{"id":3382,"date":"2024-09-02T18:05:24","date_gmt":"2024-09-02T12:35:24","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=3382"},"modified":"2025-07-16T14:58:46","modified_gmt":"2025-07-16T09:28:46","slug":"volumetric-mix","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/volumetric-mix","title":{"rendered":"Volumetric Mix"},"content":{"rendered":"<p style=\"text-align: justify;\">Volumetric Mix describes the relative volume proportions among\u00a0 the various constituent of bituminous mix.<\/p>\n<p style=\"text-align: justify;\">A bitumen mix comprises of aggregate, bitumen and air voids. Aggregates present in mix comprises of coarse and fine particles. There are voids present in aggregates some of which contains bitumen and remaining voids are filled with air. Figure below represent a schematic diagram of various volume components of bituminous mix as a whole.<\/p>\n<p style=\"text-align: justify;\">Various terms in phase diagram and specific gravities defined for bituminous mix are explained below:<\/p>\n<p style=\"text-align: justify;\"><strong>1. Theoretical or Apparent specific gravity (G<sub>t<\/sub>):<\/strong> It is the maximum specific gravity for a bitumenous mix because air is not considered in volume of mix while calculating this specific gravity<\/p>\n<p style=\"text-align: justify;\">So, Theoretical specific gravity, G<sub>t<\/sub> = W<sub>mix<\/sub> \/ Volume of (mix-air voids)<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3383 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/coarse-aggregate.jpg\" alt=\"Coarse Aggregate\" width=\"494\" height=\"247\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/coarse-aggregate.jpg 494w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/coarse-aggregate-300x150.jpg 300w\" sizes=\"auto, (max-width: 494px) 100vw, 494px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>2. Bulk specific gravity of mix (G<sub>m<\/sub>):<\/strong> It is specific gravity of mix in which air voids are also included in volume of mix.<\/p>\n<p style=\"text-align: justify;\">Bulk specific gravity of mix, G<sub>m<\/sub> = W<sub>mix<\/sub> \/ Bulk volume of mix<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3384 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/gravity.jpg\" alt=\"Gravity\" width=\"374\" height=\"55\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/gravity.jpg 374w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/gravity-300x44.jpg 300w\" sizes=\"auto, (max-width: 374px) 100vw, 374px\" \/><\/p>\n<p style=\"text-align: justify;\">Here, bulk volume of mix can be calculated by two method.<\/p>\n<p style=\"text-align: justify;\"><strong>3. Percent air void (V<sub>A<\/sub>)%<\/strong><\/p>\n<p style=\"text-align: justify;\">It is expressed as volume of air voids to total volume of mix.<\/p>\n<p style=\"text-align: justify;\">It can be obtained as follows:<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3385 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/air-void.jpg\" alt=\"Percent Air Void\" width=\"595\" height=\"290\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/air-void.jpg 595w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/air-void-300x146.jpg 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>4. Percent volume of bitumen (V<sub>b<\/sub>)%<\/strong><\/p>\n<p style=\"text-align: justify;\">It is expressed as volume of bitumen to total volume of mix.<br \/>\nIt can be obtained as follows:<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3386 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/bitumen.jpg\" alt=\"Bitumen\" width=\"389\" height=\"353\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bitumen.jpg 389w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/bitumen-300x272.jpg 300w\" sizes=\"auto, (max-width: 389px) 100vw, 389px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>5. Void in mineral aggregate (VMA)<\/strong><\/p>\n<p style=\"text-align: justify;\">It is expressed as percent of total volume of voids (bitumen + air) to total volume of mix.<br \/>\nIt can be obtained as shown below:<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3387 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/aggregate.jpg\" alt=\"Aggregate\" width=\"381\" height=\"136\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/aggregate.jpg 381w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/aggregate-300x107.jpg 300w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>6. Voids Filled with bitumen (VFB)<\/strong><\/p>\n<p style=\"text-align: justify;\">It is expressed as percentage of volume of bitumen to total volume of voids.<br \/>\nIt can be obtained as follows:<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3388 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/bitumen-1.jpg\" alt=\"Bitumen\" width=\"262\" height=\"133\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(c) Equivalent Single Wheel Load (ESWL)<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>It is defined as load on the single tyre which will cause an equivalent magnitude of stress, strain, deflection etc. at a given location to that of multiple wheel load at the same location. To maintain the maximum wheel load within the specified limit, it is necessary to provide dual wheel assembly to the rear axles of road vehicles.The effect of dual wheel assembly is not equal to two times the load of any wheel. Equivalent single wheel load is calculated by using equal stress criteria. It is a semi-rational method, known as Boyd and Foster method, based on the following assumptions:<\/li>\n<\/ul>\n<ol style=\"text-align: justify;\">\n<li>Equivalency concept is based on equal stress<\/li>\n<li>Contact area is circular<\/li>\n<li>Influence angle is 45\u00b0<\/li>\n<li>Soil medium is elastic, homogenous and isotropic<\/li>\n<\/ol>\n<ul style=\"text-align: justify;\">\n<li>In a dual wheel load assembly, let \u2018d\u2019 is the clear gap between two wheel, \u2018S\u2019 be the spacing between center of the wheels and \u2018a\u2019 be the radius of the circular contact area of each wheelTherefore, S = d + 2aThe ESWL is given by:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3390 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/single-wheel-load-.jpg\" alt=\"Single Wheel Load \" width=\"466\" height=\"335\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/single-wheel-load-.jpg 466w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/single-wheel-load--300x216.jpg 300w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3391 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/stress-concept.jpg\" alt=\"Stress Concept\" width=\"603\" height=\"217\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/stress-concept.jpg 603w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/stress-concept-300x108.jpg 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>Modified CBR-method<\/strong><\/p>\n<p style=\"text-align: justify;\">Initially, total number of commercial vehicles were considered for designing of flexible pavement using CBR method but now as per IRC-37: 2018, in modified CBR method, design traffic is defined in term of total number of cumulative standard axle loads which is calculated by an expression as given below:<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3392 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/cbr-method.jpg\" alt=\"CBR Method\" width=\"273\" height=\"87\" \/><\/p>\n<p style=\"text-align: justify;\">N<sub>s<\/sub> = Number of cumulative standard axles to be catered during<br \/>\nthe design period of \u2018n\u2019 years<br \/>\nA = Initial traffic (commercial vehicle per day) in year of completion of construction (directional traffic volume to be considered for divided carriageways, two way traffic volume may be considered for applying lateral distribution factors)<br \/>\nD = Lateral distribution factor<br \/>\nF = Vehicle damage factor<br \/>\nn = Design period, in years<br \/>\nr = Annual growth rate of commercial vehicles<\/p>\n<p style=\"text-align: justify;\">Also, the traffic in year of completion of construction may be estimated by equation:<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3393 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/axle-loads.jpg\" alt=\"Axle Loads\" width=\"135\" height=\"49\" \/><\/p>\n<p style=\"text-align: justify;\">Where, P = Number of commercial vehicle per day as per last count<br \/>\nx = Number of years between last count and year of completion of construction<\/p>\n<p style=\"text-align: justify;\">After calculating number of cumulative standard axle, total pavement thickness is determined using the design chart(IRC 37 : 2001) as given below.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3394 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/standard-axies.jpg\" alt=\"Standard Axies\" width=\"373\" height=\"357\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/standard-axies.jpg 373w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/standard-axies-300x287.jpg 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Calculation of vehicle damage factor and lateral distribution factor<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(a) Vehicle Damage Factor<\/strong><\/p>\n<p style=\"text-align: justify;\">It is defined as a equivalent number of standard axles per commercial vehicle. The vehicle damage factor is used to convert the number of commercial vehicles of different axle loads and axle configuration to the number of standard axle load repetitions.<\/p>\n<p style=\"text-align: justify;\">The vehicle damage factor for any axle load is given as:<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3395 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/vehicle-damage-factor.jpg\" alt=\"Vehicle Damage Factor\" width=\"443\" height=\"209\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/vehicle-damage-factor.jpg 443w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/vehicle-damage-factor-300x142.jpg 300w\" sizes=\"auto, (max-width: 443px) 100vw, 443px\" \/><\/p>\n<table class=\"table table-striped table-bordered table-condensed\" style=\"margin: 0 auto; width: 99%;\">\n<tbody>\n<tr>\n<th colspan=\"3\" width=\"333\">IRC recommended\u00a0 values of VDF<\/th>\n<\/tr>\n<tr>\n<th rowspan=\"2\" width=\"187\">Initial (two way) traffic volume in terms of number of commercial vehicle per day<\/th>\n<th style=\"text-align: center;\" colspan=\"2\" width=\"146\">Terrain<\/th>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\" width=\"80\"><strong>Rolling\/ plain<\/strong><\/th>\n<th width=\"66\">Hilly<\/th>\n<\/tr>\n<tr>\n<td width=\"187\">\n<p style=\"text-align: center;\">0 \u2013 150<\/p>\n<\/td>\n<td style=\"text-align: center;\" width=\"80\">1.7<\/td>\n<td style=\"text-align: center;\" width=\"66\">0.6<\/td>\n<\/tr>\n<tr>\n<td width=\"187\">\n<p style=\"text-align: center;\">150 \u2013 1500<\/p>\n<\/td>\n<td style=\"text-align: center;\" width=\"80\">3.9<\/td>\n<td width=\"66\">\n<p style=\"text-align: center;\">1.7<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"187\">&gt; 1500<\/td>\n<td style=\"text-align: center;\" width=\"80\">5.0<\/td>\n<td width=\"66\">\n<p style=\"text-align: center;\">2.8<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><strong>Triaxial Test Method<\/strong><\/p>\n<p style=\"text-align: justify;\">In 1910 L.A. Palmer and E.S. Barber proposed the design method based on Boussinesq\u2019s displacement equation for homogenous elastic single layer. The expression for pavement thickness is given as<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3397 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/triaxial-test.jpg\" alt=\"Triaxial Test\" width=\"158\" height=\"59\" \/><\/p>\n<p style=\"text-align: justify;\">Where,<br \/>\nT = Pavement thickness in cm<br \/>\nP = Wheel load in kg<br \/>\nE<sub>s<\/sub> = Modulus of elasticity of subgrade from triaxial test results in kg\/cm2<br \/>\na = Radius of contact area in cm<br \/>\n\u2206 = Design deflection (taken equal to 0.25 cm)<br \/>\nX = Traffic coefficient<br \/>\nY = Saturation coefficient<br \/>\nThe recommended values of coefficients X and Y based on ADT of design traffic and rainfall are given in Table.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3398 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/coefficients.jpg\" alt=\"Coefficients\" width=\"676\" height=\"456\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/coefficients.jpg 676w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/coefficients-300x202.jpg 300w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Burmister Method <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3399 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/burmister-method.jpg\" alt=\"Burmister Method\" width=\"163\" height=\"87\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\">This method is based on young\u2019s modulus of elasticity of different layer of pavement.<br \/>\nAs flexible pavement composed of layers and elastic modulus of top most layer is maximum.<\/p>\n<p style=\"text-align: justify;\">Eb &gt; Esb &gt; Es<\/p>\n<p style=\"text-align: justify;\">Boussinesq\u2019s analysis is a special case of Burmister\u2019s layered system analysis. He considered<\/p>\n<p style=\"text-align: justify;\">Eb = Esb = Es<\/p>\n<p style=\"text-align: justify;\"><strong>Assumptions involved in Burmister\u2019s analysis<\/strong><\/p>\n<p style=\"text-align: justify;\">(i) Materials in the pavement layers are isotropic, homogenous and elastic.<br \/>\n(ii) Pavement forms a stiffer reinforcing layer having modulus of elasticity higher than the underlying subgrade.<br \/>\n(iii) Surface layer is infinite in horizontal direction but finite in vertical direction.<br \/>\n(iv) Underlying layer is infinite in both the directions.<br \/>\n(v) The layers are in continuous contact.<\/p>\n<p style=\"text-align: justify;\">Displacement equations given by Burmister are given below.<\/p>\n<p style=\"text-align: justify;\"><strong>(i) For Flexible Plate<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3400 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/burmister-method-1.jpg\" alt=\"Burmister\" width=\"432\" height=\"183\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/burmister-method-1.jpg 432w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/burmister-method-1-300x127.jpg 300w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) For Rigid Plate<\/strong> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3402 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/boussinesq-analysis.jpg\" alt=\"\" width=\"678\" height=\"534\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/boussinesq-analysis.jpg 678w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/boussinesq-analysis-300x236.jpg 300w\" sizes=\"auto, (max-width: 678px) 100vw, 678px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/highway-engineering\/california-bearing-test\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/highway-engineering\/geometric-design\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-highway-engineering\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Highway Engineering?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Volumetric Mix describes the relative volume proportions among\u00a0 the various constituent of bituminous mix. A bitumen mix comprises of aggregate,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[921,2],"tags":[953,954,956,955],"class_list":["post-3382","post","type-post","status-publish","format-standard","hentry","category-highway-engineering","category-ce","tag-bituminous-mix","tag-percent-air-void","tag-triaxial-test-method","tag-vehicle-damage-factor"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=3382"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3382\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=3382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=3382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=3382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}