CHAPTER 19 CONCRETE AND MECHANICALLY STABILIZED EARTH RETAINING WALLS PART A—CONCRETE RETAINING WALLS 19.1 INTRODUCTION The common types of concrete retaining walls and their uses were discussed in Chapter 11. The lateral pressure theories and the methods of calculating the lateral earth pressures were described in detail in the same chapter. The two classical earth pressure theories that have been considered are those of Rankine and Coulomb. In this chapter we are interested in the following: 1. Conditions under which the theories of Rankine and Coulomb are applicable to cantilever and gravity retaining walls under the active state. 2. The common minimum dimensions used for the two types of retaining walls mentioned above. 3. Use of charts for the computation of active earth pressure. 4. Stability of retaining walls. 5. Drainage provisions for retaining walls. 19.2 CONDITIONS UNDER WHICH RANKINE AND COULOMB FORMULAS ARE APPLICABLE TO RETAINING WALLS UNDER ACTIVE STATE Conjugate Failure Planes Under Active State When a backfill of cohesionless soil is under an active state of plastic equilibrium due to the stretching of the soil mass at every point in the mass, two failure planes called conjugate rupture 833 834 Chapter 19 planes are formed. These are further designated as the inner failure plane and the outer failure plane as shown in Fig. 19.1. These failure planes make angles of a. and «0 with the vertical. The equations for these angles may be written as (for a sloping backfill) s-B a. = +- — 2 2 £-J3 "°~ 2 2 . sinytf where sin s = (19.2) „ _ ._„ when /7=0, - = 45°- — , a = - = 45°yieo - — 2 2 °n 2 2 The angle between the two failure planes = 90 - 0 . Conditions for the Use of Rankine's Formula 1 . Wall should be vertical with a smooth pressure face. 2. When walls are inclined, it should not come in the way of the formation of the outer failure plane. Figure 19.1 shows the formation of failure planes. Since the sloping face AB' of the retaining wall makes an angle aw greater than ao, the wall does not interfere with the formation of the outer failure plane. The plastic state exists within wedge ACC'. The method of calculating the lateral pressure on AB' is as follows. 1 . Apply Rankine's formula for the vertical section AB. 2. Combine P with W , the weight of soil within the wedge ABB', to give the resultant PR. Let the resultant PR in this case make an angle 8r with the normal to the face of the wall. Let the maximum angle of wall friction be 8m. If 8r > 8m, the soil slides along the face AB'of the wall. Outer failure plane ^ Inner failure plane Figure 19.1 Application of Rankine's active condition to gravity walls Concrete and Mechanically Stabilized Earth Retaining Walls 835 Outer failure plane Inner failure plane Figure 19.2 Lateral earth pressure on cantilever walls under active condition In such an eventuality, the Rankine formula is not recommended but the Coulomb formula may be used. Conditions for the Use of Coulomb's Formula 1. The back of the wall must be plane or nearly plane. 2. Coulomb's formula may be applied under all other conditions where the surface of the wall is not smooth and where the soil slides along the surface. In general the following recommendations may be made for the application of the Rankine or Coulomb formula without the introduction of significant errors: 1. Use the Rankine formula for cantilever and counterfort walls. 2. Use the Coulomb formula for solid and semisolid gravity walls. In the case of cantilever walls (Fig. 19.2), Pa is the active pressure acting on the vertical section AB passing through the heel of the wall. The pressure is parallel to the backfill surface and acts at a height H/3 from the base of the wall where H is the height of the section AB. The resultant pressure PR is obtained by combining the lateral pressure Pa with the weight of the soil Ws between the section AB and the wall. 19.3 PROPORTIONING OF RETAINING WALLS Based on practical experience, retaining walls can be proportioned initially which may be checked for stability subsequently. The common dimensions used for the various types of retaining walls are given below. Gravity Walls A gravity walls may be proportioned in terms of its height given in Fig. 19.3(a). The minimum top width suggested is 0.30 m. The tentative dimensions for a cantilever wall are given in Fig. 19.3(b) and those for a counterfort wall are given in Fig. 19.3(c). 836 Chapter 19 0.3m to///12 0.3 m min. H h- Min. batter 1 :48 Min. batter 1 :48 -HO.ltfh— v \*-B = 0.5 to 0.7//-*| * I—-B = 0.4 to 0.7#-»-| = H/8toH/6 = H/l2toH/lO (a) Gravity wall (b) Cantilever wall 03 W 0.2 m min (c) Counterfort wall Fig. 19.3 Tentative dimensions for retaining walls 19.4 EARTH PRESSURE CHARTS FOR RETAINING WALLS Charts have been developed for estimating lateral earth pressures on retaining walls based on certain assumed soil properties of the backfill materials. These semi empirical methods represent a body of valuable experience and summarize much useful information. The charts given in Fig. 19.4 are meant to produce a design of retaining walls of heights not greater than 6 m. The charts have been developed for five types of backfill materials given in Table 19.1. The charts are applicable to the following categories of backfill surfaces. They are 1. The surface of the backfill is plane and carries no surcharge 2. The surface of the backfill rises on a slope from the crest of the wall to a level at some elevation above the crest. The chart is drawn to represent a concrete wall but it may also be used for a reinforced soil wall. All the dimensions of the retaining walls are given in Fig. 19.4. The total horizontal and vertical pressures on the vertical section of A B of height H are expressed as 2 P,n = <-K,H• n (19.3) Concrete and Mechanically Stabilized Earth Retaining Walls 837 Table 19.1 Types of backfill for retaining walls Type Backfill material Coarse-grained soil without admixture of fine soil particles, very permeable (clean sand or gravel) Coarse-grained soil of low permeability due to admixture of particles of silt size Residual soil with stones fine silty sand, and granular materials with conspicuous clay content Very soft or soft clay, organic silts, or silty clays Medium or stiff clay Note: Numerals on the curves indicate soil types as described in Table 19.1 For materials of type 5 computations of pressure may be based on the value of H 1 meter less than actual value 10 20 40 Values of slope angle Figure 19.4 Chart for estimating pressure of backfill against retaining walls supporting backfills with a plane surface. (Terzaghi, Peck, and Mesri, 1996) H,=0 H Soil type Soil type 2 Soil type 3 15 10 0.4 0.8 1.0 0 0.4 0.8 1.0 0 0.4 0.8 1.0 Values of ratio H}IH Figure 19.5 Chart for estimating pressure of backfill against retaining walls supporting backfills with a surface that slopes upward from the crest of the wall for limited distance and then becomes horizontal. (Terzaghi et al., 1996) Concrete and Mechanically Stabilized Earth Retaining Walls 839 Soil type 4 Soil type 5 Note: JV Numerals on curves indicate the following * slopes 25 No. Slope 1 1.5:1 Ma;c slop; 3:1 2 1.75:1 3 2:1 ~~ 4 3:1 5 6:1 3 3 > 10 K. = 0 5 n 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Values of ratio H\IH Values of ratio H}/H Figure 19.5 Continued 2 PV=-KVH (19.4) Values of Kh and Kv are plotted against slope angle /? in Fig. 19.4 and the ratio HJH in Fig. 19.5. 19.5 STABILITY OF RETAINING WALLS The stability of retaining walls should be checked for the following conditions: 1. Check for sliding 2. Check for overturning 3. Check for bearing capacity failure 4. Check for base shear failure The minimum factors of safety for the stability of the wall are: 1. Factor of safety against sliding =1.5 2. Factor of safety against overturning = 2.0 3. Factor of safety against bearing capacity failure = 3.0 Stability Analysis Consider a cantilever wall with a sloping backfill for the purpose of analysis. The same principle holds for the other types of walls. Fig. 19.6 gives a cantilever wall with all the forces acting on the wall and the base, where Pa = active earth pressure acting at a height H/3 over the base on section AB h a >~^ P v = P a sin/"3 13 = slope angle of the backfill 840 Chapter 19 (a) Forces acting on the wall -Key -B- (b) Provision of key to increase sliding resistance Figure 19.6 Check for sliding weight of soil Wc weight of wall including base w. the resultant of Ws and Wc passive earth pressure at the toe side of the wall. Fr base sliding resistance Check for Sliding (Fig. 19.6) The force that moves the wall = horizontal force Ph Concrete and Mechanically Stabilized Earth Retaining Walls 841 The force that resists the movement is F Rtan8+P (19.5) R = total vertical force = Ws + Wc + Pv, 8 = angle of wall friction ca = unit adhesion If the bottom of the base slab is rough, as in the case of concrete poured directly on soil, the coefficient of friction is equal to tan 0, 0 being the angle of internal friction of the soil.