Principles of Differential Leveling

object in the immediate vicinity, such as the rim of a manhole cover, a rod, or the finish floor of an existing structure. This object may be given its relative sea level elevation (if it is known); or it may be given a convenient, arbitrarily assumed elevation, usually a whole number, such as 100.0 feet. An object of this type, with a given, known, or assumed elevation, which is to be used in determining the elevations of other points, is called a bench mark. PRINCIPLES OF DIFFERENTIAL LEVELING Figure 5-15 illustrates the principle of differential leveling. The instrument shown in the center represents an engineer’s level. This optical instrument provides a perfectly level line of sight through a telescope, which can be trained in any direction. Point A in the figure is a bench mark (it could be a concrete monument, a wooden stake, a sidewalk curb, or any other object) having a known elevation of 365.01 feet. Point B is a ground surface point whose elevation is desired. The first step in finding the elevation point of point B is to determine the elevation of the line of sight of the instrument. This is known as the height of instrument and is often written and referred to simply as “H.I.” To determine the H.I., you take a backsight on a level rod held vertically on the bench mark (B.M.) by a rodman. A backsight (B.S.) is always taken after a new instrument position is set up by sighting back to a known elevation to get the new H.I. A leveling rod is graduated upward in feet, from 0 at its base, with appropriate subdivisions in feet. In figure 5-15, the backsight reading is 11.56 feet. Thus, the elevation of the line of sight (that is, the H.I.) must be 11.56 feet greater than the bench mark elevation, point A. Therefore, the H.I. is 365.01 feet plus 11.56 feet, or 376.57 feet as indicated. Next, you train the instrument ahead on another rod (or more likely, on the same rod carried ahead) held vertically on B. This is known as taking a foresight. After reading a foresight (F.S.) of 1.42 feet on the rod, it follows that the elevation at point B must be 1.42 feet lower than the H.I. Therefore, the elevation of point B is 376.57 feet minus 1,42 feet, or 375.15 feet. GRADING The term “grade” is used in several different senses in construction. In one sense, it refers to the steepness of a slope; for example, a slope that rises 3 vertical feet for every 100 horizontal feet has a grade of 3 percent. Although the term “grade” is commonly used in this sense, the more accurate term for indicating steepness of slope is “gradient.” In another sense, the term “grade” simply means surface. On a wall section, for example, the line that Figure 5-15.—Procedure for differential leveling. 5-10