The Number of Set Ups in Lines as Weights in the Precise Levelling

The main method for monitoring of vertical displacements of engineering constructions and estimation of deformation processes is the precise geometric levelling. This method is also essential for defining the state height systems, which are the base of any vertical engineering network. An extremely important factor about the final accuracy of a geometric levelling network is not only the accuracy of measurements, but also the choice of the weights, applied in its adjustment. The recent specification for the precise levelling in Bulgaria allows two types of weights. The first ones are the classical weights, which are inversely proportional to the lengths of levelling lines L, in the form w= 1⁄L. The second type of weights are inversely proportional to the number of set ups in the lines n, i.e. w= 1⁄n. The purpose of the current research is to show that there is not significant difference in the results, which would be produced by both types of weights, especially for the territory of Bulgaria. In order to prove this fact, we adjusted the network of the Third Levelling Bulgaria by both types of weights. The differences between the standard errors of the adjusted heights of the identical benchmarks in the network, produced by adjustments with both weights, vary in the range ±0.5 mm. The differences between the adjusted heights of the same benchmarks in the network, obtained in both variants of adjustment of the network, vary from -1.1 mm to 1.3 mm. The distributions of the last differences approximate normal distribution with the expectation µ = 0.12 mm and standard deviation σ = 0.61 mm. These results can be explained by the high correlation between the length of the levelling lines and the number of the set ups. We estimated that the coefficient of correlation between L and n in the case of the Third Levelling of Bulgaria is equal to 0.976. The general conclusion is that we cannot expect any significant increase of the adjustment accuracy of a levelling network, if we change the weights w= 1⁄L with the weights w= 1⁄n. This conclusion is especially valid for networks developed through flat areas, where the most of lengths of the sights are approximately equal