Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

104. The reader is presumed to be acquainted with the manner of finding the areas and cubes of simple geometric figures and bodies. The following fifteen figures show the forms which may be taken by the cross section of a railroad in cutting; for embankment invert the same. They are easily separable into simple figures.

105. The formation of tables for the amount of earth in level cutting is very simple. The area of the following section, where B is the base, and R the horizontal dimension of the slope, is

or finally

i. e., the base of a rectangle by its height. Multiply this by 100 and divide the product by 27; or divide by 27
100, and we have the cubic amount in a prism one hundred feet long. The road-bed being nineteen feet wide, and slopes one and a half to one, the formula for the amount of a prism one hundred feet long is

and assuming the base of rock cutting as eighteen feet, and slope one quarter to one, and embankment eighteen feet at subgrade, we have, rock,

and embankment,

the figure being inverted for embankment. For a prism of ten or of one thousand feet in length, we have only to move the decimal point. In forming a table, proceed as follows:—

It is evident from inspection of fig. 55, that c exceeds c^o by h × 2r; and that c″ exceeds c′ by h′ × 2r′; and so on as far as we go; this increase being constant, we have then to find the area of c, and for the area c + c′ double c, and add the increment; whence the rule:—

Having found the increase (which varies with the angle of the slope) for the second section, add the increase to twice the first. For the third, add twice the increase to three times the first; and for the nth, add n – 1 times the increment to n times the first area, or algebraically calling a the first area, a′ the second, a″ the third, aⁿ the nth area, and we have

We might operate at once upon the cubic contents, but for the length to which some decimals run; some indeed circulating.

106. The table thus made may be of the following form:—

i. e., cut being eight feet, each one hundred feet length gives nine hundred and nineteen cubic yards; one thousand feet, 9190 yards, and ten feet of length 91.9 cubic yards.

107. The preceding system is intended only for approximate estimates. Let one person read off the cuts or fills from the profile, a second give the corresponding number of yards by the table made as above, while a third sets the figures down; being careful to separate the cuts from the fills.

For final measurements, none but the prismoidal formula should be used; the length of the prismoids being taken at each one hundred feet, and nearer when the ground is rough.

108. As an example of the comparative amounts given by the above formula, and by the common method of averaging end areas, take the following, the slopes being 1½ to 1.

By averaging end areas we have

And by the prismoidal formula,

cubic feet in favor of the method of end areas.

109. The prismoidal formula is algebraically

or, verbally, to the sum of the end areas add four times the middle area, and multiply the result by one sixth of the length; the middle area being the area made upon the mean height of the two ends. Thus if the length is one hundred feet, and one end ten feet high, the other twenty feet high, and slopes one and a half to one, the cubic amount is, (the base being twenty-two feet,)

110. Some writers have considered that the grades of a road should be so adjusted as to equalize the cutting and the filling. The total rise and fall might not be much affected by this, but the mechanical effect of grades might. A perfect balance between the cuts and fills is not to be desired. The whole cost of earthwork must be a minimum, and it is often cheaper to waste and borrow, than to make very long hauls, and to form the grade line by interchange of material on the profile only.

111. The transverse slopes depend upon the nature of the soil in which the cut is made. Gravel will stand at a slope of one and a half horizontal to one vertical, and in some cases one and a quarter, or even one to one. Clay stands nearly vertical for some time, but finally assumes a very flat slope, in some cases two, three, and even four horizontal to one vertical. In places where a stratum of clay underlies more reliable earth, to avoid a very long slope, it may be economical to support the clay by a wall, and to slope the earth only.

112. Care should be taken in every case to secure good drainage and to protect the slopes by surface drains at the top. The drains in long cuts should be slightly inclined to insure the running off of the water. A fall of ten feet per mile is enough; five will answer in many cases. On side hill cuts a surface drain along the top of the upper slope will do good service. On many high embankments, catchwater drains, commencing at the road-bed and gradually sloping to the base, will prevent, in a great degree, cutting of the bank.

113. Embankments, when made rapidly, should be finished to the full width, somewhat above true grade, to allow for the after settlement. (See specification.)

114. The following allowances have been made for the shrinkage of material in some parts of America.

The bulk of quarried rock on the contrary increases from twenty-five to fifty per cent.

115. When embankments are carried up slowly, in layers of three or four feet at a time, the after settling is very little; when carried up all at once it will be more. The full width must be kept, even above the required height. Fig. 56 shows the forms of a bank both before and after settlement.

The best method of forming a bank of bad material is to ram the layers as in fig. 57; thus the tendency is to consolidate by settling, and not to destroy the work by sliding.

116. In the formation of embankments it is not always advisable to make the whole bank from an adjoining cut or cuts. The length of haul may be too long. In this case it is customary to waste a part of the cut and to borrow earth from some nearer point for the bank. That the transport shall be effected in the most economical manner, the product of the cube of earth, by the mean distance, (the distance between the centres of gravity, of excavation and embankment) must be a minimum. To determine the theoretical minimum expense, the problem becomes very complicated on account of the great number of variable elements entering therein; and the result obtained is applicable only to a particular case. Local circumstances more than any other thing, determine the position of a borrow pit, and the path over which the material is to be transported.

OF THE AVERAGE HAUL.

117. To find the cost of the movement of earth on any section, we must have, the total amount of earth to be moved, and the average haul; the latter being the distance through which, if the whole amount were moved, the cost would be the same as the sum of the costs of moving the partial amounts their respective distances. To find the average haul proceed as follows: First, find the distance between the centres of gravity of each mass both before and after moving, which may be done with sufficient accuracy for practice by inspection of the profile. Next,

118. Divide the sum of the products of the partial amounts by their respective hauls, by the total amount; the result is the average haul in feet. Or algebraically, representing the partial amounts by m, m′, m″, m‴, the respective hauls by d, d′, d″, d‴, the total amount by S, and the average haul by D, we have

Example.—Let column 1 show the partial amounts in cubic yards. Column 2 the corresponding hauls.

Proof.—Assume the cost of moving 1,000 yards one foot as ten cents, the costs of the separate masses are

also the cost of moving 16,000 yards 475 feet is

119. The movement of earth is effected by shovels, barrows, horses and carts, or by cars. In round numbers we can move earth

As the haul increases, the number of vehicles of transport remaining the same, the number of excavators must decrease. Earths easily removed do not admit of so large a haul, with a given number of excavators, as hard earths. The nature of the ground, form of carts, kind of horses, season of the year, and price of labor are some of the elements entering the problem of transport. The best illustration of the matter will be found among the very able writings of Ellwood Morris, Esq., C. E., in the Journal of the Franklin Institute. Knowing the value of wages, the nature of the earth and length of haul, it is easy to see what mode of transport must have the preference.

CONTRACTOR’S MEASUREMENTS.

120. The price of executing any piece of work is paid to the contractor at stated intervals, generally once each month. The amount of work done at these partial payments is obtained by instrumental reference to the ground. Towards the completion of operations the most correct and easiest method of finding the rate of progress is to deduct the amount already done from the total as given by primary measurement. The full price is not paid to the contractor, but a percentage is kept back, which insures a faithful performance of work. It is impossible to establish a pro rata price at first, owing to the uncertain nature of the work; what appears to be earth may be rock. By deducting a maximum price estimate for all but one of the items, an approximate pro rata value for that one may be determined. An analysis of cost will define the minimum limit for advantage to the contractor; and the pro rata value less the percentage, the maximum for the company’s benefit.

121. When a level is to be drained, or the water carried off from the surface of a swamp, the first point to be ascertained is the location of the lowest outfall. The direction in which aquatic plants lie show the natural fall of the water, these always pointing down stream. When the most available outlet has been decided upon, a main drain should be set out, from which oblique branches are to be cut, pointing in the direction of the current; into these all minor cuts are to be collected so that the whole district may be equally drained. The fall should be greatest at the most remote points, decreasing as the amount of water increases. Large and deep rivers run sufficiently fast when the fall is one foot per mile. For small rivers, double that is necessary. Ditches and ordinary drains require eight feet per mile. When the water is made to pass away from the surface, it should flow very gradually, that the sides and bottom of the ditches may not be worn away by friction; it should be in constant motion that the channel may be kept clean and increase in velocity as it proceeds. When the surface is a perfect level, the drains should of course be made straight.

After the quantity of water has been determined by careful observation, the section of the main and branches must be fixed, so that regarding both their areas and velocities, the main drain will not be overcharged.

To facilitate the current, the sides should be inclined about one and a quarter to one; and the breadth of base should be two thirds of the depth of water. These results are obtained from the practice of English engineers, who have given a great deal of attention to the subject.

Drains cut through bogs, may have sides nearly, if not quite vertical, as the fibres of plants forming the soil resist the action of the water.

SUBSOIL DRAINING.

Geology has assisted this operation very materially by rendering us acquainted with the quality and nature, as well as of the succession of strata. The soils which are impervious are usually the heaviest, and the porous are those of lighter quality. Clays, when they receive water, will only part with it by evaporation, when left in a natural state; and therefore to make such a surface fit for a useful end requires considerable ingenuity, and often great expense. Such a soil is not rendered unstable by underground springs, and may be effectually drained by boring through, and letting the water off into an under stratum, when this is of a porous nature.

When land abounds with springs, or is subject to the oozing out of subterraneous water, draining is effected in a different manner. Springs have their origin in the accumulation of rain water, which falling upon the earth, after passing the porous strata, lodges upon the impervious, and glides along the sloping surface until it crops out, generally in some valley where it forms a watercourse.

Descending streams are easily taken care of by collecting them into a body before they reach the low lands.

When a morass is to be drained, the strata upon which it reposes should be examined, and if, as is often the case, a layer of clay intervenes between the substratum and the mossy covering, which holds the water, by tapping this in well chosen places, the whole will sink away.

A fine example of embankment upon a bad bottom was performed by Mr. Stephenson, on the Great Western Railroad, England, at the crossing of Chatmoss. This moss was so soft that cattle could not walk upon it, and an iron bar sank into it by its own weight. The moss was first thoroughly drained by a system of longitudinal and cross drains, and the embankment made of the lightest material possible—the dried moss itself. Without this treatment, the moss would have sank beneath the bank alone; it now supports the passage of the heaviest railroad trains.

METHOD OF CONDUCTING OPERATIONS.

122. The organization of the engineer corps upon a railroad is as follows, differing somewhat in different parts of the country.

The Chief Engineer has entire charge of all the work, of all assistants, appointing and dismissing members of the corps, designing of all structures, making of specifications, and of all mechanical operations incident to the thorough, correct, and timely construction of the road; and should be able also to specify, generally, the amount and character of the equipment needed.

The Resident Engineer has charge of the detailed construction of from twenty-five to fifty miles of road, according to the nature of the work, being responsible to the chief engineer for the proper execution of the orders from headquarters; he returns to the chief engineer a monthly account of the exact condition of his work, both as to the amount executed, and also that remaining to be done.

The assistants of the resident engineer are a leveller and transit man; to whom, under his supervision, is the duty of laying out, measuring, and estimating the work. The leveller has with him one or more rodmen. The transit man, two chainmen, and one or more axemen.

In some cases, added to the above are inspectors of masonry, bridging, and superstructure. These are necessary only when the road embraces a great number of mechanical structures; too many to leave the proper time to the resident engineer for his other duties. Once each month the exact amount of graduation, bridging, and masonry executed is obtained by the resident and his assistants. The chief engineer applies the prices to these amounts, and the percentage deduction being made, the estimate is ready for the treasurer.

123. The abstract prepared from the monthly estimate should show clearly, without unnecessary figures, the amount of work completed, and also that remaining to be done.

For convenience, the various blanks used on railroads should fold to the same form and size. The blanks are,

The contract and specification are given in chapter IV. The resident’s monthly return to the chief engineer is somewhat as follows:—

Monthly return of work done on the first division of the A and B Railroad, for the month ending ——, showing also the whole amount of work up to ——; also the present estimate for completion.

The resident engineer’s assistants return to him weekly a statement of the amount and value of the force employed upon the several sections, and monthly the exact amount of work done on the same, for each of which there should be a blank. The above forms may be printed and folded in 8vo., or may be the continuous headings of a large sheet.