Baker's Rules.—Sir Benjamin Baker, from an extended experience in the construction of walls under many differing conditions, and after numerous experiments upon the thrust of earth, gives' the following statement of his views upon the design of retaining walls: Experience has shown that a wall one-quarter of the height in thickness, and battering 1 inch or 2 inches per foot on the face, possesses sufficient stability when the hacking and foundation are both favorable. The Author, however, would not seek to justify this proportion by assuming the slope of repose to he about 1 to 1, when it is perhaps more nearly 11 to 1, and a factor of safety to he unnecessary, but would rather say that experiment has shown the actual lateral thrust of good filling to be equivalent to that of a fluid weighing about 10 pounds per cubic foot, and allowing for variations in the ground, vibrations, and con tingencies, a factor of safety of 2, the wall should be able to sustain at least 20 pounds fluid pressure, which will be the case if one-quarter of the height in thickness.
It has been similarly proved by experience that under no ordinary conditions of surcharge or heavy backing is it necessary to make a retaining wall on a solid foundation more than double the above, or one-half of the height in thickness. Within these limits the engineer must vary the strength in accordance with the conditions affecting the particular case.
The rules of Sir Benjamin Baker give walls considerably lighter than those of Trautwine, and the tendency in recent practice has been to somewhat reduce the thicknesses for walls backed with good materials and built under favorable conditions. Where from lack of drainage or other cause, the backing is liable to get into soft condition, it may be necessary to considerably increase thickness.
128. Using Formulas in Design.—The design of a wall to sustain a bank of earth is a comparatively simple matter once the earth pressure has been determined. The difficulties met are those of judging the character of the material and its probable pressure against the wall. it is probable that in most instances the full pressures that theoretically might come upon the wall are not actually developed. The design should Ix made for the worst conditions which may reasonably be expected to occur, but the construction of heavy walls to provide for bad conditions which are not likely to occur, and which may be met by proper attention to drainage and proper care in placing the hacking, is unnecessarily expensive and wasteful.
For NvaIIs with vertical or nearly vent ical backs, Poncelet's for mulas, taking into account the friction of the earth on the back of The Actual Lateral Pressure of Earth, Van \ostram1 Science Series, and Proceedings, Institution of Civil Engineers, Vol. 1\V, p. 153.
the wall, ghe thicknesses for walls which agree fairly well with the results of experience and not differing greatly from the rules sug gested by Sir Benjamin Baker.
In designing by this method, the pressure of earth is obtained by the use of Formula (1), or from 'fable XVII, a section of wall is assumed and its sufficiency investigated.
E.ramplc masonry wall, 22 feet high, is to support a bank of earth whose surface has an upward slope of 1 to 3 front the top of the %ya11. The hacking is ordinary earth whose friction angle may be taken at Weight of masonry is 150 pounds and of earth 100 pounds per cubic foot. Pind proper section for the wall.
.' olution.—Try a rectangular wall with thickness of 7.5 f et. From Table XVII, we find Q=.33. Then and sliding could not occur.
Battered Face. The face of the teal] may be battered, so as to diminish the width at top by one-third, using the same width of base without decreasing its stability.
Battered Back. A wall with battered back may be used. Assume a top thickness, a=5.5, and base thickness, b= 0.5. The angle made by the back of the wall with the horizontal 20'. From l 00 X 22 X 22 X47 Table XVII, we find Q=.17, then = R cuts the base practically at one-third its width from the toe.
The crushing stress at the toe is pounds, a little less than for the rectangular wall.
tan (3= 8170 24750-8270 = within safe limits but somewhat more than for the rectangular wall.
Example 2.—A retaining wall 20 feet high is to support a hori zontal bank of earth carrying a railway track. If the maximum train load is taken at 800 pounds per square foot of surface, and the angle of friction of the earth at find the thickness of wall required by Poncelet's formula. w=150 pounds and e=100 pounds per cubic foot.
Solution.—Assume a thickness of wall of 9 feet. From Table XVII, we have Q=30. Then (3) eh' = +w1i Q = =10800 pounds H =P cos 0 =10S00 X .866 = 9350 pounds, and V= 10800 X .5 = 5400 pounds.
The resultant thrust cuts the base within the middle third, and a little less width might answer.
The crushing stress at the toe of the wall is The minimum thickness allowable for a solid wall is that which causes the resultant thrust (II) to cut the base at a distance x=1/3 from the toe of the wall. For a rectangular wall, the width bears a direct ratio to the height for any particular values for weights of materials and angles of friction. 'Table XX gives minimum values of thickness ratio, by Poncelet's formula for walls in which the weight of masonry is taken as 150 lb., ft..; and the weight of earth as 100 lb. ft .3 For battered or stepped on the back the tniniutum thickness given in the table may be used as the average thickness at the middle of the height. This gives a broader base to the wall and gives a larger factor of safety against overturning, but requires the same volume of masonry to keep the resultant thrust within the middle third of the base.
Walls computed as rectangular may be battered on the face to an extent which lessens the top thickness by one-third without increas ing the base thickness. This slightly decreases the resisting moment, but increases the value of x, lessens the pressure at the toe, and does not impair the stability of the wall.