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Cut-and-Fill Volume Computations When designing and constructing a vertical highway alignment crest curve, Sta 0 + 00 is being connected to Sta 1 +00, with both stations at the same elevation of 10.5.. El 10,5 10 Sta 0+00 El 10 Sta 1 +00 Sta 0 + 50 For this vertical curve alignment, three consecutive stations: Stations 0 +00, 0 + 50, and 1 + 00, have the following section (1.e., across the stations) elevations -- as shown under "Field Book Entries" below, in an excerpt from a Surveyor's Field Book Sketch all three station sections, compute cut (.e., excavation) and fill areas, and, using the average end-area method, determine the cut and fill volumes to obtain the 100 vertical curve - described below. Express the cut and fill volumes in cu yd For a 5-point extra credit, determine the cut-and-fill volumes between Stations 0+00 and 1+00: 1. Using the average end-area method, and using for end-areas only the section areas at Station 0 + 00 and Station 1 +00, and 2. Using the prismoidal method. (Hint: use the section area at Station 0+50 as the Am in the equation for volume: Distance Between Stations Al and A2 V=(A + 4Am + A2) Field Book Entries Station ser S 20 S10 NIO 20 Sta S 20 S 10 10 1 20 11.0 0 +00 9.5 10.0 10.0 11.0 Sta 0+ % 9.0 4 10.0 10.0 % -4 -0.5 -1.0 10.0 10.0 10.0 10.5 - 10,0 - 2.5 - 2.0 0 0 1.0 0 + 50 11.5 % 11.5 11.0 11.0 10.0 10.5 10.5 | 10.625 10.5 Sta 04 10.5 10.5 11.0 10.5 10.0 0.5 -0.5 0.125 1.0 0.5 1 +00 % 10.5 OS 9.0 10.666 10.5 10.5 10.0 Sya 10.0 10.0 10.0 10.0 10.0 -10.0 - 9.5 :-1.0 0.6667 0.5 0.5 0 - 9.0 Sign Convention: Positive % - Ydenotes "cut", and negative % - denotes "ALL" By the same token, "cut" areas are posi- tive, and all areas are negative. Net Areas (ft) - For Use when Employng the Average End-Area Volume Computation Method Stations s 20 - $10 S 10-C 6-N 10 N 10-N 20 Sta 0+00 Sta 0+ 50 Sta 1 +00 2 Equations for Determining Cut-and-Fill Volumes Using the Simpler Average End-Areas Method and the More Accurate, Albeit More Complicated, the Prismoidal "Egyptian " Method Equation for Determining Cut-and-Fill Volumes: For the Average End-Areas Method - Volume - Average End-Arca * Distance between Stations Ai + Az V= x Distance Between Stations For the Prismoidal ("Egyptian") Method - V=(A + 4A + A2) Distance Between Stations where Am is a hypothetical arca midway between any two consecutive stations Ai+A -(Ai+4 Distance Between Stations + A2) * * Important Note: This simplified (A - =%(Ar+A:)) version of the Prismoidal Method equation gives no more accuracy over the simpler Average End-Areas Method. Thus, to benefit from the added accuracy provided by the Prismoidal or "Egyptian" Method, the A- should not be considered the average of A and As, but, rather, it should be computed by averaging the corresponding heights used to compute the area A, and A, along with the average of the widths (or bases) of any pair of consecutive stations. Computation for Cut-and-Fill Approximate Volumes - (2 points) Using the End-Areas Average Method of Computation Ave Out Area Ave Area Cut Volume F Volume Cut Volume ty Full Vlamed 2