The following table, which gives the volume in cubic yards contained on a 100-foot length for areas varying from 1 to 30 square feet, will be found to be of great assistance in making estimates. The yardage for any section can be found as follows: Find the mean area of the section to the nearest hundredth; from the table find the volume corresponding to the mean area. It may not be possible to do this directly, but by adding quantities corresponding to various areas whose sum equals the mean area and by moving the decimal point to the right or left, the yardage for any area whatsoever can be found very rapidly. Multiplying the volume corresponding to the area by the length of the section divided by 100 gives the total volume of the section. TABLE No. 1 CUBIC YARDS OF EXCAVATION OR EMBANKMENT FOR AVERAGE END AREAS The following example illustrates the use of the table: Assume that the average area of the sections for a length of 500 feet is 23.46 square feet. To find the volume proceed as follows: When specifications contain an overhaul clause, it will be necessary in some cases to make a mass diagram in order to find the places at which it is economical to borrow material. Usually, w FIG. 32. however, the cuts and fills are so related that a study of the estimate alone will be sufficient to determine this detail. The quantity of material contained in the surface may be computed as follows: Fig. 32 shows a surface of uniform depth formed by intersecting planes. Let d = depth in feet and w width in feet. = wd The volume for a length of L feet will be L. 27 If d is not uniform and the depths at the center and sides d1 + 2 d + dz are d, d1, d2, respectively, the average depth is 4 will give the volume. Fig. 33 shows a surface composed of curves, either circular or parabolic. In this case the area required is that bounded by the two curves. This area may be found by adding the areas of the segment acb and the rectangle abfe and subtracting from this sum the area of the segment e df. If the curves are FIG. 33. circular or parabolic in form these areas can be found without difficulty. As above, the area times the length will give the volume. A complete estimate, besides the amount of grading and surfacing, will contain quantities of all the work to be done, such as linear feet of guard rail, drain pipe and culvert pipe of various sizes, concrete, ledge excavation, curbing, catch basins, etc. CHAPTER V DRAINAGE OBJECT OF DRAINAGE. In the construction of any type of road or pavement, drainage is of the utmost importance. Water is one of the most destructive agents encountered in the construction and maintenance of highways. Provisions for drainage should be made so that water will not stand on the surface or at the sides of the roadway. Another object of drainage is to remove from the subsoil the water which, under certain conditions, has a tendency to rise to the surface. Since the loads which come on a road surface must ultimately be borne by the natural soil, it is obvious that a dry condition of the subsoil is a prerequisite for the proper accomplishment of this duty, since a soil which is saturated with water will have practically no supporting power whatsoever. Drainage may be properly considered under two main heads, namely, subdrainage and surface drainage. SUBDRAINAGE CONDITIONS ENCOUNTERED. The kind of soil, the location of the road, and the climatic conditions are factors which influence the necessity for subdrainage. If the subsoil of a road is of a sandy or gravelly nature and the road is located on high ground so that the water as it seeps through the soil readily runs off, subdrainage is not necessary. On the other hand, a clayey or any other plastic soil which readily retains water will, in some locations, become almost impassable unless properly subdrained. Through low places where the water ponds at the side of the road, keeping the subsoil constantly saturated, subdrains will affect a marked improvement. Oftentimes springs will occur on hillsides which, unless led from the road by subdrains, will soften the subsoil with a consequent failure of the surface at these points. A stratum of rock may lie near the surface and water will collect in its depressions and tend to soften the overlying road. Deep clay soils, and particularly those of stiff clays which do not contain any considerable proportion of coarse sand, should have the water removed from them as much as possible and be kept in a dry state. Certain types of loams are practically as bad as clays when wet. Quicksands have absolutely no supporting power, but if properly underdrained they may serve as a suitable foundation. If water is allowed to remain in the subsoil in cold weather, the ground freezes and expands, thus loosening the soil. In the spring the ice melts, the soil becomes softened by the water and is churned up by the traffic until the road surface is ruined. There are conditions where frost may prove to be harmless, as is shown in the semi-arid regions west of the Mississippi River. There is practically no water in the ground in this locality during the winter when it is frozen, and consequently there is no expansion by the freezing of water in the soil. For this reason there is no heaving or disturbance of the ground. It is quite essential when the frost comes out of the ground in the spring to provide means so that the water below the surface which has accumulated by the thawing will be immediately carried away. Since the thawing action takes place below as well as near the surface, if the resultant water is not removed the foundation will soon soften. Subdrains properly placed will remove this water. The hydrostatic pressure of water in places higher than the level of the highway may force the water slowly up through the soil, which fact may explain the presence of water in a road during a thaw where it was known that the ground when frozen was perfectly dry. There are a variety of ways by which subdrainage can be accomplished. PIPE DRAINS. One of the best and cheapest methods of accomplishing subdrainage is by means of lines of tile pipe. The Pipe. The pipe may be made of either cement or vitrified clay. The cement pipes are generally made with plain ends and the vitrified pipes with bell and spigot ends. The pipes are made in 1-foot lengths for the smaller diameters and in 2-foot lengths for the larger diameters. The pipe for drains should be of good quality, of uniform diameter, with no blisters or bubbles on the inner surface. The pipe should also be free from fire cracks as well as cracks caused by transportation or handling. All clay pipe must be thoroughly vitrified. Glazing, however, is not absolutely essential. Concrete pipe for drains should be made of the best quality American Portland cement and clean sand and fine gravel in proportions of not less than one part cement and four parts sand and gravel. The gravel used should contain no pebbles whose diameter exceeds 3/4 of an inch. The concrete must be mixed wet and thoroughly rammed into the molds before setting begins. The pipe should be allowed to season for at least three months in a temperature above 40 degrees Fahrenheit before being used. Cost of Pipe. The cost of drain pipe varies with the size of pipe, point of delivery, and the amount purchased. These are average prices f. o. b. factory in carload lots. The requisite size of pipe of water to be carried and There are several formulas determined. The assump Determination of Size of Pipe. required depends upon the amount the grade to which the pipe is laid. by means of which the size can be tions that must be made, however, in applying a formula to any particular case are such as to render an accurate determination of the proper size impossible. For instance, the amount of water to be carried off cannot be more than roughly approximated, and very little reliable data relative to the flow of water in pipes of this kind is obtainable. The amount of water is |