Assuming the cross section of the surface of the pavement to be an arc of a circle, its radius is approximately 400 ft. The differ ence in length between the arc and the chord can he computed with sufficient accuracy by the following well-known formula: in which a equals the length of the arc, c equals the length of the chord (the width of the street), and r equals the radius of curva ture of the arc. In the above example, the length of the arc is 0.192 inch greater than the width of the street. The rise at the crown is practically proportional to the difference in length between the arc and its chord. The expansion for 20° F. is (1000,003,4 X 20 X 40 X 12 = 0.032,6 inch, which is practically one sixth of the difference between the normal length of the arc and the chord of a 40-foot pavement having a 6-inch crown. Therefore an increase of temperature of 20° above the 30° considered in the preceding paragraph. i. e., a total rise of 50° F., will lift the crown of the pavement approximately 1 inch from the foundation pro vided the curbs are immovable.
Of course, the preceding investigation is only approximate, but it shows the possibility of a pavement's being lifted from its foundation through the action of heat. Whether or not the pave ment will be lifted from the foundation will depend upon (1) the solidity of the curbs, (2) the rigidity of the filler. (3) the thickness of the joints. (4) the temperature of the pavement when the joints were filled (5) the maximum temperature. and (6) the duration of the high temperature.
If the bricks lat• from the foundation. why does not the very flat arch thus formed break down when a heavy vehicle comes upon it? The bricks of the pavement are firmly cemented to• gether, and the whole acts somewhat as a bent beam, and there is so much flexibility in this brick beam that it deflects and touches the foundation at points sufficient to prevent the destruction d the arch, and still is unsupported at enough points to give out a rumbling sound.
In cold weather, the pavement may be lifted from its foundation by the freezing of the water in the earth outside of the curbs forcing the curbs inward. It is well known that water in freezing expands with considerable force; and if each curb of s 40-foot pavement is forced inward 1 of an inch, the crown of the pavement will be lifted more than an inch from the foundation. This result will occur only when the subsoil outside of the curbs freezes while it is at least nearly saturated with water.
It is claimed that the lifting of a brick pavement in cold weather is due to the freezing of the water absorbed by the brick. In support of this view it is claimed that pavements made of brick having a high absorptive power more frequently give out a rum bling sound than those made of brick having a low absorptive power. The theory hardly seems plausible, since at best the per
cent of water absorbed is very small and its expansion would be taken up to a considerable extent by the air remaining in the pores of the brick. The facts offered in support of the above theory doubtless have some other interpretation.
Sometimes spots only a few feet in diameter give out a rumbling sound; and on account of the limited area of these spots, the rumbling can not be due to either of the causes discussed above. These spots are probably due to a shrinkage of the sand cushion by its drying out. A small per cent of water adds con siderably to the volume of fine sand, and hence if the sand cushion is wet when laid and dries out after the cement filler has set, the brick will be left unsupported. These spots disappear with the use of the pavement—probably by the breaking of the cement and the settling of the bricks.
It is claimed that the rumbling is due to the shrinkage of the concrete; but this can not be correct as the bricks are not laid until the concrete is firmly set.
It is also claimed that the rumbling is due to large pebbles in a thin sand cushion, which keep the bricks from obtaining a firm bed in the sand; but this is at least doubtful, since such pebbles would probably be crushed during the rolling, and besides many such pebbles would be required to produce the observed noise.
The longitudinal expansion can be taken up either by filling three or four transverse joints with tar, each 25 or 30 feet, or by inserting a 1-inch tar-joint each 40 or 50 feet.
In one case a 1-inch expansion joint at each curb and two transverse tar-joints every 50 feet required one barrel (50 gallons) of tar for each 274 square yards of a pavement 36 feet between curbs, or say 1 gallon of tar for each 5 or 6 square yards of pave ment. In another case, a i-inch expansion joint at each curb and a i-inch transverse expansion joint at each 35 feet required 237 gallons of tar for 2.870 square yards of pavement or 1 gallon for each 12 square yards.