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RetainingRetaining WallsWalls PartPart II LateralLateral EarthEarth PressurePressure TheoryTheory GravityGravity andand MSEMSE WallsWalls Outline of Retaining Wall Material  Part I  Reference Materials  Review of Lateral Earth  Verruijt Chapters 32-38 Pressures  FHWA NHI-06-089  Concrete Gravity Chapter 10 Retaining Walls  MSE (Mechanically Stabilised Earth) Walls  Part II: Sheet Pile Walls  Cantilever Walls  Anchored Walls  Braced Cuts RetainingRetaining WallsWalls  Necessary in situations where gradual transitions either take up too much space or are impractical for other reasons  Retaining walls are analysed for both resistance to overturning and structural integrity  Two categories of retaining walls  Externally Stabilized  Internally Stabilized Types of Retaining Walls Lateral Earth Pressure Topics

● States of Lateral Earth Pressure ● Theories of Lateral Earth  At-Rest (Neutral) Earth Pressure Pressure  Active Earth Pressure  Jaky (At-Rest Pressures)  Passive Earth Pressure  Planar Failure Surface  It’s possible to have in-between  Rankine (Active, Passive) states, but we usually don’t  Coulomb (Active, Passive) discuss these in elementary  Non-Planar Failure Surface retaining wall design  Log-Spiral Theory (Active, Passive)

Lateral Earth Pressure Coefficient

At-Rest (Neutral) Earth Pressures

Active Earth Pressures

Passive Earth Pressures

Relationship of the Different Stress States

Rankine Earth Pressure

● Assumes Mohr-Coulomb failure conditions for the soil ● Does not include effects of wall-soil friction ● Can be extended to include sloping backfill (see Coulomb Theory) ● Also includes provision for cohesive soils (see chart at right)

Coulomb Failure Theory

● Includes effects of wall-soil friction through use of failure wedge theory ● Can also be used with sloping backfill walls ● Is very UNCONSERVATIVE for passive pressures with high values of wall friction ● Formulas to the right assume that δ is positive for both active and passive pressures

Coulomb Earth Pressure Theory

Log-SpiralLog-Spiral ModelModel  Assumes log spiral failure surface behind wall  Requires use of

suitable chart for KA and KP  Requires different chart for vertical wall and horizontal backfill (vertical wall shown at left)  With AASHTO specifications, only log-spiral charts for K are necessary P

TypicalTypical ValuesValues ofof WallWall FrictionFriction

Maximum wall friction suggested for design: Active: δ = 2φ’/3 Passive: δ = φ’/2 Also: δ = tan-1(sin(φ)) WallsWalls withwith CohesiveCohesive BackfillBackfill  Retaining walls should generally have cohesionless backfill, but in some cases cohesive backfill is unavoidable  Cohesive soils present the following weaknesses as backfill:  Poor drainage  Creep  Expansiveness  Most lateral earth pressure theory was first developed for purely cohesionless soils (c = 0) and has been extended to cohesive soils afterward EffectsEffects ofof SurfaceSurface LoadingLoading ExampleExample ofof SurchargeSurcharge LoadingLoading GroundwaterGroundwater EffectsEffects  Steps to properly compute horizontal stresses including groundwater effects:  Compute total vertical stress  Compute effective vertical stress by removing groundwater effect through submerged unit weight; plot on

Po diagram  Compute effective horizontal stress by multiplying effective vertical stress by K  Compute total horizontal stress by directly adding effect of groundwater unit weight to effective horizontal stress GroundwaterGroundwater ExampleExample External vs. Internal Stability

ExternalExternal StabilityStability ProblemsProblems Concrete Gravity Walls

DesignDesign ParametersParameters

forfor RigidRigid WallsWalls • Contact Pressure on Foundation: Use Shallow Foundation Bearing Capacity Methods • Overall Stability: use slope stability methods Global Stability of Retaining Walls TypicalTypical DimensionsDimensions forfor Cast-in-Cast-in- PlacePlace ConcreteConcrete RetainingRetaining WallsWalls DesignDesign ProcedureProcedure forfor Cast-in-PlaceCast-in-Place WallsWalls CantileverCantilever WallWall DesignDesign ExampleExample CantileverCantilever WallWall DesignDesign ExampleExample

AASHTO approach for lateral earth pressure theories: Coulomb active, Log-spiral passive CantileverCantilever ExampleExample CantileverCantilever ExampleExample Cantilever Example CantileverCantilever ExampleExample CantileverCantilever ExampleExample • Notes o Global stability can be evaluated using the same methods used for slope stability analysis o Factors of Safety for cast-in- place concrete cantilever walls: • Sliding: FS > 1.5 • Overturning in soil: FS > 2.0 • Overturning in rock: FS > 1.5 • Bearing Capacity: FS > 3.0 o Eccentricity: within kern LateralLateral SqueezeSqueeze KeyedKeyed FoundationFoundation forfor SlidingSliding ResistanceResistance FailureFailure CausesCauses forfor RetainingRetaining WallsWalls RetainingRetaining WallWall DrainageDrainage Mechanically Stabilized Earth (MSE) Walls

Overview of MSE Walls

● Definitions ● Soil Regions – Mechanically Stabilized Earth Wall (MSEW) is a – generic term that includes reinforced soil (a term Retained backfill is the fill material used when multiple layers of inclusions act as located between the mechanically reinforcement in soils placed as fill). stabilized soil mass and the natural – Geosynthetics is a generic term that soil. encompasses flexible polymeric materials used in – geotechnical engineering such as geotextiles, Reinforced backfill is the fill material in geomembranes, geonets, and grids (also known which the reinforcements are placed. as geogrids). – Foundation Soil is the soil under the – Facing is a component of the reinforced soil system used to prevent the soil from raveling out MSE wall and its reinforced backfille between the rows of reinforcement. Common – All three of these can be different facings include precast concrete panels, dry cast modular blocks, metal sheets and plates, (generally,) or the same (infrequently) gabions, welded wire mesh, shotcrete, wood lagging and panels, and wrapped sheets of geosynthetics. The facing also plays a minor structural role in the stability of the structure. For RSS structures it usually consists of some type of erosion control material.

ApplicationsApplications ofof MSEMSE WallsWalls AdvantagesAdvantages andand DisadvantagesDisadvantages ofof MSEMSE WallsWalls • Advantages • Disadvantages o Require a relatively large space behind o Use simple and rapid the wall or outward face to obtain enough construction procedures and do wall width for internal and external stability. not require large construction o MSEW require select granular fill. (At sites equipment. where there is a lack of granular soils, the cost of importing suitable fill material may o Do not require experienced render the system uneconomical). craftsmen with special skills for o Suitable design criteria are required to construction. address corrosion of steel reinforcing elements, deterioration of certain types of o Require less site preparation exposed facing elements such as than other alternatives. geosynthetics by ultra violet rays, and potential degradation of polymer o Need less space in front of the reinforcement in the ground. structure for construction o Since design and construction practice of operations. all reinforced systems are still evolving, specifications and contracting practices o Reduce right-of-way acquisition. have not been fully standardized, o Do not need rigid, unyielding especially for RSS. o The design of soil-reinforced systems often foundation support because requires a shared design responsibility MSE structures are tolerant to between material suppliers and owners deformations. and greater input from agencies geotechnical specialists in a domain often o Are cost effective. dominated by structural engineers. o Are technically feasible to heights in excess of 25 m (80 ft). MSEMSE WallWall FacingsFacings MSEMSE WallWall ConstructionConstruction Types of Reinforcement • Geogrids  Steel Strips o High Density Polyethylene (HDPE) o The currently commercially available geogrid. These are of uniaxial strips are ribbed top and bottom, 50 manufacture and are available in up to 6 mm (2 inches) wide and 4 mm (5/32- styles differing in strength. inch) thick. Smooth strips 60 to 120 o PVC coated polyester (PET) geogrid. mm (2-d to 4¾-inch) wide, 3 to 4 mm Available from a number of manufacturers. They are characterized (c to 5/32-inch) thick have been used. by bundled high tenacity PET fibers in • Steel Grids the longitudinal load carrying direction. For longevity the PET is supplied as a o Welded wire grid using 2 to 6 W7.5 to high molecular weight fiber and is further W24 longitudinal wire spaced at characterized by a low carboxyl end either 150 or 200 mm (6 or 8 inches). group number. The transverse wire may vary from • W11 to W20 and are spaced based Geotextiles on design requirements from 230 to o High strength geotextiles can be used principally in connection with reinforced 600 mm (9 to 24 inches). Welded soil slope (RSS) construction. Both steel wire mesh spaced at 50 by 50 polyester (PET) and polypropylene (PP) mm (2 by 2-inch) of thinner wire has geotextiles have been used. been used in conjunction with a welded wire facing. Some MBW systems use steel grids with 2 longitudinal wires. Steel Reinforcement GeogridGeogrid ReinforcementReinforcement MSEMSE BackfillBackfill • From a reinforcement capacity point  MSE walls require high quality of view, lower quality backfills could be backfill for durability, good used for MSEW structures; however, drainage, constructability, and a high quality granular backfill has the good soil reinforcement advantages of being free draining, interaction which can be obtained providing better durability for metallic from well graded, granular reinforcement, and requiring less materials. Many MSE systems reinforcement. There are also depend on friction between the significant handling, placement and reinforcing elements and the soil. compaction advantages in using granular soils. These include an In such cases, a material with increased rate of wall erection and high friction characteristics is improved maintenance of wall specified and required. Some alignment tolerances. systems rely on passive pressure on reinforcing elements, and, in those cases, the quality of backfill is still critical. These performance requirements generally eliminate soils with high clay contents. MSEMSE DesignDesign FlowchartFlowchart DesignDesign ofof MSEMSE WallsWalls • External Stability • Internal Stability Notes on Design of MSE Walls

● As with gravity walls, ● The failure surface divides the reinforcement strips/grids into we will focus on sliding two regions and overturning – The region to the left of the failure surface – Bearing capacity will be ● Length Lr depends upon the location secondary of the failure surface at a given elevation – Global stability will not ● This region cannot contribute to the be considered in this pull resistance of the reinforcements course – The region to the right of the failure surface

● ● Length Le depends upon the length of In addition, we will the strips/grids needed to resist the consider the pull of the wall – The total length of the mechanical integrity of reinforcement at any level in the the reinforcement system is the sum of these two (internal stability) ● Both can vary with each level but in some cases Le can be simplified Internal Stability

● Computation of Lr – This will vary with elevation – It is zero at the base of the wall – It increases as shown as the failure surface slopes upward from the base, depending upon the type of reinforcement – This can be laid out in CAD for exact values for each layer Internal Stability

● Computation of Le – Le is the result of the static equilibrium between the wall pulling on the reinforcement to the left

(Treq) and the frictional resistance of the soil acting on the reinforcement in the

resistant zone (Tten)

● We include a factor of safety in this computation

Internal Stability

Internal Stability

Internal Stability

Structural Integrity of the Geogrids

Structural Integrity of the Geogrids

MSEMSE WallWall FactorsFactors ofof SafetySafety (ASD(ASD Design)Design) MSEMSE WallWall DesignDesign CriteriaCriteria DesignDesign ExampleExample • Given • Given o Project Nature • A typical urban highway o Foundation Soils retaining wall design with • φ' = 30˚. (clayey sand, precast concrete panels dense) • Geogrid reinforcement • Vertical spacing of strips = • Allowable bearing 750 mm (based on selection capacity - 300 kPa. of wall configuration.) The • first row is located 375 mm Differential settlements on from the topmost panel the order of 1/300 are o Design Height, External Loads estimated. • Total design height H = 7.8 o Reinforced (Wall) Backfill m, to gutter grade. 3 • Required panel height = 7.5 • φ = 34 ˚, γT = 18.8 kN/m , m vertical. δ = 11˚, Ka = 0.28 (Rankine) • Uniform traffic surcharge = 9.4 kPa. o Retained Backfill 3 • φ = 30 ˚, γT = 18.8 kN/m , Ka = 0.33 (Rankine) Design Example

● Given ● Find – Factors of Safety – MSE Wall to suit these parameters ● External Stability – Sliding = 1.5. ● Solution – Maximum foundation – pressure < allowable The most detailed bearing capacity. solution is in the – Eccentricity < L/6 spreadsheet on the – Global stability > 1.3. instructor’s website ● Internal Stability – We will explore a more – Pullout = 1.5. compact solution as well – Mechanical = 1.5. Notes on the Spreadsheet Solution

● It is important to compute ● It is also important to the elevation of each compute the distance of level of reinforcement in each reinforcement level order to compute the from the bottom of the vertical (and horizontal) wall, as this determines effective stress the value of Lr

● Ka is the same for all ● It is interesting to note levels because the that Le is the same for reinforced backfill is most levels; we will see uniform why

Simplified Computation of Le

● It can be simplified under ● More conditions: the following conditions: – Surcharge at soil – Uniform spacing of the surface is uniform and reinforcement levels does not vary with – Distance from top depth reinforcement level to surface of the soil is half the spacing – Distance from bottom reinforcement level to base of wall is half the spacing

Simplified Computation of Le

● Substituting, Le > 0.81 m (very close to spreadsheet)

● L = Lr + Le, which will vary with depth – It is frequently better to make all of the reinforcement lengths the same for a rectangular shaped reinforcement area

Structural Integrity of Reinforcement

● Generally pick a reinforcement, first perform the purely geotechnical calculations ● If final inequality is not met, pick a new geogrid

with a higher Tallow and recalculate as necessary ● May be necessary to reduce spacing as well

Notes on Sliding and Overturning

● Computations are shown ● Overturning Forces in spreadsheet – Resisting: weight of ● Sliding Forces reinforced backfill, acting at its centroid – Resisting: friction along base, based on weight of – Driving: same as sliding, reinforced backfill and acting 1/3 from bottom of friction with foundation soil reinforced backfill – Driving: “triangle” pressure ● Bearing capacity and of retained backfill on settlement of footing reinforced backfill same as with gravity walls

BasicBasic ConceptConcept ofof MSEMSE ReinforcementReinforcement DesignDesign (Elevation(Elevation View)View) withwith SteelSteel StripsStrips GabionGabion WallsWalls SoilSoil NailingNailing QuestionsQuestions