Module 7 (Lecture 26) RETAINING WALLS

Transcription

1 Module 7 (Lecture 26) RETAINING WALLS Topics 1.1 COMMENTS RELATING TO STABILITY 1.2 DRAINAGE FROM THE BACKFILL OF THE RETAINING WALL 1.3 PROVISION OF JOINTS IN RETAINING-WALL CONSTRUCTION 1.4 GRAVITY RETAINING-WALL DESIGN FOR EARTHQUAKE CONDITIONS 1.5 MECHANICALLY STABILIZED RETAINING WALLS 1.6 GENERAL DESIGN CONSIDERATIONS COMMENTS RELATING TO STABILITY When a weak soil layer is located at a shallow depth-that is, within a depth of about 1.5 times the width of the retaining wall-the bearing capacity of the weak layer should be carefully investigated. The possibility of excessive settlement also should be considered. In some cases, the use of lightweight backfill material behind the retaining wall may solve the problem. In many instances, piles are used to transmit the foundation load to a firmer layer. However, often the thrust of the sliding wedge of soil, in the case of deep shear failure, bends the piles and eventually causes them to fail. Careful attention should be given to this possibility when considering the option of pile foundations for retaining walls. (Pile foundations may be required for bridge abutments to avoid the problem of scouring). As illustrated in examples 1, 2, and 3 the active earth pressure coefficient is used to determine the lateral force of the backfill. The active state of the backfill can be established only if the wall yields sufficiently, which happen in all cases. The degree of wall yielding will depend on its height and the section modulus. Furthermore, the lateral force of the backfill will depend on several factors, as identified by Casagrande (1973):

2 a. Effect of temperature b. Groundwater fluctuation c. Readjustment of the soil particles due to creep and prolonged rainfall d. Tidal changes e. Heavy wave action f. Traffic vibration g. Earthquakes Insufficient wall yielding when combined with other unforeseen factors may generate a larger force on the retaining structure compared to that obtained from the active earth pressure theory. Casagrande (1973) investigated the distribution of lateral earth pressure behind a bridge abutment (in Germany) with a slag backfill, as shown in figure Laboratory tests on the slag backfill gave angles of friction between 37 and 45, depending on the degree of compaction. For purposes of comparison, the variation of the Rankine active earth pressure with φφ = 37 and φφ = 45 is also shown in figure Comparing the actual and theoretical pressure distribution diagrams indicates: a. The actual lateral earth pressure distribution may not be triangular. b. The lateral earth pressure distribution may change with time. c. The actual active force is greater than the minimum theoretical active force. The primary reason that many retaining walls designed with theoretical active earth pressure perform satisfactorily is the use of a large factor of safety. Recently, Goh (1993) analyzed the behavior of a retaining wall using the finite element method and proposed the simplified earth pressure distribution shown in figure Figure 7.17 Bridge abutment on piles backfilled with granulated slag )after Casagrande, 1973)

3 Figure 7.18 Simplified lateral earth pressure (σσ h ) profile: (a) retaining wall; (b) pressure distribution behind wall stem; (c) pressure distribution behind virtual wall (after Goh, 1993) Figure Continued

4 DRAINAGE FROM THE BACKFILL OF THE RETAINING WALL As the result of rainfall or other wet conditions, the backfill material for a retaining wall may become saturated. Saturation will increase the pressure on the wall and may create an unstable condition. For this reason, adequate drainage must be provided by means of weepholes and/or perforated drainage pipes (see figure 7. 19). The weepholes, if provided, should have a minimum diameter of about 4 in. (0.1 m) and be adequately spaced. Note that there is always a possibility that the backfill material may be washed into weepholes or drainage pipes and ultimately clog them. Thus a filter material needs to be placed behind the weepholes or around the drainage piles, as the case may be; geotextiles now were that purpose. Whenever granular soil is used as a filter, the principles. Should be followed. Example 4 gives the procedure for designing a filter. Example 4 Figure 7.19 Drainage provisions for the backfill of a retaining wall Figure shows the grain-size distribution of a backfill material. Using the conditions outlined in section 10, determine the range of the grain-size distribution for the filter material.

5 Figure 7.20 Solution From the grain-size distribution curve given in figure 7. 20, the following values can be determined, DD 15(BB) = 0.04 mm DD 85(BB) = 0.25 mm DD 50(BB) = 0.13 mm Conditions of Filter 1. DD 15(FF) should be less than 5DD 85(FF) that is, = 1.25 mm 2. DD 15(FF) should be greater than 4DD 15(BB) that is, = mm 3. DD 50(FF) Should be less than 25DD 50(BB) that is, = 3.25 mm. 4. DD 15(FF) should be less than 20DD 15(BB) that is, = 0.8 mm These limiting points are plotted in figure Through these points two curves can be drawn that are similar in nature to the gain-size distribution curve of the backfill material. These curves define the range for the filter material to be used.

6 PROVISION OF JOINTS IN RETAINING-WALL CONSTRUCTION A retaining wall may be constructed with one or more the following joints: 1. Construction joints (figure 7. 21a) are vertical and horizontal joints that are placed between two successive pours of concrete. To increase the shear at the joints, keys may be used. If keys are not used, the surface of the first pour is cleaned and roughened before the next pour of concrete. 2. Contraction joints (figure 7. 21b) are vertical joints (grooves) placed in the face of a wall (from the top of the base slab to the top of the wall) allow the concrete to shrink without noticeable harm. The grooves may be about 0.25 to 0.3 ( 6 to 8 mm) wide and 0.5 to 0.6 in. ( 12 to 16 mm) deep. 3. Expansion joints (figure 7. 21c) allow for the expansion of concrete caused by temperature changes; vertical expansion joints from the base to the top of the wall may also be used. These joints may be filled with flexible joint filers. In most cases, horizontal reinforcing steel bars running across the stem are continuous through all joints. The steel is greased to allow the concrete to expand. 4. Figure 7.21 (a) Construction joints; (b) contraction joint; (c) expansion joint GRAVITY RETAINING-WALL DESIGN FOR EARTHQUAKE CONDITIONS Even in mild earthquakes, most retaining walls undergo limited lateral displacement. Richards and Elms (1979) proposed a procedure for designing gravity retaining walls for earthquake conditions that allows limited lateral displacement. This procedure takes into consideration the wall inertia effect. Figure shows a retaining wall with various forces acting on it, which are as follows (per unit length of the wall):

7 Figure 7.22 Stability of a retaining wall under earthquake forces a. WW ww = weight of the wall b. PP aaaa = active force with earthquake condition taken into consideration The backfill of the wall and the soil on which the wall is retaining are assumed cohesionless. Considering the equilibrium of the wall, it can be shown that WW ww = 1 2 γγ 1HH 2 (1 kk vv )KK aaaa CC IIII [7.27] Where γγ 1 = unit weight of the backfill CC IIII = sin (β δ) cos (β δ)tan φφ 2 (1 kk vv )(tan φφ 2 tan θθ ) [7.28] And θθ = tan 1 kk h (1 kk vv ) For detailed derivation of equation (28), see Das (1983). Based on equation (27 and 28), the following procedure may be used to determine the weight of the retaining wall, WW ww, for tolerable displacement that may take place during an earthquake. 1. Determine the tolerable displacement of the wall, Δ. 2. Obtain a design value of kk h from kk h = AA aa 0.24 vv 2 AA aa Δ 0.25 [7.29]

8 In equation (29), AA aa and AA vv are effective acceleration coefficients and Δ is displacement in inches. The magnitudes of AA aa and AA vv are given by the Applied Technology Council (1978) for various regions of the United States. 3. Assume that kk vv = 0, and, with the value of kk h obtained, calculate KK aaaa from equation (32). 4. Use the value of KK aaaa determined in step 3 to obtain the weight of the wall (WW ww ). 5. Apply a factor of safety to the value of WW ww obtained in step 4. Example 5 Refer to figure For kk vv = 0 and kk h = 0.3, determine: Figure 7.23 a. Weight of the wall for static condition. b. Weight of the wall for zero displacement during an earthquake c. Earthquake of the wall for lateral displacement of 1.5 in. during an earthquake For part c, assume that AA aa = 0.2 and AA vv = 0.2. for parts a, b, and c, use a factor of safety of 1.5.

9 Solution Part a For static conditions, θθ = 0 and equation (28) becomes CC IIII = sin (β δ) cos (β δ)tan φφ 2 tan φφ 2 For ββ = 90, δδ = 24 and φφ = 36, CC IIII = sin (90 24) cos (90 24) tan 36 tan 36 For static conditions, KK aaaa = KK aa, so = 0.85 WW ww = 1 2 γγhh2 KK aa CC IIII For KK aa [table 5 from chapter 6], WW ww = 1 2 (16)(5)2 (0.2349)(0.85) = 39.9 kn/m With a factor of safety of 1.5, WW ww = (39.9)(1.5) = 59.9 kn/m Part b For zero displacement, kk vv = 0, CC IIII = sin (β δ) cos (β δ)tan φφ 2 tan φφ 2 tan θθ tan θθ = CC IIII = kk h = 0.3 = kk vv 1 0 sin (90 24) cos (90 24) tan 36 tan = 1.45 For kk h = 0.3, φφ 1 = 36 and δδ = 2φφ/3, the value of KK aaaa 0.48 (table 7 chapter 6). WW ww = 1 2 γγ 1HH 2 (1 kk vv )KK aaaa CC IIII = 1 2 (16)(5)2 (1 0)(0.48)(1.45) = 139 kn/m With a factor of safety of 1.5, WW ww = kn/m Part c For a lateral displacement of 1.5, in., kk h = AA aa 0.2AA vv 2 AA aa Δ 0.25 = (0.2) (0.2)(0.2) 2 (0.2)(1.5) 0.25 = 0.081

10 tan θθ = CC IIII = kk h = = kk vv 1 0 sin (90 24) cos (90 24) tan 36 tan = WW ww = 1 2 γγ 2HH 2 KK aaaa CC IIII 0.29 [Table 7] WW ww = 1 2 (16)(5)2 (0.29)(0.957) = 55.5 kn/m With a factor of safety of 1.5, WW ww = 83.3 kn/m MECHANICALLY STABILIZED RETAINING WALLS GENERAL DESIGN CONSIDERATIONS The general design procedure of any mechanically stabilized retaining wall can be divided into two parts: 1. Satisfying internal stability requirements 2. Checking the external stability of the wall The internal stability checks involve determining tension and pullout resistance in the reinforcing elements and the integrity of facing elements. The external stability checks include checks for overturning, sliding and bearing capacity failure (figure 7. 24). The following sections will discuss the retaining wall design procedures with metallic strips, geotextiles, and geogrids. Figure 7.24 External stability checks (after Transportation Research Board 1995)

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