Water Well Journal
Issue link: https://read.dmtmag.com/i/705618
or bottom of the common formation to be measured that is best represented at all three locations. Keep in mind, it is best to use a common datum for the X, Y, and Z axis of measure- ment throughout the process (feet, meters). Once you have set up the graphical problem, it is time to measure the distances. I should point out a graphical solution accuracy is directly dependent on skill of measurement and attention to detail when plotting. Determining the strike and dip of a formation or planar sur- face is accomplished by finding the strike line or intermediate point along the line between the highest and lowest points cor- responding to the elevation of the mid-point. To find the strike line, first draw a line connecting the highest contact point, C, to the lowest contact point, A. You can then use the following equation to find the strike line mid-point, D, that corresponds to mid-point, B. Line AD = Line AC × (B – A) (C – A) (Compton 1962) or as shown in Figure 1: Line AD = 2458 × (4180 – 4080) = 1536 (4240 – 4080) Once you have located the strike line mid-point D along Line AC, draw a connecting line from contact point B to point D along Line AC. The strike line or hinge point is located along the line from contact point B to point D. To find the di- rection of the dip, draw a line at a right angle to the strike line or 90 degrees to the strike line through the lowest point at contact point A. The Line AE is the dip line and represents the direction of the dip of the formation or planar surface. To find the dip angle, you can use the following equations: Tan (Dip Angle) = (B – A) Line AE (Compton 1962) or Dip Angle = Tan -1 (B – A) Line AE You can use tangent tables to assist in solving the first equation. If you have a calculator with the Cotangent function, the second equation can be useful. Going back to Figure 1 and using tangent tables, the dip angle is 3 degrees, 30 minutes. Tan -1 (4180 – 4080) equals a dip angle of 3.51 degrees. 1630 Using a compass or protractor to measure the direction of Line AE will give the direction of dip, or measuring the direc- tion Line BD will give the direction of the strike line. Follow- ing the right hand rule for strike and dip notation, which puts the dip direction to the right of the strike line, in this exercise would show the formation contact planar surface striking at 228° with a dip of 3.51° dipping to the northwest quadrant. A more simplistic notation of this is 228°/3.5° NW. Dealing with groundwater, hydraulic gradient is often an important consideration. As described by Bates and Jackson in their Dictionary of Geological Terms, hydraulic gradient in an aquifer is referred to as: "The rate of change of total head per unit of distance of flow at a given point and in a given direc- tion." (Bates and Jackson 1984) To determine the direction and hydraulic gradient of groundwater, the three-point problem is set much the same as for a geologic surface. However, instead of using a geologic contact for measurement, the static water level in three wells are measured. It is best to use wells installed and screened similarly within the same aquifer and not in a straight line. Groundwater gradient can shift on a local scale; therefore, measurement wells should be located close enough to accu- rately realize local effects. Determining the static water level elevation is accom- plished by subtracting the depth to water from the measuring point at the well surface from the elevation of the measuring point. For instance, if the static water level is 100 feet below the measuring point at the top of the casing, and the top of casing elevation is 2000 feet mean sea level (MSL), then the static water level elevation is 1900 feet MSL. Determining hydraulic gradient can be accomplished graphically by using the three-point problem with the addition of the following equation: Hydraulic Gradient = (D – A) Line AE (Heath 1983) When notating groundwater movement, the direction of the groundwater gradient is utilized instead of the contour or strike line. Therefore, as shown in the example in Figure 2, the hydraulic gradient would be expressed as: Hydraulic Gradient = (22.5 – 20.2) = 0.019039 ft/ft or 100.52 ft/mile at 194.0° SW 120.8 Hydraulic gradient lines are often considered the direction of flow lines while the perpendicular lines to the gradient are considered equipotential lines or lines of equal head. The de- FIELD NOTES from page 27 waterwelljournal.com 28 August 2016 WWJ Figure 2. Example of the three-point method. Modified from Compton1962 and Heath 1983. Courtesy Raymond L Straub Jr., PG