SOLID MASONRY WALLS 126. Stability of Walls.—A masonry retaining wall may fail in either of three ways: 1. By overturning or rotating about its toe.
2. By crushing the masonry.
3. By sliding on a horizontal joint.
Insufficient foundation is probably the most common cause of failure of retaining wall;. This is not, however, due to failure of the «•a11 itself, but to Lack of sufficient footing or other support placed upon compressible or soft soils or to hick of proper drainage. This is discussed in Art. 36.
In Fig. 64, A is a wall with vertical face supporting a hank of earth as shown.
Let P= thrust of earth against the wall; V= Vertical component of P; 11 =horizontal component of P; 11 = of wall acting through its center of gravity; 1? = resultant pressure on base A B; b=widtll of base of wall; a= width of top of wall; d= distance from face of wall to its center of gravity; compression on masonry at toe of wall; x=distance from toe of wall to point of application of resultant pressure upon the base; (3= angle made by 1? with base of wall.
Resisting moment of the thrust about the toe of the wall at B is 211,= H V This moment tends to overturn the wall by causing rotation about. B, and is resisted by the moment of the weight of wall in the opposite direction. This moment is When these moments are equal (.11,,— the resultant R obtained by combining P and IV passes through B and the wall is on the point of overturning. The ratio is the factor of safety against overturning.
When is greater than 3[, R will cut the base of the wall to the right of B. Placing we have from which we find the distance of the point of application of R from B: This point of application of R may also be found graphically as shown in Fig. 63.
The resultant IZ should always cut the base of the wall within its middle third (.z>b 3) in order that the pressure may be distrib uted over the whole section of the base and there may be no tend ency for the joint to open, or no tensile stress developed at the inner edge (A) of the section.
Crushing of unit stress at the toe of the wall (B) must not exceed the safe crushing strength of the masonry. The distribution of stress over the section depends upon the position of the point of application of the resultant (1?). When i=b 3, the
2( stress at A will be zero, and the stress at B, ) If .r be less than b,'3, the pressure will be distributed over a distance 3.r Resistance to Sliding depends upon the development of sufficient friction in any joint through the wall to overcome the pressure parallel to the joint. Thus (Fig. 64) in order that no sliding occur at the base of the wall, the frictional resistance in the joint A B must he greater than the horizontal component of the thrust R. This will be the case when I? makes an angle (a) with the normal to A B that is less than the angle of friction of masonry sliding upon masonry.
Tan 13= must be less than the coefficient of friction of the masonry.
In the construction of heavy walls, resistance to sliding may be increased by breaking joints so that no continuous joint exists through the wall. Joints inclined from the front to the back of the wall are also sometimes used so as to bring the resultant pressure more nearly normal to the joint.
127. Empirical Design.—En the practical designing of retaining walls, engineers have commonly used empirical rules given by certain prominent authorities, or have assumed dimensions based upon their own experiences. The uncertain and conflicting nature of the assumptions used in producing the formulas based upon the various theories, and the lack of satisfactory experintental data has caused the use of dimensions shown by experience to be safe and in very many instances probably quite excessive.
Trautwine's rules have been extensively used for many years, and are as follows I for vertical walls: When the backing is deposited loosely, as usual, as when dumped carts, cars. etc., Wall of cut stone, or first-class large ranged rub ble, in mortar 35 of its entire vertical height Wall of good common scabbled mortar-rubble, or brick 4 of its entire vertical height Wall of well-scabbled dry rubble i of its entire vertical height With good masonry, however, we may take the height from the ground surface tsp, instead of the total height as above indicated. When the wall has a sloping or offset back, the thickness above given may be used as the mean thickness, or thickness at the mid height.