err on the safe side, and give an unnecessarily large margin for safety.

His experiments also showed that the wall might start to fall but not fall, and that it required considerable jarring to cause it to fall. When the movement began the face did not remain plane but became curved. This shows why in practice walls have assumed a curved face, and yet stand securely for many years. After a slight movement has taken place, the pressure due to the earth is slightly relieved, and the whole mass takes up a new position of equilibrium, until finally the earth nearly supports itself.

The more

477. Form of Section of Retaining Walls. usual form of cross section is that in which the back of the wall is built vertically, and the face with a batter varying between one base to six perpendicular, and one base to twenty-four perpendicular. The former limit having been adopted, for the reasons already assigned, to secure the joints from the effects of weather; and the latter because a wall having a face more nearly vertical is liable in time to yield to the effects of the pressure, and lean forward.

478. The most advantageous form of cross section for economy of masonry is the one (Fig. 68) termed a leaning

D

P

Fig. 68-Represents a section O of a leaning retaining wall with a sloping face AD and the back BC counter-sloped.

retaining wall. The counter slope, or reversed batter of the back of the wall, should not be less than six perpendicular to one base. In this case strength requires that the perpendicular let fall from the centre of gravity of the section upon the base, should fall so far within the inner edge of the base, that the stone of the bottom course of the foundation may present sufficient surface to bear the pressure upon it.

479. Walls with a curved batter (Fig. 69) both upon the face and back, have been used in England, by some engineers, for quays. They present no peculiar advantages in strength

over walls with plane faces and backs, and require particular care in arranging the bond, and fitting the stones or bricks of the face.

480. Measures for increasing the Strength of Retaining Walls. These consist in the addition of counterforts, in the use of relieving arches, and in the modes of forming the embankment.

481. Counterforts give additional strength to a retaining wall in several ways. By dividing the whole line of the wall into shorter lengths between each pair of counterforts, they prevent the horizontal courses of the wall from yielding to the pressure of the earth, and bulging outward between the extremities of the walls; by receiving the pressure of the earth on the back of the counterfort, instead of on the corresponding portion of the back of the wall, its effect in producing rotation about the exterior foot of the wall is diminished; the sides of the counterforts acting as abutments to the mass of earth between them may, in the case of sand, or like soil, cause the portion of the wall between the counterforts to be relieved from a part of the pressure of the earth behind it, owing to the manner in which the particles of sand become buttressed against each other when confined laterally, and offer a resistance to pressure.

482. The horizontal section of counterforts may be either rectangular or trapezoidal. When placed against the back of a wall, the rectangular form offers the greater stability in the case of rotation, and is more economical in construction; the trapezoidal form gives a broader and therefore a firmer con

nection between the wall and counterfort than the rectangular, a point of some consideration where, from the character of the materials, the strength of this connection must mainly depend upon the strength of the mortar used for the masonry.

483. Counterforts have been chiefly used by military engineers for the retaining walls of fortifications, termed revêtements. In regulating their form and dimensions, the practice of Vauban has generally been followed, which is to make the horizontal section of the counterfort trapezoidal, making the height of the trapezoid ef (Fig. 70), which corresponds to the

length of the counterfort, two-tenths of the height of the wall added to two feet, the base of the trapezoid ab corresponding to the junction of the counterfort and back of the wall, one-tenth of the height added to two feet, and the side cd which corresponds to the back of the counterfort equal to two-thirds of the base ab. The counterforts are placed from 15 to 18 feet from centre to centre along the back of the wall, according to the strength required.

484. In adding counterforts to walls, the practice has generally been to regard them only as giving additional stability to the wall, and not as a means of diminishing its volume of masonry of which the addition of the counterforts ought to admit.

485. Relieving Arches are so termed from their preventing a portion of the embankment from resting against the back

of the wall, and thus relieving it from a part of the pressure. They consist (Fig. 71) of one or more tiers of brick arches

built upon counterforts, which act as the piers of the arches. In arranging a combination of relieving arches and their piers, the latter, like ordinary counterforts, are placed about 18 feet apart between their centre lines; their length should be so regulated that the earth behind them resting on the arches, and falling under them with the natural slope, shall not reach the wall between the arch and the foot of the back of the wall below the arch. The thickness of the arches, as well as that of the counterforts, will depend upon the weight which the arches sustain. The dimensions of the wall will be regulated by the decreased pressure against it caused by the action of the arches, and the point at which this pressure

acts.

486. Whenever it becomes necessary to form the embankment before the mortar of the retaining wall has had time to set firmly, the portion of the embankment next to the wall may be of a compact binding earth placed in layers inclining downward from the back of the wall, and well rammed; or of a stiff mortar made either of clay, or sand, with about th in bulk of lime. Instead of bringing the embankment directly against the back of the wall, dry stone, or fascines may be laid in to a suitable depth back from the wall for the same purpose. The precaution, however, of allowing the mortar to set firmly before forming the embankment, should never be omitted except in cases of extreme urgency, and then the bond of the masonry should be arranged with peculiar care, to prevent disjunction along any of the horizontal joints.

487. Walls built to sustain a pressure of water should be regulated in form and dimensions like the retaining walls of embankments. The buoyant effort of the water must be taken into account in determining the dimensions of the wall, whenever the masonry is so placed as to be partially immersed in the water.

488. Heavy walls, and even those of ordinary dimensions, when exposed to moisture, should be laid in hydraulic mortar. Grout has been tried in laying heavy rubble walls, but with decided want of success, the successive drenchings of the stone causing the sand to separate from the lime, leaving when dry a weak porous mortar. When the stone is laid in full mortar, grout may be used with advantage over each course, to fill any voids left in the mass.

489. Beton has frequently been used as a filling between the back and facing of water-tight walls; it presents no advantage over walls of cut, or rubble stone laid in hydraulic mortar, and causes unequal settling in the parts, unless great care is taken in the construction.

490. When a weight, arising from a mass of masonry or earth, rests upon two or more isolated supports, that portion of it which is distributed over the space, or bearing between any two of the supports, may be borne by a block of stone, termed a lintel, laid horizontally upon the supports, by a combination of blocks termed a plate-bande, so arranged as to resist, without disjunction, the pressure upon them; or by an arch.

491. Lintel. Owing to the slight resistance of stone to a cross strain, and to shocks, lintels of ordinary dimensions cannot be used alone with safety, for bearings over five or six feet. For wider bearings, a slight brick arch is thrown across the bearing above the lintel, and thus relieves it from the pressure of the parts above.

492. Plate-bande. The plate-bande is a combination of blocks cut in the form of truncated wedges. From the form of the blocks, the pressure thrown upon them causes a lateral pressure which must be sustained either by the supports, or by some other arrangement (Fig. 72).

The plate-bande should be used only for narrow bearings, as the upper edges of the blocks at the acute angles are liable to splinter from the pressure. If the bearing exceeds 10 feet, the plate-bande should be relieved from the pressure