Journal of Surveying Engineering

This study examines the problem of the intersection of a spiral curve with a circle, which especially occurs in the design of junctions. To achieve the requirements, an iterative method which has been programmed, is suggested with full mathematical formulas. Assessments of selected examples are made, and the results are tabulated. The intersection points are derived by starting first from a upper limit and second from a lower limit. If the same points are obtained when the iteration starts from both the upper and lower limits, the circle intersects the spiral at one point. If they are different points, the circle intersects the spiral at two points. However, if the iteration does not converge there are two cases for the problem: the circle either is tangent to the spiral or does not intersect it. In the tangent case, a method is suggested in order to find the tangent points at a sufficient precision.

Stringent accuracy specifications required that particular care be taken in the provision of geodetic control for the construction of the Superconducting Super Collider. The design and implementation of the surface geodetic control networks are described. The horizontal network was realized by Global Positioning System measurements, and the vertical network by means of precise geodetic leveling. The highly expansive soils in the project area required that the horizontal and vertical surface monuments be designed to be stable for the duration of the construction of the project. The methodology adopted for the densification of horizontal and vertical control from the surface networks to the shaft area, and an innovative technique used for the transfer of control into the underground facilities are described. The underground networks were designed so as to minimize the geometric weakness inherent in tunnel surveys. In the interests of economy, removable tunnel brackets were developed and used for the large number of horizontal underground monuments. Survey results for five tunnel half-sector breakthroughs are reported.

Dynamic deformation monitoring of structures such as long bridges, towers, and tall buildings, for the purpose of determining structural vibrations, is now possible using global-positioning-system (GPS) technology. Current non–GPS techniques for measuring structural vibrations (these include vibration measurement with accelerometers, vibration measurement with a laser interferometer, and vibration measurement with an electronic distance measurement instrument) are first briefly outlined, with advantages and disadvantages noted. The specific application, measurement of structural vibrations in the Calgary Tower, Calgary, Alberta, Canada, using GPS receivers in differential mode, is then described. The results show that the Calgary Tower, under wind loading, vibrates with a frequency of about 0.3 Hz in both north-south and east-west directions. The 0.3 Hz vibration frequency measured on the Calgary Tower is within the range of 0.1 Hz to 10 Hz expected for structures of this type. When the capability of GPS to monitor structural vibrations is verified by further tests, it could be adopted as a standard technique.