{"id":32,"date":"2018-12-31T11:14:55","date_gmt":"2018-12-31T11:14:55","guid":{"rendered":"https:\/\/www.howtoexcel.info\/Civil\/?p=32"},"modified":"2021-09-29T06:57:53","modified_gmt":"2021-09-29T05:57:53","slug":"earthwork-volume","status":"publish","type":"post","link":"https:\/\/www.howtoexcel.info\/Civil\/earthwork-volume\/","title":{"rendered":"Earthwork Volume Using Simpson’s Rule"},"content":{"rendered":"

Step by step procedure to find out volume of earthwork using Simpson’s Rule<\/i><\/span><\/p>\n

This article is about using Simpson’s rule (also known as Prismoidal Rule) to find out the quantity of earthwork by means of contour maps. The procedure is explained here with the help of an example. In the example here below, the map is divided into 6 horizontal and 6 vertical grids each of 5m interval. The reduced levels are given at the intersections. Let us find out the volume of earthwork.<\/p>\n

<\/p>\n

Let us first note down the reduced levels in a tabular form.<\/p>\n

<\/p>\n

A three dimensional view will look like the following.<\/p>\n

<\/p>\n

Suppose the final level for filling is 24.1m. Then the required depth of filling at each point is as given in the table below.<\/p>\n

<\/p>\n

The area on the side of each grid can be found out as follows<\/p>\n

<\/p>\n

Each side can be considered as a trapezoid. Hence the area of each side<\/p>\n

<\/p>\n

eg: (0.98+0.97)\/2 x 5 = 4.875<\/p>\n

(0.80+0.80)\/2 x 5 = 4.000<\/p>\n

Now the volume according to Simpson’s rule is as follows<\/p>\n

<\/p>\n

<\/p>\n

eg: (4.875+3.375)=8.25<\/p>\n

4 x (4+3.75+3.925)=46.7<\/p>\n

2 x (3.575+3.875)=14.9<\/p>\n

Total = 69.85<\/p>\n

Total earth filling volume = 341.425 x (d\/3)<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0=341.425 x (5\/3) = 569.042 M3<\/sup><\/strong><\/p>\n

Note: We express thanks to https:\/\/www.e-quantities.com\/volumes.htm<\/span><\/a> for bringing up an error in this page to our notice which now has been rectified. You may download the excel file detailing\u00a0 volume calculation using Trapizoidal Rule here<\/a>.<\/span><\/p>\n

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Step by step procedure to find out volume of earthwork using Simpson’s Rule This article is about using Simpson’s rule (also known as Prismoidal Rule) to find out the quantity of earthwork by means of contour maps. The procedure is explained here with the help of an example. In the example here below, the map … <\/p>\n

Continue reading “Earthwork Volume Using Simpson’s Rule”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/posts\/32"}],"collection":[{"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/comments?post=32"}],"version-history":[{"count":19,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":126,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/posts\/32\/revisions\/126"}],"wp:attachment":[{"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/categories?post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.howtoexcel.info\/Civil\/wp-json\/wp\/v2\/tags?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}