 + Pp Fs = ≥ 1.5 PH PA cosα D D1 c1,φ1,γ1 Extend heel R c2,φ2,γ2 Provide key B Install tiedown anchors(if φ large) 3) Bearing capacity failure. Fs=3=qu/qmax 4) Deep Seated Shear Failure : Base Pressures : qall : allowable bearing capacity of foundation soil Sum of vertical Ws PV forces Wc PA ΣM R − ΣM D Wc+Ws+Pv x = ΣV P Possible failure H ΣV e B e = − x surface 2 Weak soil CONVENTIONAL ANALYSIS A A ΣV 6e qmax = (1± ) B x min B*1 B qmin B/2 qmax 5) CHECK FOR SETTLEMENTS (Conventional) : B 6) REINFORCEMENT DESIGN (Structural Design) : qmin > 0 (no tension) qmax < qall 5 Gravity Retaining-Wall Design for Comments Relating to Stability Earthquake Conditions Coulomb’s active earth pressure theory can be extended to The lateral force of the backfill will depend on (Casagrande, take into account the forces caused by an earthquake. 1973); γ α horizontal EQ acc .comp . k = Effect of temperature (freeze and thaw), h acc .due to gravity , g kvW γ Groundwater fluctuation, c=0 vertical EQ acc .comp . k v = khW φ Readjustment of the soil particles due to creep and θ φ g H β β prolonged rainfall, W φ 1 2 β θ ~0,6H δ PAE = H (1− kv )K θ 2 AE δ Tidal changes, 0,5H Pae φ β sin2 ( + − ) δ K = φ Heavy wave action, AE β 2 δ θ α 2 sin( + )sin(θ − − ) cos sin sin( − − )1+ Traffic vibration, −1 kh α θ = tan sin( − − )sin( + β) Earthquakes. 1−kv Drainage from the Backfill of the Retaining Sheet Pile Walls Wall ¾are widely used for both large and small waterfront structures. ¾used for ¾Beach erosion protection ¾Stabilizing ground slopes ¾Shoring walls of trenches and other excavations and for cofferdams. Bowles, 1997 6 Sheet Pile Walls Sheet Pile Walls Types: Sheet Piles can be categorised as: Cantilever Sheet Pile Walls Wooden a) Cantilever Precast concrete -Used for small retaining height (20 ft ≅ 6 m above dredge line) b) Anchored Steel Permanent : sands, gravels Construction Methods: Temporary : other soils 1. Backfilled structure -Stability of cantilever sheet pile wall : due to passive 2. Dredged structure resistance developed below the lower soil surface Sheet pile connections: a) Thumb and finger type b) Ball and socket type Cantilever Sheet Pile Walls Anchored Sheet Pile Walls Failure Additional support to sheet pile walls can be given by backs mode Active h Active (anchored) near the top of the wall (Used in deep excavation & water front construction ). Dredge Passive line d R 0 0 A Tie Rod 0 (steel cables) Active Passive Passive h *fixing moment at 0 Design Idealisation Net Passive Resistance below ‘0’ : given with ‘R’ . Bending ⇒ design : Σ M = 0 → determine ‘d’. c Moment Then ‘d’ is increased arbitrarily by %20 to allow for simplification d Active Passive Diagram of procedure . (1.2d : embedment) Σ Fh= 0 → determine R Note: depth of tension crack < depth of tie. ( Check Pp ≥ R / over 0,2d ) 7 Anchored Sheet Pile Walls Sheet Piles with Anchors When there is a deep excavation DESIGN PROCEDURE: Anchor 1- Calculate Active & Passive Pressures in terms of A A h (unknown) depth of embedment , ‘d’ . 2- Usually Fs=2 is applied to passive pressures 3- Take ΣMA =0 ; obtain cubic equation in terms of ‘d’. Solve for ‘d’. Increase d by 20% in quay walls. Active Active Passive Passive R 4- Take ΣFh=0 ; solve for T. d 0 0 5- Plot moment diagram & determine maximum Active Passive bending moment. Determine required cross section. Moment Diagram Note: Solved with equivalent beam method. Types of anchor used in sheet pile walls are: 1. Anchor plates and beams 2. Tie backs 3. Vertical anchor piles 4. Anchor beams supported by batter (compression and tension) piles Das, 1995 Das, 1995 8 Braced Cuts (Braced Excavations) TERZAGHI & PECK (1967) EMPIRICAL PRESSURE DIAGRAMS Systems to support the sides of excavations 0,25 H 0,25 H γ To support walls of deep or shallow narrow trenches. Top view Side view (sand) wales H φ 1 2 0,50 H 3 0,75 H cu (clay) struts 0,25 H 0.65 KA γ H 4c KA =1−m Sheet medium to dense 0.2 γ Hto0.4 γ H γ H KA γH piling SAND Stiff CLAY soft to medium CLAY EARTH PRESSURES AGAINST BRACING SYSTEMS TERZAGHI & PECK (1967) EMPIRICAL PRESSURE DIAGRAMS Braced Cuts: Earth Pressure function of Wall Displacement: 1) 0,65 Times Rankine Active Fixed Bracing systems 2) N:stability number N= γH if N < 4 (elastic equilibrium) Represented by empirical pressure cu envelopes 3) N > 4 plastic equilibrium at the bottom ( N=γH/cu > 4) ACTIVE m is usually 1,0 , but m=0,4 for soft NC clays. (Retaining walls) 4) N > 7 Heaving Strut Loads: A=A B=B1+B2 REINFORCED EARTH A A C=C1+C2 B B1 B2 D=D HINGES C C1 C2 to make the D D A,B,C,D Strut Loads system Reinforced earth is a construction material comprising determinant Braced Cuts soil that has been strengthened by tensile elements Wall construction & anchorage installation in stages. such as metal rods and/or strips, nonbiodegradable fabrics (geotextiles), geogrids. 1 2 3 4 5 The beneficial effects of soil reinforcement derive from a) soil’s increased tensile strength and anchor b) the shear resistance developed from the friction at the R/C wall soil-reinforcement interfaces. 9 REINFORCED EARTH REINFORCED EARTH Two types of geogrids: a) Biaxial and b) Uniaxial Geotextiles have four primary uses in foundation engineering: 1. Drainage 2. Filtration 3. Separation 4. Reinforcement – increases the load-bearing 1.Longitudinal rib capacity of the soil 2.Transverse bar 3.Transverse rib 4. Junction REINFORCED EARTH Facing Coarse grained REINFORCED EARTH (flexible) soil (drained) Reinforcement 0,3H (tensile stresses) A Fill *steel : life 120 years z PASSIVE Zone ACTIVE Zone At-rest *other materials; 0,5H RESISTANCE -aluminium alloys -plastics H Footing -geotextiles C FACING : *Pre-cast concrete units (limited relative movement) Lv Le *U-shaped steel sections arranged horizontally COST : *more economic than concrete cantilever retaining wall Active FAILURE : *Tensile failure of one element leads to progressive collapse of the entire structure Max. tensile stress curve *Local slipping leads to redistribution of tensile stress and gradual B Lateral Earth Pressure p deformation of structure (not necessarily collapse) ≅Probable failure surface 10