234 RETAINING WALLS. CHAP. V. 



cement and kerosene should be mixed thoroughly and the coal tar then added. In cold weather 

 the coal tar may be heated and additional kerosene added to take account of the evaporation. 

 This paint not only covers the surface but combines with it, so that two or three coats are some- 

 times required. While the surface of the concrete should be dry, coal tar paint will adhere to 

 moist or wet concrete. In building retaining walls in sections, the end of the finished section should 

 be coated with coal tar paint to prevent the adhesion to the next section. 



For methods of waterproofing masonry, see methods of waterproofing bridge floors in Chap- 

 ter IV. 



DESIGN OF RETAINING WALLS. The design of masonry retaining walls will be 

 illustrated by the design of the retaining walls for West Alameda Avenue Subway, taken from 

 the author's "The Design of Walls, Bins and Grain Elevators," second edition. 



Design of Retaining Walls for West Alameda Avenue Subway, Denver, Colorado. The 

 height of the walls varied from 8 ft. to 29 ft. 3 in., while the foundation soil varied from a compact 

 gravel to a mushy clay. The design of the maximum section, which rests on a compact gravel, 

 will be given. The concrete was mixed in the proportion of i part Portland cement, 3 parts sand 

 and 5 parts screened gravel. Crocker and Ketchum, Denver, Colo., were the consulting engineers. 

 The wall is shown in Fig. 9 and in Fig. 10. 



The following assumptions were made: Weight of concrete, 150 Ib. per cu. ft.; weight of 

 filling, w = 100 Ib. per cu. ft.; angle of repose of filling, if : i (< = 33 40'); surcharge, 600 Ib. 

 per sq. ft., equivalent to 6 ft. of filling; maximum load on foundation, 6,000 Ib. per sq. ft. 



Solution. After several trials the following dimensions were taken: Width of coping 2 ft. 

 6 in., thickness of coping i ft. 6 in., batter of face of wall % in. in 12 in., batter of back of wall 

 3^ in. in 12 in., width of base 15 ft. 2 in. (ratio of base to height = 0.52), front projection of 

 base 4 ft., other dimensions as shown in Fig. 9. The calculations were made for a section of the 

 wall one foot in length. 



The property back of the wall will probably be used for the storage of coal, etc., and it was 

 assumed that the surcharge came even with the back edge of the footing of the wall. The resultant 

 pressure of the filling on the plane A-2 was calculated by the graphic method of Fig. 5 and Fig. 6, 

 and was found to be P' = 17,290 Ib. The weight of the filling in the wedge back of the wall is 

 W = 16,435 lb-> acting through the center of gravity of the filling. The resultant of P' and 

 W is P = 23,850 Ib. = the resultant pressure of the filling on the back of the wall. The weight 

 of the masonry is W = 33,144 Ib., acting through the center of gravity of the wall, and the re- 

 sultant of P and W is E = 52,510 Ib. = the resultant pressure of the wall and the filling upon 

 the foundation. The vertical component of E is F = 49,580 Ib., and cuts the foundation, b = 2.1 

 ft. from the middle. 



1. Stability Against Overturning. The line OD in this case is nearly parallel to the line QW 

 which brings the point 5 in Fig. 9 at a great distance from the point W. The factor of safety 

 against overturning was calculated on the original drawing and found to be/o > 25. 



2. Stability Against Sliding. The coefficient of friction of the masonry on the footing will 

 be assumed to be tan <f>' = 0.57 and <' = 30. Through 0, Fig. 9, draw OQ, cutting the base of 

 wall 5/1 at 6, and making an angle <' = 30 with a vertical line through 6. Then the factor of 

 safety against sliding will be 



/. = QM'/RM = 2.5 



This is ample as the resistance of the filling in front of the toe will increase the resistance 

 against sliding. 



3. Stability Against Crushing. In Fig. 9 the direct pressure will be pi = 49,580/15.21 

 = 3,220 Ib. per sq. ft. 



The pressure due to bending will be 



pi = 6F-bfd 2 = (6 X 49,580 X 2.i)/23i.4 = 2,700 Ib. per sq. ft., and the maximum 

 pressure is 



p = 3,220 + 2,700 = + 5.92O Ib. per sq. ft. 



