Journal of Surveying Engineering

Current methods used for estimating the volume of pit excavation assumes that the ground profile between the grid points is linear (based on the trapezoidal rule), or nonlinear (based on Simpson's 1/3 and 3/8 formulas). Generally speaking, the nonlinear profile formulas provide better accuracy than the linear profile formulas. However, all the methods mentioned have a common drawback: The joints (grid points) of any two straight lines (the trapezoidal rule), quadratic polynomials (Simpson's 1/3 formula), or cubic polynomials (Simpson's 3/8 formula) form sharp corners. Consequently, these models may not describe the ground profile well. In this paper, formulas based on an extension of the cubic spline polynomial are presented. The grid of this new method is constructed by choosing the variational points of the ground profile and then dividing the pit's area into rectangles of unequal size. Therefore, the new formulas can be used for estimating the excavation volume of a pit divided into a grid with unequal intervals. Further, due to the characteristics of the cubic spline polynomial, a curve modeled by this polynomial can match the ground profile well. The new formulas should provide better accuracy than the other methods mentioned.

The vertical motions of 11 control points in the Northern part of Israel (Haifa North‐East) are studied seasonally for a period of one full year (October 1988 to September 1989). The purpose of this paper is to compare the mathematical equivalence between various leveling‐adjustment techniques, namely, the classical minimum variance estimate, free net method, and the least‐squares collocation method, by using, as an example, a number of leveling loops in Northern Israel. A comparison of results showed that there were no significant differences between the free net and the least‐squares collocation methods (LSC). The elevation differences between the bench marks for the free net and condition equations method were the same, but the estimated heights were different. Even though the LSC technique is much more complicated and time consuming, it confirms the stability of points on the bedrock and the vertical movement of points on the high‐tension poles. It is, therefore, convenient to use either the free net method or the LSC method on projects concerning precise leveling.

Measurements and results derived from the three‐dimensional Global Positioning System (GPS) are more accurate than classical geodetic observations and methods used until recently to define conventional horizontal (geometric) da‐tums, e.g., the North American Datum of 1983, the final readjustment of which was finished in 1986, thus the notation NAD 83 (1986). The situation may not be strictly the same with respect to vertical (physical) datums such as the National Geodetic Vertical Datum of 1929 (NGVD 29) because an accurate geoid is required. In this paper comparisons of standard datums [NAD 83 (1986), NGVD 29] with recent GPS results in the state of Florida are analyzed. Their relationship with a very long baseline interferometry (VLBI) reference frame is also discussed. The investigation shows that overall the relative accuracy of NAD 83 (1986) in Florida is between 1/200,000 and 1/500,000 or from five to two parts per million (ppm), yet still not as good as the two‐dimensional results derived from GPS.

Intermediate transition and sidehill cross sections are normally established when the roadway section changes from cut to fill or vice versa. The average-end-area (AEA) and pyramid formulas are employed in practice for computing the cut and fill volumes. This technical note proposes a pyramid frustum (PF) formula that can be used instead of the AEA formula. Because the volumes formed in the transition areas are frustum-like solids, the PF formula is more accurate than the AEA formula. The proposed formula, which is a function of only the end areas and the distance between them, is as simple as the AEA formula. The PF formula should be of interest to the highway engineers concerned with achieving greater accuracy in volume computations.