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U.S.Departmentof TransportationFederal HighwayAdministration

Publication No. FHWA-TS-80-224August 198

(Reprinted july 199

Highway Subdrainage Design

-.


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PREFACE

The author wishes to express his sincere appreciation to theFederal Highway Administration and the many individuals and agenciesthat provided assistance during the preparation of this Manual. Inparticular, the author wishes to thank Mr. Edwin Granley of theImplementation Division of the Office of Development of FHWA, whoserved as project manager throughout the project. His patience andunderstanding will long be remembered.

The successful completion of this Manual would not have beenpossible without the wholehearted cooperation and technical assistanceof Mr. George W. Ring of the Pavement Systems Group of the Structuresand Applied Mechanics Division of the FHWA Office of Research. Hiscontinued support and encouragement are very much appreciated.

The author is very grateful to the members of the TransportationResearch Board Committee A2K06 on Subsurface Drainage for theirsupport of this project, for their review of the manuscript and theirvaluable suggestions. The contribution of the many other reviewersof the manuscript is also gratefully acknowledged.

Finally, the author wishes to express his appreciation to Mrs.Linda Sutherland for her untiring efforts in the preparation of themanuscript of the Manual.

NOTICEThis document is disseminated under the sponsorship of theDepartment of Transportation in the interest of informationexchange. The United States Government assumes no liab ilityfor its contents or use thereof.The contents of this report reflect the views of the Officeof Development of the Federal Highway Administration, whichis responsible for the facts and the accuracy of the datapresented herein. The contents do not necessarily reflectthe official views or policy of the Department of Trans-portation.This report does not constitute a standard, specificat ion,or regulation.The United States Government does not endorse products ormanufacturers. Trade or manufacturers' names appear hereinonly because they are considered essential to the object ofthis document.


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Report No. FHWA-TS-80-224

HIGHWAY SUBDRAINAGE DESIGN

Lyle K. Moulton, Ph.D., P.E.Professor of Civi l EngineeringWest Virginia Universityand

Principal EngineerTRIAD Engineering Consultants, Inc.Morgantown, West Virg inia

Sponsored by

Federal Highway AdministrationOffices of Research and DevelopmentWashington, D.C. 20590

Auoust 1980


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SUMMARY

Chapter I - General ConsiderationsThis Chapter is devoted to a general discussion of the adverse effectsof subsurface water, the types and sources of subsurface water and itsmovements, and the types of subsurface drainage installat ions that canbe used either singly or in combination, to control this water.(Pages l-40)

Chapter II - Data Required for Analysis and DesignLists the data requirements for analysis and design and presents recom-mended procedures for assembling these data. (Pages 41-58)

Chapter III - Pavement DrainagePresents methods and recornnended criter ia for the control of groundwaterand infiltration in pavement structural sections. (Pages 60-113)

Chapter IV - Control of GroundwaterDeals with the more general control of groundwater away from the pavement.(Pages 114-140)

Chapter V - Construction and MaintenancePresents a discussion of the construction and maintenance aspects ofsubdrainage systems. Recornnendations are presented for constructiontechniques designed to insure that the subsurface drainage systems willactually function in the manner in which they were designed to function.Chapter V also presents recomnendations for maintenance procedures designedto insure that subsurface drainage systems continue to perform satisfact-orily for the life of the facil ity. In addition, the utilizat ion ofsubsurface drainage for remedial purposes or in connection with pavementrehabilitation is discussed. (Pages 141-153)


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TABLE OF CONTENTSPage

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures ....................... viiChapter I - GENERALCONSIDERATIONS ............. 1

1.1 - Introduction . . . . . . . . . . . . . . . . . . . . . 11.2 - Adverse Effects of Subsurface Water . . . . . . . . . 2

1.2.1 Stability of Slopes .............. 31.2.2 Pavement Performance .............. 31.2.3 Economic Considerations ............ 13

1.3 - Occurrence and Movement of Subsurface Water ..... 131.3.1 Types of Subsurface Water . . . . . . . . . . . 131.3.2 Sources of Subsurface Moisture . . . . . . . . . 131.3.3 Seepage (Movement) of Subsurface Moisture . . . 18

1.4 - Type and Uses of Highway Subdrainage . . . . . . . . . 211.4.1 Classifications of Highway Subdrainage ..... 211.4.2 Longitudinal Drains .............. 261.4.3 Transverse Drains ............... 261.4.4 Drainage Blankets ............... 301.4.5 Well Systems .................. 351.4.6 Miscellaneous Drainage ............. 40

Chapter II - DATA REQUIREDFOR ANALYSIS AND DESIGN ...... 412.1 - General . . . . . . . . . . . . . . . . . . . . . . . 412.2 - Geometry of Flow Domain . . . . . . . . . . . . . . . 41

2.2.1 Highway Geometry ................ 412.2.2 Subsurface Geometry .............. 442.3 - Properties of Materials ............... 452.3.1 Index Properties ................ 452.3.2 Performance Characteristics .......... 45

iii


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Table of Contents (continued)

2.4 - Climatological Data . . . . . . . . . . . . . . . . . .Page

552.4.1 Precipitation .................. 552.4.2 Depth of Frost Penetration ........... 55

2.5 - Miscellaneous Considerations . . . . . . . . . . . . .Chapter III - PAVEMENT DRAINAGE . . . . . . . . . . . . . . . .

.3.1 -- General . . . . . . . . . . . . . . . . . . . . . . .3.2 - Quantity of Water to be Removed . . . . . . . . . . . . 61

3.2.1 Infiltration .................. 613.2.2 Groundwater .... ; .............. 633.2.3 Melt Water From Ice Lenses ........... 683.2.4 Vert ical Outflow ................ 733.2.5 Net Inflow ................... 84

3.3 - Analysis and Design of Drainage Layers . . . . . . . . 873.3.1 Thickness and Permeability ........... 873.3.2 Filter Requirements ............... 983.3.3 Special Considerations ............. 101

3.4 - Analysis and Design of Collection Systems . . . . . . . 1033.4.1 General Considerations ............. 1033.4.2 Longitudinal Collectors ............. 1043.4.3 Transverse Collectors .............. 1103.4.4 Outlets ..................... 111

Chapter IV - CONTROL OF GROUNDWATER . , 1 . . . , . . . , s . , II44.1 - General......................;.4.2 - Longitudinal Interceptor Drains ............4.3 - Multiple Interceptor Drains . . . . . . . . . . . . . . 1234.4 - Symmetrical Drawdown Drains . . . . . . . . . . . . . . 1244.5 - Miscellaneous Groundwater Control Measures . . . . . . 134

586061

114114

4.6 - Filter Protection in Groundwater Control . . . . . . . 137

iv


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Table of Contents (continued)Page

Chapter V - CONSTRUCTION ND MAINTENANCE . . . . . . . . . . . . 1415.1 - General . . . . . . . . . . . . . . . . . . . . . ...1415.2 - Construction Operations . . . . . . . . . . . . . . . . 141

5.2.1 General Precautions . . . . . . . . . . . . . . . 1415.2.2 Sequence of Construction Operations andInspection . . . . . . . . . . . . . . . . . . . 1435.3 - General Maintenance . . . . . . . . . . . . . . . . . . 144

5.3.1 Cleaning of Collector Pipes ........... 1445.3.2 Maintenance of Outlets .............. 1445.3.3 Miscellaneous Maintenance and OtherConsiderations .. .' .............. 1465.4 - Subsurface Drainage and Pavement Rehabilitation . . . . 146

REFERENCES...........................154

V


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LIST OF TABLESPage

1. Typical values of soil permeability . . , . . . . . . . . . 477. Approximate correlation between permeability andUnified Soil C lassification (59) . . . . . . . . . . . . 483. Average values of soil permeabilities (50) . . . . . . . . 49I-I. Guidelines for selection of heave rate or frostsusceptibility classification for use in Figure 38 . . . 725. Guidelines forusing Equations (12) through (16)to compute net inflow, q , for design of pavement

drainage . . . . . . .n. . . . . . . . . . . . . . . . . 866. Summary of recommended inspection activitiesassociated with subsurface drainage systeminstallation . . . . . . . . . . . . . . . . . . . . . . 1457. Description of drainage problems in pavement re-habilitation and their possible solution (adaptedfrom Ring (25)) . . . . . . . . . . . . . . . . . . . . . 151

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LIST OF FIGURES Page1. Potentially Unstable Cut Slope Resulting From Un-controlled Groundwater Flow . . . . . . . . . . . . . . 42. Typical Cut Slope Failure - Secondary Route 6339, MooreCounty, Tennessee (Photo Courtesy of William D.Trolinger, Tennessee Department of Transportation) . . 53. Potentially Unstable Fill Slope Resulting From theDamming of Wet Weather Groundwater Flow . . . . . . . . 64. Typical Slope Failure in Sidehill Fill - State Route30, Rhea County, Tennessee (Photo Courtesy of WilliamD. Trolinger, Tennessee Department of Transportation) . 75. Action of Free Water in A. C. Pavement StructuralSections Under Dynamic Loading . . . . . . . . . . . . 86. Pumping Phenomena Under Portland Cement ConcretePavements . . . . . . . . . . . . . . . . . . . . . . . 97. Capillary Moisture Migrating Toward Freezing FrontTo Feed The Growth of Ice Lenses . . . . . . . . . . . 118. Seepage of Meltwater From Ice Lenses Into PavementStructural Section . . . . . . . . . . . . . . . . . . 129. Capillary Moisture as a Function of The History ofWatertable Position (28) . . . . . . . . . . . . . . . 14

10. Schematic Illustration of the Occurrence of Groundwaterin a Gravity-Flow System . . . . . . . . . . . . . . . 1611. Schematic Illustration of the Occurrence of Groundwaterin an Artesian System . . . . . . . . . . . . . . . . . 1712. Points of Entrance of Water Into Highway PavementStructural Sections . . . . . . . . . . . . . . . . . 1913. Paths of Flow of Surface and Subsurface Water inPortland Cement Concrete Pavement StructuralSections . . . . . . . . . . . . . . . . . . . . . . . 2214. Longitudinal Interceptor Drain Used to Cut OffSeepage and Lower the Groundwater Table . . . . . . . . 23

vii


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List of Figures (continued)Page

15. Symmetr ical Longitudinal Drains Used to Lowerthe Water Table . . . . . . . . . . . . . . . . . . e . 24

16; Longitudinal Collector Drain Used to Remove WaterSeeping Into Pavement Structural Section . . . . . . . 25

17. Multiple, Multipurpose, Longitudinal Drain Installations 2718. Multiple Longitudinal Drawdown Drain Installation . . . . 2819. Transverse Drains on Superelevated Curve . . . . . . . . 2920. Transverse Interceptor Drain Installation in RoadwayCut With Alignment Perpendicular to Existing

Contours . . . . . . . . . . . . . . . . . . . . . . . 31Zla. Plan Showing Drainage Details and Boring Locationsat Towle Slide (35) . . . . . . . . . . . . . . . . . . 3221b. Profile and Typical Section of Drainage Trenchat Towle Slide (35) . . . . . . . . . . . . . . . . . . 3322. Applications of Horizontal Drainage Blankets . . . . . . 3523. Drainage Blanket (Wedge) on Cut Slope Drained byLongitudinal Collector Drain . . . . . . . . . . . . . 3624. Drainage Blanket Beneath Sidehill Fi ll Outletted byCollector Drain . . . . . . . . . . . . . . . . . . . . 3725. Wel l System Used for Draining Unstable Slope (36) . . . . 3826. Typical Sand Drainage Wel l Installation . . . . . . . . . 4027. Path of Subsurface Water in Drainage Layer . . . . . . . 4328. Chart For Estimating Coefficient of Permeability ofGranular Drainage and Filte r Materials . . . . . . . . 5129. Typical Gradations and Permeabi lities of Open Graded

Bases and Filter Materials (5,16) '. . . . , . . . . . . 5230. Chart For Determining Yield Capacity (Effect ivePorosity) . . . . . . . . . . . . . . . . . . . . . . . 5331. Summary of Results of Al l Standard Laboratory FreezingTests Performed by the Corps of Engineers Between1950 and 1970 (64) . . . . . . . e . . . . . a . . . . 64

viii


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32. The 1 Hour/l Year Frequency Precipitation Ratesfor the United States (66) . . . . . . . . . . . . . . . 5633. Maximum Depth of Frost Penetration in the UnitedStates (69) . . . . . . . . . . . . . . . . . . . . . . 5734. Rigid Pavement Section In Cut-Dimensions and Detailsfor Examples 1, 3, 11, 13, 14 and 17 . . . . , . . . . . 6435. Flexible Pavement Section In Fill - Dimensions andDetails for Examples 2; 12 and 15. . . . . . . . . . . . 6536. Chart for Determining Flow Rate in Horizontal DrainageBlanket . . . . . . . . . . . . . . . . . . . . . . . . 6737. Artesian Flow of Groundwater Into a Pavement DrainageLayer - Dimensions and Details for Example 4 . . . . . . 6938. Chart for Estimating Design Inflow Rate of Melt WaterFrom Ice Lenses . . . . . . . . . . . . . . . . . . . . 7139. Vertical Outflow Toward An Underlying Watertable . . . . . 7440. Vertical Outflow Toward an Underlying Layer of Very

High Permeability . . . . . . . . . . . . . . . . . . . 7541. Vertical and Lateral Outflow Through Embankmentand its Foundation . . . . . . . . . . . . . . . . . . . 7642. Transient Flow Net for the Case of Vertical OutflowToward an Existing Horizontal Watertable - Dimensionsand Details for Example 6 0 . . . . . . . . . . . . . . 7843. Chart for Estimating Vertical Outflow From PavementStructural Section Through Subgrade Soil to aSloping Underlying Watertable . . . . . . . . . . . . . 8044. Chart for Estimating Vertical Outflow From a PavementStructural Section Through the Subgrade to an Under-lying High Permeability Laye r . . . . .'. . . . . . . . 8245. Chart for Estimating Vertical Outflow From a PavementStructural Section Through Embankment and FoundationSoil.......................... 83

ix


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46.47. Time Dependent Drainage of Saturated Layer (27, 79) . . .48. Plan and Profile of Proposed Roadway - Dimensions andDetails for Example 16 . . . . . . . . . . . . . . . .49.

50.51.

52.53.54.55.56.

57.58.59.60.

Chart for Estimating Maximum Depth of Flow Causedby Steady Inflow (12) . . . . . . . . . . . . . . . . .

Proposed Subsurface Drainage System for FlexiblePavement on Fill-Dimensions and Details forExample16 . . . . . . . . . . . . . . . . . . . . . .Gradation Bands for Subbase, Drainage Layer, andEmbankment Material - Examples 16 and 18 . . e . . . .Layout of Proposed Drainage System Showing Direction ofFlow in Drainage Layer - Details and Dimensions forExample16 . . . . . . . . . . . . . . . . . . . . . .Gradation Bands for Subbase, Filter Layer and SubgradeMaterial - Example 17 . . . . . . . . . . . . . . . . .Gradation Bands For Filter Layer and EmbankmentMaterial - Example 18 . . . . . . . . . . . . . . . . .Typical Location of Shallow Longitudinal Collector PipesTypical Location of Deep Longitudinal Collector Pipes . .Nomogram Relating Collector Pipe Size with Flow Rate,Outlet Spacing and Pipe Gradient - Adapted FromCedergren (5,16) . . . . . . . . . . . . . . . . . . .Recommended Detail for Outlet Pipe and Marker (16) . . .Multiple Interceptor Drain Installation . . . . . . . . .Flow Toward a Single Interceptor Drain . . . . . . . . .Flow Toward a Single Interceptor Drain When theDrawdown Can be Considered to be Insignificant at aFinite Distance, Li, from the Drain . . . . . . . . . .

888993

9495

97100102105106

108113115116

118

/

I


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61. Chart for Determining Flow Rate in Interceptor Drains . . 12062. Chart for Determining Drawdown Curves for InterceptorDrains . . . . . . . . . . . . . . . . . . . . . . . . 12163. Example No. 21 - Flow Net, Dimensions and Details . . . . 12264. Example No. 22 - Dimensions and Details Required for theuse of Figures 61 and 62. . . . . . . . . . . . . . . . 12565. Example No. 22 - Flow Net, Dimensions and Details . . . . 12666. Division of a Symmetrical Drawdown Drain ProblemInto Two Equivalent Fragments . . . . . . . . . . . . . 12867. Free Water Surfaces Based on Gilboy Modification ofDupuit Theory . . . . . . . . . . . . . . . . . . . . . 12968. Chart for Determining Flow Rate in Symmetrical Underdrains 13169. Chart for Determining the Maximum Height of Free WaterSurface Between Symmetrical Underdrains . . . . . . . . 13270. Example No. 23 - Flow Net, Dimensions, and Details . . . 13371. Localized Surface Drains. (a) Cross-Section of Fill.(b) Draining a Single Spring. (c) Draining a Groupof Springs. After Cedergren (11) . . . . . . . . . . . 13672. Typical Filter System for Interceptor Drain UsingOnly Filter Aggregates . . . . . . . . . . . . . . . . 13873. Typical Filter System for Interceptor ,Drain UsingCoarse Filter Aggregate and Filter Fabric . . . . . . . 13874. Typical Components of Prefabricated Fin Drains (96) . . . 14075. Installation of Prefabricated Fin Drain in Trench (96). . 14076. Drains at Cracks and Joints (25) . . . . . . . . . . . . 14977. Combined Edge and Joint Drains (25) . . . . . . . . . . . 149

xi

----^- .--. -..- . .-__. _


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List of Figures (continued)

Page78. Utilizing New Edge and Lateral Drains WithExisting Drain Pipe (25) . . . . . . . . . . . . . . . 15079. Providing New Drainage Capabilities Through theShoulder (25) . . . . . . . . . . . . . . . . . . . . 150

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symbbl

inIIvdni

x-1.4.-I.01lb

Approximxto Convrcsions :o Metric Marsurrs

wbw VW Kww Ylll l ipl~ b1

LENGTH

indw 2.6fnl 30v=d. 0.9mile4 1.4

AREAupwmlndm 6.64--M 0.03- vd* 0.6SquN. mitw 2.6MS 0.4

MASS (wright)28

0.460.9

VOLUMEumpoms Stable-l 1slivid -I 30cuw 0.24pinw 0.47Qurrs 0.96gallau 3.6cubic twt 0.03cubic yards 0.76

TEMPERATURE (rxxct)

METRIC CONVERSIONFACTORS

millil iDrSmilli l iter*milli l itatrIitsrSli:efs,lU,l,,,*,scubtc meterscubic meters

Approximrtr Convrrsiors fton Yatric MIDSW~S

#d,~~,E=~S 0.06cantimlus 0.4RlU@f 3.3mu,* 1.1kilatrs 0.6

AREAsquua cm1ilm1rs 0.16squu. mm,* 1.2square kilmatews 0.4kecu*s l10,ooo m? 2.6

MASS (mif iht)lwmr 0.036hiMgums 2.2mules Iloo knl 1.1

VOLUMEmilhlilws 0.03liters 2.1heiS 1.04liters 0.26cubic meters 36cubic meterr 1.3

TEMPERATURE (oxrct)

*FOF 32 96.6 a2


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Chapter I - GENERALCONSIDERATIONS1.1 - Introduction

It would be difficult, if not impossible, to select the date whenthe early road builders first became aware of the need for adequatesubsurface drainage. However, there is some evidence that this need wasrecognized almost as soon as formal road building began (1,2)l. Certain-ly, by the middle of the 18th Century, it was understood that appro-priate subsurface drainage was absolutely necessary for the satisfactorylong term performance of roadways. The subsequent introduction of"french drains" and the pavement systems of Tresaguet and MacAdam showsnot only an understanding of the problem, but an attempt to incorporateinto the roadway design formal measures for the satisfactory removalof water from the pavement structure and subgrade (2,3). In the yearsthat have followed these early beginnings, the number of publishedaccounts of research dealing with highway subsurface drainage hasundergone a substantial growth (4,5). In addition, there has been asteady growth in the knowledge and availability of solutions to pro-blems of fluid flow through porous media (6,7,8,9,10,11,12). Conse-quently, we now recognize and understand many of the problems that canbe created by excessive subsurface moisture, and we have the meansavailable to provide for the satisfactory control of this moisture.It is the purpose of this manual to provide the designer with the toolsto analyze subdrainage problems and to design subsurface drainagefacilities to adequately solve these problems.It is difficult to separate the design of subsurface drainage from

the design o f other elements of a highway. In fact, it cannot, in thefinal analysis, be eliminated from consideration with respect to thestability of slopes, design of pavements, etc. However, as far as.the assembly of data on highway geometry and material properties isconcerned, we do need a starting point. Thus, it is recommended thatthe normal highway and pavement design practice be followed to developgeneral cross-sections, whether this involves individual detailedanalysis and design or the utilization of design standards. This willyield a highway geometry and material properties that can then be sub-jected to analysis and design for subsurface drainage. This proceduremay result in some changes in the design in order to provide adequatedrainage as recommended in this manual, but it is felt that thisapproach tends to be less confusing than attempting to incorporatedetailed consideration of subsurface drainage into the design fromthe outset. It will also permit.the use of specialized personnel forthe analysis and design of subsurface drainage, if this is consideredto be desirable. /'

1Numbers in parenthesis refer to the reference list, which beginson page 154.1


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The remainder of Chapter I is devoted to a general discussion ofthe adverse effects of subsurface water, the types and sources ofsubsurface water and its movements, and the types of subsurface drain-age installations that can be used either singly or in combination,to control this water. Chapter II lists the data requirements foranalysis and design and presents recommended procedures for assemblingthese data. Chapter III presents methods and recommended criteria forthe control of groundwater and infiltration in pavement structuralsections. Chapter IV deals with the more general control of ground-water away from the pavement, and Chapter V presents a discussion ofthe construction and maintenance aspects of subdrainage systems. Re-commendations are presented for construction techniques designed toinsure that the subsurface drainage system will actually function inthe manner in which it was designed to function. Chapter V alsopresents recommendations for maintenance procedures designed to in-sure that subsurface drainage systems continue to perform satisfac-torily for the life of the facility. In addition, the utilization ofsubsurface drainage for remedial purposes or in connection with pave-ment rehabilitation is discussed.

Many of the techniques for the analysis and design of subdrainagesystems have been simplified for inclusion in this manual, and con-siderable use is made of solutions in chart form. Examples are pre-sented to illustrate the recommended analysis and design proceduresand the use of the various charts.Although it is felt that the treatment of highway subsurfacedrainage in this publication is a comprehensive one, the infinitevariety of seepage and drainage problems that can occur in nature is

such that absolute coverage is impossible. The methods of analysisand design presen ted here are considered to be tools to aid in solvingsubsurface drainage problems - there are no standard solutions. Thesubdrainage problems encoun tered on each highway, or section of highway,will commonly be different and will require individual considerationand treatment. This manual can help in this regard, but it cannotsubstitute for the efforts of a well trained and experienced designerworking with reliable field and laboratory data and exercising goodengineering judgment.1.2 - Adverse Effects of Subsurface Water

Excessive and uncontrolled subsurface water is known or suspectedto have been responsible for a very large amount of unsatisfactoryhighway performance and many outright failures (5). In general, theseadverse effects of subsurface water can be placed in two general cate-gories: (a) slope instability, including the sloughing and sliding ofcut slopes and sidehill fills; and (b) unsatisfactory pavement perfor-

2


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mance as manifested in premature rutting, cracking, faulting, incre-asing roughness, and a relatively rapid decrease in the level ofserviceability.1.2.1 Stability of Slopes. Slope instability results when theapplied shear stresses exceed the strength of the soil or rock massalong a potential sliding surface. Subsurface water can contribute tothis instability by increasing the stress level and decreasing theshear strength. Seepage forces, resulting from the viscous drag thatis created by the flow of water through a porous medium, can add sub-stantially to the level of the stresses that must be resisted. Atthe same t ime, the porewater pressures within the slope reduce thelevel of effective normal stresses, thus reducing the effectiveshear strength (11,13). The result could be minor slope sloughing ora complete slope failure; Figure 1 shows schematically the developmentof one type of subsurface flow that can lead to cut slope instability.

Figure 2 shows a typical cut slope failure for which the uncontrolledflow of groundwater was, at least partially, responsible. The mannerin which a sidehill fill can function to dam the natural flow ofgroundwate r is illustrated in Figure 3. This trapping of the ground-water can result in a loss of strength of the natural soil and/or thefill and lead to its ultimate collapse, as shown in Figure 4 .1.2.2 Pavement Performance. Excessive moisture in the pavementstructure (surface, base and subbase) and the underlying subgrade cancause a wide variety of problems, leading to early pavement distressand ultimately to complete destruction of the pavement, if remedialmeasures are not undertaken.If the pavement structural section and subgrade can become satu-rated, by groundwater, and/or infiltration, its ability to transmitthe dynamic loading imposed by traffic can be greatly impaired (5,14,15,16).In asphaltic concrete pavement systems, this impairment is pri-marily the result of the temporary development of very high pore waterpressures and the consequent loss of strength in unbound base, sub-base and subgrade under dynamic loading (5,16). This action isillustrated schematically in Figure 5. In some instances, the pre-ssures induced in the free water may be sufficient to cause it to beejected through cracks in the pavement surface along with suspendedfines (5). A similar ejection of water and fines, or pumping, canoccur at the joints or edges of Portland cement concrete pavements,although the mechanism is different.Shortly after a Portland cement concrete pavement has been corn-pleted, it is possible that small spaces can exist under the jointsbecause of the thermally induced upward curl of the pavement slabs(see Figure 6a). These spaces can become enlarged under the action

3


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f

Original Ground,-Proposed Cut Slope

f OriginalWatertable

QProposedRoadway

Drawdown CurvePotential Sliding Surface of Seepage

Figure 1. Potentially Unstable Cut Slope ResultingFrom Uncontrolled Groundwater Flow


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n

5


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a

6


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.U

al

7


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Direction of Travel

Cracks Partially or CompletelyFilled with Water\ I 1Asphalt Pavement (Flexible)

Subgrade Soil(Saturated)

Unloaded A.C. Pavement

-. . .- L .. : . . _ _ , .. o. ;: L - -

\ - -\L - ;

1=Deflection of Subgrad e

Loaded A.C. Pavement

Note: Vertical dimensions of deformationsare exaggerated for clarity.

Figure 5. Action of Free Water in A.C. Pavemen t StructuralSections Under Dynamic Loading (16)


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Direction of Travel

Subgrade Soil(Saturated).

(b)Unloaded P.C.C. Pavement(a>

Note: Vertical dimensions ofdeformations areexaggerated for clarity.

Direction of Travel

:Ybe;q. .d:.-.&y+) ,:' :.: Water is Violently Displaced ;B - +,: :"d,j- .... r.CJ'O-'..~'TA,,-.t Carrying Suspended Fines ,~~;~-Y:-. ;f.- . 0 . .:0

Loaded P.C.C. Pavement

Figure 6. Pumping Phenomena Under PortlandCememt Concrete Pavements (16)


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of traffic because of the local ized compaction or permanent deformationof the underlying materials caused by slab deflection. When the baseand subgrade are saturated and free water exis ts beneath the joint, anapproaching wheel load causes the trail ing edge of the slab to deflectdownward (see Figure 6b), sending a fluid pressure wave or water jetin a forward direction. As the wheel passes over the joint, the trai l-ing slab rebounds upward as the leading edge of the next slab is de-flected downward (see Figure 6~). This results in erosion of materialfrom under the leading edges, ejection of water and fines from thejoints, and the deposition of some material under the trail ing edges(17). Should this pumping continue for any extended period of time,faulting may occur and the pavement slabs may crack because of thelack of adequate support (5,16,18). Distress in pavement slabs canalso be caused by pumping along the edges of the pavement. These phe-nomena have been studied extensively and, although a number of remedialmeasures have been suggested, it appears that the most effective ap-proach to the problem is to prevent the accumulation of water beneaththe pavement slabs by means of a combination of effective joint sealsand subsurface drainage (5,16).

Another adverse effect that uncontrolled moisture can have onpavement systems results from the several phenomena which are collec-tively referred to as frost action (19,20). Frost action requires thepresence of a readily available supply of subsurface moisture, frostsusceptible soils, and a sustained period of subfreezing temperatures.If all these requisites are satisfied, then moisture will migratethrough the capillary fringe (Sec. 1.3) toward the freezing front tofeed the growth of ice lenses, as illustrated in Figure 7. During theactive freezing period, the growth of ice lenses can result in sub-stantial heave of the overly ing pavement structure. This can causesignif icant damage to a pavement, particularly if differential frostheaving is experienced. However, the most potentially destructiveeffect of frost action is associated with the loss of support duringspring thaw. The thawing of the ice lenses leaves the subgrade soi lsaturated, or possibly supersaturated, resulting in a substantial re-duction in its strength. Moreover, since the thawing generally takesplace from the top down, the only way the excess moisture can drainfrom the subgrade soi l is by flowing into any available voids thatmay exist in the pavement structural section, as shown in Figure 8.If the pavement structure (base, subbase) is not adequately drained,it may become saturated with the water being squeezed from the subgradeand the destructive mechanisms previously discussed (Figure 5 and 6)may become operative. The resulting pavement deterioration is gen-eral ly referred to asspring breakup (19,20).

The frequent or sustained presence of excess moisture in pavementcomponents and intermittent exposure to cyc les of freezing and thawingcan result in the loss of structural integrity. In Portland cementconcrete pavements containing certain aggregates, this may appear asD-cracking (21,22), and as stripping or accelerated weathering in bit-uminous mixtures (23). In either case there is evidence that excluding10


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---

.z--~Frost Susceptible - - ~ -Soilt t i t

t t

Freezing Front

MoistureMigration

V- - Free Watertable 7

Figure 7. Capillary Moisture Migrating Toward Freezing FrontTo Feed The Growth of Ice Lenses


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Seepage From ThawingSubgrade SoilPavement Surface

Very Wet (Saturate d) Thawed Soil

Thawing FromUnfrozen Soil Bottom-Up

Figure 8. Seepage of Meltwater From Ice LensesInto Pavement Structural Section


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excess moisture or providing for its rapid removal with appropriatedrainage can be beneficial in minimizing damage from these causes (5).

1.2.3 Economic Considerations. In the preceding paragraphs,many of the adverse effects of excessive and uncontrolled subsurfacewater on highway performance have been discussed. However, in manyinstances, the economic considerations can overshadow the physicalaspects of unsatisfactory highway performance. For example, in severalareas of the United States, very large annual expenditures are requiredfor remedial construction and maintenance connected with landslides(13,24). In many cases, it has been found that uncontrolled subsur-face waters have played an important role in causing the failures. Inmost instances, the correct ive measures have included the installationof some type of subsurface drainage (13,24). Although definitiverecords are rarely available, it is very likely that the lack of ade-quate subsurface drainage also leads to large annual expenditures forpavements, in the form of shortened life and increased maintenanceand rehabilitation costs (5,16,25). The economic comparisons andcost-benefit analyses that are available have demonstrated that therecan be a very substantial long term economic advantage in providing foradequate subsurface drainage where needed as part of the original de-sign and construction (5,16).1.3 - Occurrence and Movement of Subsurface Water

1.3.1 Types of Subsurface Water. Subsurface water can exist ina variety of forms, including (a) water vapor, (b) bound moisture (c)capil lary moisture, and (d) gravitational or free water (6,7,10,12).Water vapor i s generally present in the pores above the zone ofsaturation. Although water movement in the vapor phase has beenstudied extensively, for our purposes the total amount of water trans-mitted in the vapor phase can be considered negligible, and it willnot be given further consideration.Bound moisture is generally considered to be of two types: (a)hygroscopic (absorbed) moisture and (b) oriented (pellicular) water.Hygroscopic moisture is so tightly bound to the surface of the soilparticles that it is considered to be immobile, and it can only beremoved after being transformed into the vapor phase by some means,such as drying at elevated temperatures. The oriented moisture is

not considered to be as tightly bound as hygroscopic moisture. Al-though it can be moved under the action of an attraction gradient, itwill not flow under the force of gravity and, therefore, wil l not begiven further consideration.Capillary moisture is water held in the pores of a soil above thelevel of saturation (water table, free water surface, or phreaticline) under the action of surface tension forces, as shown in Figure 9a.The height of the capil lary fringe and the shape of the moisture-tension

13


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n0)r-4

14


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curve is a function of the pore size distribution in the soil, whichis related to its grain size distribution and density (26,27). Figure9b shows that the degree of saturation resulting from capillarity isalso a function of the history of the position of the water tab le (28).Direct consideration of this phenomenon in seepage analysis is difficult,but it can be considered indirectly by modifying the concept of porosity(see Sec. 2.3). It is important to recognize that since capillarymoisture is held in the pores of the soil above the free water surface,against the force o f gravity, it cannot be removed by gravity. Thus,the only means available for the control of capillary moisture arethrough lowering the water table with appropriate subdrainage or pro-viding for a positive barrier (27) against capillary rise.

Gravitational or free moisture is water in liquid form that isfree, as its name implies, to move under the force of gravity and/orhydraulically induced pressure gradients. It will, therefore, obey thelaws of fluid mechanics and hydraulics. The control of free water willbe our primary concern hereafter, and it will be for this purpose thatthe subsurface drainage will be designed.

1.3.2 Sources of Subsurface Water. The analysis and design ofhighway subsurface drainage systems involves the consideration of sub-surface water from a wide variety of sources. However, it is conven-ient to consider these sources of drainable subsurface water in twobroad general categories: (a) groundwater, which is defined as thewater existing in the natural ground in the zone of saturation belowthe water table and (b) infiltration, which is defined (for the pur-poses of this publication) as surface water that gets into the pave-ment structural section by seeping down through joints or cracks inthe pavement surface, through voids in the pavement itself, or fromditches along the side of the road.

The main source of groundwater is precipitation, which may pene-trate the soil directly or may enter streams, lakes or ponds and per-colate from these temporary storage areas to become groundwater. Thissource may be supplemented by artificial recharge in the form ofirrigation. The occurrence of groundwater from these sources isillustrated schematically in Figure 10. The groundwater shown inFigure 10 is part of a "gravity-flow system" in that one of theboundaries defining the flow domain is a free water surface. Anothercommon occurrence of groundwater is in the "artesian system" as illus-trated in Figure 11. Under these circumstances, a "perched" watertable may exist and the water in the confined or partially confinedaquifer may be under substantial fluid pressure.Although the free water from melting ice lenses Commonly existsabove the water tab le, as shown in Figure 8, it is generally consideredthat this is groundwater. The water that feeds the growth of icelenses originates at the base of the capillary fringe (i.e. at thewater table),this source. and no frost action could take place without water from15


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Capillary FringeTranspdratron

/-Irrigation /-- tInfluent Stream

soi.1 moisture MovingDOWII After a Rain

Zone of Saturation Wmdwater)

Figure 10. Schematic Illustration of the Occurrence ofGroundwa ter in a Gravity-Flow System


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TNonflowing Artesian WellGroundround/-

Surfaceatertable Well

Recharge AreaF.lowing Artesian ---- ----Piezometric

WatercaDA=

Figure 11. Schematic Illustration of the Occurren ceof Ground water in an Artesian System


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The main source of water that infiltrates into the pavementstructural section is also precipitation. Water that fal ls on thesurface of the pavement shoulders or median can get into the pave-ment surface, base and subbase through a variety of entrance pointsas illustrated in Figure 12. In the case of concrete pavements, thegreatest amount of infiltration would be expected to occur.alonglongitudinal and transverse construction joints and at the jointsbetween the concrete slabs and the shoulders. However, as time goeson, additional infiltration may take place through cracks in the con-crete slabs and shoulders (5,16,29). For bituminous pavements, theprimary initial sources of infiltrationmay be along the longitudinaljoints at the shoulders and the construction joints between stripsof paving. Additional longitudinal and transverse cracking may occurafter a time, even in well designed and constructed bituminous pave-ments, providing additional sources of infiltration (5,16,29). More-over, some water may seep downward through voids in the pavement sur-face itself, although this is not commonly thought of as being oneof the major sources of infiltration (29).

The infiltration of water into the pavement structural sectionwould appear, on the face of it, to be a simple phenomenon. However,the interaction between the type and frequency of openings permittinginfiltration, the rate of water supply, and the permeability andambient moisture conditions of the underlying materials is most complex.Thus, the estimation of the amount of infiltration that must be con-trolled by subsurface drainage requires careful consideration. Thisis discussed in greater detail in Section 3.2.1.1.3.3 Seepage (Movement) of Subsurface Water. Generally, seepageis defined as the movement, or flow, of a fluid through a permeableporous medium. In particular , the fluid with which we are concernedis water, and the permeable porous media are soils, rock and thestructural elements of pavements. The porosity is defined as the

ratio of the volume of the pore spaces to the total volume of thematerial. The extent to which porous media will permit fluid flow,.I.e., its permeability, is dependent upon the extent to which thepore spaces are interconnected and the size and shape of the inter-connections (10,30).Based on his classic experiments on the flow of water throughsand filter beds, Darcy (31) concluded in 1856 that the flow of waterthrough porous media is governed by a simple linear law (Darcy's Law),which is generally stated in the form

V = ki, (1)where v is the discharge velocity; k is a constant of proportionality,called the coefficient of permeability; and i is the hydraulic gradient,.I.e., the ratio of change of total head, h, with respect to distance, s,

18


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Figure 12.

Direction of Fl

Points of Entrance of Water Into HighwayPavement Structural Sections (16)


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in the direction of flow. In its most general form, the hydraulicgradient can be expressed as

although, quite commonly, the total derivative dh/ds, or the finitedifference form Ah/As, is employed. Equation (1) can be put in amore useful form by multiplying by the cross-sectional area, A, of theflow domain. This yields an expression for the flow rate, q, in theformq = kiA (3)

The validity of Darcy's Law is known to be contingent upon theexistence of laminar flow (10,27,30,32,33). For most natural soilsand low permeability granular materials, this condition will besatisfied over a wide range of hydraulic gradients. However, formore open graded granular materials the flow may becomenonlaminar,even at relatively low hydraulic gradients (27,32,34). Under thesecircumstances, it is still possible to use Darcy's Law for practicalseepage analysis if appropriate consideration has been given to thisphenomenon in evaluating the coefficient of permeability. This isexplained in greater detail in Section 2.3.2.It should be noted, at this stage, that the coefficient of per-meability, upon which equations (1) and (3) depend, varies over avery wide range, depending on the nature of the porous media (seeSec. 2.3.2) through which flow is taking place. In natural deposits,and even in some compacted soils, it may be much greater in onedirection than in another (6,7,8,10,12). This phenomenon should beconsidered, whenever possible, in arriving at practical solutionsto highway subdrainage problems.The movement of groundwater in the vicinity of a highway may begoverned entirely by natural phenomena and hydraulic gradients thatare the direct outgrowth of the controlling topographic, hydrologicand geological features as shown in Figures 10 and 11. More oftenthan not, however, the highway construction causes some kind ofdisruption in the natural pattern of flow. For example, a highwaycut may intersect the existing water table as shown in Figure 1, ora fill may serve to dam the natural flow of groundwater as shown in

Figure 3. The installation of subsurface drainage to control thisgroundwater results in a further alteration of the flow pattern. Thefinal configuration of the flow domain is dependent upon both the

20


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initial groundwater flow conditions and the characteristics of thesubsurface drainage system that is installed.On the other hand, the movement of infiltration in the pavementstructural section is governed largely by the permeability of the com-ponents of the pavement system, the longitudinal grade of the roadwayand the pavement cross (transverse) slope. The general patterns ofsurface and subsurface flow associated with infiltration are shownfor a Portland cement concrete pavement in Figure 13. Although, thejoint and crack patterns (points of inflow) are different for a bit-uminous concrete pavement, the geometry of the surface and subsurfaceflow is essentially the same as that shown in Figure 13.

1.4 - Types and Uses of Highway Subdrainage1.4.1 Classifications of Highway Subdrainage. Systems of high-ways subsurface drainage can be classified in a variety of ways accord-ing to; (a) th e source of the subsurface water they are designed tocontrol, (b) the function they perform, and (c) their location andgeometry. It is important, at this point, that these classificationsbe put in perspective and that the associated terminology be unders toodin order to avoid confusion in later sections of this manual.A groundwater control system, as the name implies, refers to sub-surface drainage specifically designed to remove and/or control the flowof groundwater. Similarly, an infiltration control system is designedto remove water that seeps into the pavement structural section. Often,however, subdrainage may be required to control water from both sources.Although some of the physical features of the two subdrainage systemsmay be different, quite commonly they are very much alike (see ChaptersIII and IV).A subsurface drainage system may perform one or more of the fol-lowing functions: (a) interception or cutoff of the seepage above animprevious boundary; (b) draw-down or lowering of the water table; and(c) collection of the flow from other dra inage systems. These func-tions are illustrated in Figures 14, 15 and 16 respectively. Althougha subdrainage system may be designed to serve one particular function,commonly it will be expected to serve more than one function. For ex-ample, the interceptor drain shown in Figure 14 not only cuts off the

flow from the left, but it draws down the water table so that it doesnot break out through the cut slope.The most common way of identifying subdrainage systems is in termsof their location and geometry. Familiar classifications of this typeinclude; (a) longitudinal drains, (b) transverse and horizontal drains,(c) drainage blankets, and (d) well systems. These will be discussedin detail in Sections 1.4.2, 1.4.3, 1.4.4 and 1.4.5, respectively.It should be noted that these types of subdrainage may be designed to

21


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22


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Nw

7 Original Ground

lxnterceptor Drain

Figure 14. Longitudina l Intercepto r Drain Useia;;eCutOff

Seepage and Lower the Groundw ater


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-

24


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Roadwayt

Pervious Base or SubbaseCourse (Drainage Blanket)

Figure 16. Longitudinal Collector Drain Used to RemoveWater Seeping Into Pavement Structural Section.


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control both groundwater and infiltration and/or to perform any of thefunctions outlined above.

1.4.2 Longitudinal Drains. As the name implies, a longitudinaldrain is located essentially paralle l to the roadway centerline bothin horizontal and vert ical alignment. It may involve a trench of sub-stantial depth, a collector pipe and a protective filter of some kind,as shown in Figure 14 and 15; or it may be less elaborate, as shownin Figure 16. The degree of sophistication employed in the designof longitudinal drains wil l depend upon the source of the water thatis to be drained and the manner in which the drain is expected tofunction (see Chapters III and IV).

Sometimes, systems of longitudinal drains of different types canbe employed effectively. An example of such an application is pre-sented in Figure 17, which shows a multiple drain installation in asuperelevated section of an expressway cut in a wet hillside. In orderto intercept the flow and draw down the water table below the left cutslope, it was necessary to use two lines of relatively deep longitu-dinal drains. As shown in Figure 17, the collector drain (beneaththe left shoulder) serves to drain any water that may get into thebase or subbase of the left lanes as a result of infiltration or frostaction. A similar function is performed by the shallow collectordrain along the left edge of the right lanes.

The combination of groundwater conditions and highway cross-sections shown in Figures 14, 15, and 17 were such that the ground-water could be intercepted and/or drawn down well below the pavementsections with no more than two lines of longitudinal underdrains. How-ever, this is not always possible, particularly when the water tableis very high and the roadway section is very wide, as shown in Figure18. In this case, the flow of groundwater might have saturated thesubgrade and the pavement structural section over at least a part ofits width if the third longitudinal drain had not been installed be-neath the median. Even more complicated roadway geometries are pos-sible, and more elaborate subdrainage configurations may be requiredfor modern highways , particularly in the vic inity of interchanges.

1.4.3 Transverse and Horizontal Drains. Subsurface drains thatrun laterally beneath the roadway are classified as transverse drains.These are commonly located at right angles to the roadway centerline,although in some instances, they may be skewed in the so-cal led"herringbone" pattern.Transverse drains may be used at pavement joints to drain infi l-tration and groundwater in bases and subbases. This is particularlydesirable where the relationship between the transverse and longitu-

dinal grades is such that flow tends to take place more in the longi-tudinal direction than in the transverse direction. An example ofthis type of installation is shown in Figure 19. In this illustration,

26


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I/1/

cn : : I

* I 1111

l-ia

27


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Original Groundroposed Cut Slope Original Watertable\

Drawdwn Curve WitThree DrainsDrawdown Curve With OnlyTwo Outside Drains (DashedPortion Shows TheoreticalLocation of Phreatic LineIf Only Soil Were Present)

Figure 18. Multiple Longitudinal Drawdown Drain Installation


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Interceptor DrainDetail

TransverseLegend

Water Flow PathsCross SlopeLongitudinal Grade

Figure 19. ~-- --Transverse Drams onSuperelevated Curve (16)


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the transverse drains have been used in conjunction with a horizontaldrainage blanket and longitudinal collector drain system. This canprovide a very effective means for rapid removal of water from thepavement section.Transverse drains may involve a trench, collector pipe and pro-tective filter, as shown in Figure 19, or they can consist of simple"french drains" (i.e. shallow trenches filled with open graded aggre-

gate), although this is not generally recommended. As with longitu-dinal drains, the degree of sophistication employed depends on thesource of the subsurface water and the function of the drain.When the general direction of the groundwater flow tends to beparallel to the roadway (this occurs commonly when the roadway is cut

more or less perpendicular to the exist ing contours), transverse drainscan be more effective than longitudinal drains in intercepting and/ordrawing down the water table. This application is illustrated inFigure 20.

Some caution should be exercised in the use of transverse drainsin areas of seasonal frost, since there has been some experience withpavements undergoing a general frost heaving except where transversedrains were installed, thus leading to poor riding quality during win-ter months.Horizontal drains consist of nearly horizontal pipes drilled into

cut slopes or sidehill fills to tap springs and relieve porewater pres-sures (See Sec. 4.5, p. 135). In ordinary instal lations, the ends ofthe perforated small diameter drain pipes are simply left projectingfrom the slope and the flow is picked up in drainage ditches. However,in more elaborate installations, drainage galleries or tunnels may berequired to carry large flows, and some type of pipe collector systemmay be used to dispose of the water outside of the roadway limi ts (11).An example of a drainage installation of this type, used in connectionwith a landslide stabilization project (11,35), is shown in Figures21a and Zlb.

1.4.4 Drainage Blankets. Generally speaking, the term drainageblanket is applied to a very permeable layer whose width and length(in the direction of flow) is large relative to its thickness. Pro-perly designed drainage blankets can be used for effective control ofboth groundwater and infiltration.

The horizontal drainage blanket can be used beneath or as an inte-gral part of the pavement structure to remove water from infiltrationor to remove groundwater from both gravity and artesian sources. Al-though relat ively pervious granular materials are often utilized forbase and subbase courses, these layers wil l not function as drainageblankets unless they are specifically designed and constructed to doso. This requires an adequate thickness of material with a very high30


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31


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Horizontoi Drains

\Limit of Slide),

// I-2 Collector Pipes; B #Perforated PipesII

------

SCALE IN FEETI I0 SO 100 200

II

i----

Figure 21a. Plan Showing Drainage Details and BoringLocations At Towle Slide (35)


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E M B A N K M E N T

MAfERALELQCATCD HAILWJAUt t I2 IN COLLECTOR PIPE

\8 IN PERFORATED PIPE-em_ \ . \ -4IEALC IN ?LLY

/- ORIGINAL RAlLROAO L 10 6 IO 20

HORIZ. DRAIN-ORIGINAL GROUNO

62-l IGROUND LINE

FREEWAY AFTER SLIM

- , 1 HORIZ. DRAIN WET SHALL B

PERMEA BLE MATERIAL -

WET SILTY CLAY IORIGINALSANDY SILTY CLAY

:?L,

INTERBEDDEDVOLCANIC AS AND COLLECTOR PIPE /j

II- 5OOt FT

ICALf, 1 ICCT0-0

Figure 21b. Profile And Typical Section of DrainageTrench At Towle Slide (35)


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coefficient of permeability, a positive outlet for the water collected,and, in some instances, the use of one or more protective filter lay-ers (5,16).

Two types of horizontal drainage blanket systems are shown inFigure 22. In Figure 22a, a horizontal blanket drain is used in con-nection with shallow longitudinal collector drains to control both in-filtration and the flow of groundwater from an artesian source. Notethat a protective filter layer has been used to prevent the subgradesoi l from being washed into and, thus clogging the drainage layer. InFigure 22b, a horizontal blanket drain is used to remove water that hasseeped into the pavement by infiltration alone. In this case, theoutlet has been provided by "daylighting" the drainage blanket (opengraded base course). liowever, it is not uncommon for this type ofoutlet to become clogged and cease to function effectively. A morepositive means of outletting the drainage blanket would have beenthrough the use of the longitudinal drain shown dashed in Figure 22b.In any event, the subbase has also been designed as a filter in thisinstance to prevent intrusion of the subgrade soi l into the basecourse under the action of traffic (27). When the longitudinal gradeis large enough to control the direction of flow, transverse drains maybe required to outlet the drainage blanket as shown in Figure 19.

Drainage blankets can be used effectively to control the flow ofgroundwater from cut slopes and beneath sidehill fil ls. Examples ofthese uses are illustrated in Figures 23 and 24, respectively. Asshown in Figure 23, the drainage blanket used in connection with alongitudinal drain, can help to improve the surface stability (relievesloughing) of cut slopes by preventing the development of a surfaceof seepage (see Figure 1) and by its buttress action. The blanketdrain shown in Figure 24 prevents the trapping of wet weather flow be-neath the fil l and minimizes the buildup of high porewater pressuresthat can lead to slope instabili ty (see Figures 3 and 4).

1.4.5 Well Systems. Systems of vertical wells can be used tocontrol the flow of groundwater and relieve porewater pressures inpotentially troublesome highway slopes. In this application, they maybe pumped for temporary lowering of the water table during constructionor simply left to overflow for the relief of artesian pressures. Moreoften, however, they are provided with some sort of collection systemso that they are freely drained at their bottoms. This may be accom-plished by the use of tunnels, drilled-in pipe outlets (ll), or hori-zontal drains. Typical well drainage systems that were used to helpin the stabil ization of wet slopes are shown in Figures 21a and 21b(35) and Figure 25 (36).

Sand filled vertical wells (sand drains) can be used to promoteaccelerated drainage of soft and compressible foundation materialswhich are undergoing consolidat ion (the squeezing out of water) as aresult of the application of a surface loading such as that producedby a highway embankment (11,37,38,39,40). An instal lation of this type34


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Original Ground- iezometric LevelIn Artesian Layer

---Drainage Blanket

Piezometer

Seepage From Artesian Source II

(a>

Roadway4 Daylighted Granular

Drainage Blanket(Base Course)

l-i

I

Ground Drainage PJanketSubbase Designed (Longitudinal CollectorAs a Filter Drain)\

Figure 22. Applications of Horizontal DrainageBlankets.

35


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/-Proposed Cut Slope Roadway

---4 \ --; -4 -- WatertableL DrawdownCurve

Cut SlopeBlanket LL ongitudinalCollector Drain Lcorizontal Drainage Blanket

Figure 23. Drainage Blanket (Wedg e) On Cut Slope DrainedBy Longitudinal.Collector Drain


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I I37


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(a) Plan of Effected Area

(b) Layout of Drainage System24

2ftmin

(c) Details of Wells Used For Drainage.

Figure 25. Wel l System Used For DrainingUnstable Slope (35)

38


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is illustrated schematically in Figure 26. The design and construc-tion of sand drains for foundation stabilization is a rather special-ized undertaking requiring detailed consideration and understanding ofthe three dimensional consolidation process (38,401. Thus, this aspectof highway subdrainage is considered to be outside the scope of thispublication and it will not be given further consideration.

1.4.6 Miscellaneous Drainage. Frequently, during the course ofhighway construction and maintenance operations, local seepage con-ditions are encountered which require subsurface drainage to removethe excess moisture or relieve porewater pressures. These conditionsmay require small drainage blankets with pipe outlets, longitudinalor transverse drains, or some combination of these drainage systems

11) l Although subdrainage of this type is highly individualized,its importance should not be minimized and its design should be approach -ed with the same care as the design of more elaborate subdrainagesystems.

39

,


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._.:.: ....i.I / .:, . - : ,:;. , , :_ : ., fl.1. --f--f+ ; . :.-:-,

: I ., . .-. _... . ,. ., , , .\ \ 1. . t-: n;/::.I :,:: 1.;:; .g- . -.:..:..: . . ,,, . I.... - . .- .* . ., . . . . ;:. 1.. ._ , _.:..: ,-*.;,,-,,-=l ar. * -----I: 3-. .

*.*I. .-. . . . . . .-.

.-., i. , .,.-.

;. I.--: ay.._. .( . I : : . ,_ . ,- . 1.:: . 1- i ;_- , : .< : :*, _. ,... : .^ _. . _. ,1.. .. .~ :, . . .: . :

40


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Chapter II - DATA REQUIRED FOR ANALYSIS AND DESIGN

2.1 - GeneralThe validity of the analysis and design procedures presented inthe following chapters is dependent, to a large degree, upon theaccuracy and completeness of the data upon which the computations arebased. Unfortunately, the nature of the seepage phenomena and ma-terials involved is such that the determination of exact input datais impractica l, if not impossible. However, every effort should bemade to develop input data that is as realistic as possible whilepreserving an appropria te measure of conservatism.The data required for analysis and design of subsurface drainagecan be placed in four general categories: (a) the geometry of theflow domain; (b) the properties of the materials; (c) the climatological

data; and (d) miscellaneous considerations.The geometry of the flow domain involves both the geometric de-sign of the highway and the prevailing subsurface conditions. Ithelps to define the various subsurface drainage problems and providesthe bounda ry conditions that govern their solution.The fundamental material properties are an important aid toclassifying materials and helping to predict how they will perform,particularly with respect to their ability to transmit the flow ofwater (i.e. their permeability).The climatological data provide an important insight into thefundamental source of all subsurface water (i.e. precipitation) andthe potentially adverse effects of frost action.There are a number of other considerations that may have aninfluence on the design of subdrainage systems. These includethe impact of the subdrainage system on the existing groundwaterregime and other aspects of design; the influence of a subdrainagesystem, or lack of it, on the sequence of construction operations;and the economic considerations related to the use of subsurfacedrainage.

2.2 - Geometry of the Flow Domain2.2.1 Highway Geometry. Almost all of the geometric designfeatures of a highway can exert some influence upon the analysisand design of. subsurface drainage. Therefore, before attemptingto undertake this work, the designer should be armed with as muchinformation as possible on these features. Included should be suf-ficiently detailed profiles and cross-sections to permit assemblyof the following data for each section of roadway under consideration:41


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(a) longitudinal grades; (b) transverse grades (including super-elevation); (c) widths of pavement and shoulder surface, base and sub-base; (d) required thickness of pavement elements based on normalstructural design practice for the particular area under consideration;(e) depths of cuts and fill s; (f) recommended cut and fil l slopes;and (g) details of ditches and other surface drainage facil ities.Much of this information might be obtained from a detailed set of"typical cross-sections". However, a set of roadway cross-sectionsshowing orig inal ground and at least the gross features (i.e. cutand fil l slopes, ditches, etc.) of the proposed construction is con-sidered to be a necessity.

In addition, it is considered desirable to have a topographicmap of the highway corridor upon which the final highway alignmenthas been superimposed. This map should be prepared to such a scale(100 or 200 scale) that features pertinent to both surface and sub-surface drainage can be clearly identified. For example, streams,lakes, and seasonally wet areas above the highway may constituteknown boundaries to the flow domain. There is also some evidencethat landslide potential, and thus, the potential need for subsur-face drainage, can be predicted by careful evaluation of selectedtopographic features (24).As indicated in Section 1.3.3, and showy. qualitatively in Fig-ure 13, the flow of water in the pavement structural section (drain-age layer) may be largely controlled by the longitudinal grade ofthe roadway, g and its cross slope, S I This is shown in a morequantitative fashion in Figure 27. Ig cal l be demonstrated (12)that the length of the flow path, L, can be expressed as

L = w \i 1 -i- (glsJ2>where W is the width of the drainage layer, as shown in Figure 27.The slope of the flow path, S, is given by the expression (12)-.-

S = 7/F g2 (5)The values of the various combinations of longitudinal and transversegrades to be encountered on the project should be tabulated in a formconvenient for the calculation of L and S for possible use in analysisand design (see Section 3.3). However, there are two anomaliesassociated with this work that may be encountered. Firs t, it isclear that whenever the transverse grade approaches zero, the lengthof the flow path given by Equation (4) approaches infini ty. Inpractice, this particular relationship between longitudinal andtransverse grades will be a local one, and the length of the flowpath wil l be governed by the grades of adjacent sections of roadwayand/or the distance to the nearest transverse drain. Second, itis obvious that, if either the cross slope or the longitudinal gradeis varying with the stationing along the roadway, the flow path

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j-Cross Slope (SC)/

Horizontal3LongitudinalGrade (g)

Subbase

WCollector Drain

Figure 27. Path of Subsurface Water in Drainage Layer


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cannot be linear as shown in Figure 27, but will be curved, as shownin Figure 19. Under these circumstances, some approximation will haveto be introduced (see Example 16 in Section 3.3). In any event, thistype of data constitutes an important input to analysis and design ofsubdrainage to control some types of groundwater and water from infil -tration. Therefore, particular care should be taken in assemblingthis information.

2.2.2 Subsurface Geometry. The nature and limits of the flow do-main, i.e., its subsurface boundaries, should be accurately established.In general, this wil l require a thorough program of subsurface explor-ation and geologic evaluation. This work should be sufficiently de-tailed to permit the development of soil and rock profiles and to de-fine the prevailing groundwater conditions. In many parts of thenation, agricultural and/or geological maps are available that can bevery useful in planning the subsurface exploration program. It shouldbe noted, at this point, that good subsurface explorations are a vitalpart of the basic design procedure for highways (41), and very littleadditional work of a specia l nature is required for the analysis anddesign of subsurface drainage systems.

The various methods of subsurface exploration and sampling havebeen described in detail in numerous publications (41,42,43), and noattempt will be made to repeat this information here. However, somehelpful suggestions and recommendations will be presented.Often, a great deal of valuable information pertaining to existing

subsurface drainage conditions can be obtained by careful examinationof the site in the field. This can be especially true if the visitat ioncan be made during, or just following, a wet period. It may be pos-sible to observe wet-weather springs or other evidence of intermittentseepage that might not show up during some dryer period. In addition,the type and condition of the vegetation in the area may give someclue to the soil and groundwater conditions. Lush green foliage andthe presence of species of plants and trees that are known to requirea high water table can be significant indicators of potential ground-water problems.

During the subsurface explorations, specia l attention should bedirected at obtaining all possible data that might relate in any wayto subsurface drainage. Any evidence of artesian pressures or lossof wash water during drilling should be noted, and any unusual strati-fication (e.g. granular layers or lenses within a more cohesive stra-tum) should be recorded. The sampling should be coordinated so thatrepresentative samples are obtained for laboratory testing from allstrata that may be involved in the seepage phenomenon. This includescut materials that will later be placed in fills. When it is knownor suspected that there may be-significant seasonal fluctuations in thewater table, it is considered to be good practice to install plast ictubing in the bore holes so that the water table level can be monitoredover some period of time. Such installat ions are not expensive andcan provide much valuable information.

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Under some circumstances, it may become desirable to conductspecial tests to evaluate the in-situ permeability of materialsduring the subsurface explorations (see Section 2.3.2). This needshould be anticipated in advance, if possible, so that the sub-surface explorations can be properly programmed to provide the mostinformation for the lowest possible cost.2.3 - Properties of Materials

2.3.1 Index Properties. The index properties of materials areconsidered to be those which help to identify and classify the ma-terial. They may also be an important indicator of material perfor-mance. In assembling pertinent data for the analysis and design ofsubsurface drainage, we are primarily concerned with those propertieswhich exert an influence on seepage phenomena. Included in thiscategory are: (a) grain size characteristics, (b) plasticity char-acteristics (Atterberg limits), and (c) soil classification (seeSection 2.3.2).

For natural soils which may exist within the flow domain, eitherin cuts or fills, representative samples should be subjected to grainsize analysis using standard test methods (44). This is particularlyimportant where it is anticipated that protective filters may berequired to prevent finer soil particles from being washed or "pumped"into drainage layers. For granula r materials to be used in base,subbase, drainage blankets, filters, etc., it is considered highlydesirable that representative samples of the actual construction ma-terials be subjected to grain size analysis. However, it is recognizedthat this may not always be practical, and it may be necessary towork from the specified gradation limits for these materials. In someinstances, the subdrainage analysis and design procedures may leadto the modification of existing gradation specifications or the de-velopment of new criteria for establishing gradation limits.

The Atterberg limits (45,46) of natural soils along with their grainsize distributions permit the soils to be classified in a meaningfulway with respect to their behavioral characteristics. Although avariety of soil classifications are in use (47,48,49), there appearsto have been more work done in relating the permeability, capillarityand frost susceptibility of soils with their Unified Soil Classification(20,48,50) than with any other system. Thus, it is recommended thatsufficient laboratory data be developed for representative soil samplesto permit their classification by this system.2.3.2 Performance Characteristics. While there are a wide rangeof engineering properties of materials with which we must be concernedin highway design, for the purposes of this publication, we will con-sider only those properties that control the flow of subsurface water.Thus, included in the data required for analysis and design are (a) the

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coefficient of permeability, k, (b) the effective porosity (yieldcapacity), n', and (c) the frost suscept ibility of the material. Inaddition, it may be necessary to assemble data on other performancecharacteristics which govern these parameters.Among the material properties which may influence the coefficientof permeability are (a) the grain size distribution, (b) the packing(dry density, void ratio, porosity), (c) the mineralogical composition,(d) the nature of the permeant, and (e) the degree of saturation (28).Moreover, it would appear that most of the properties influencing thecoefficient of permeability also influence capi llarity and the yieldcapacity. This will be given further consideration later in thissection.The coefficient of permeability can be determined by (a) in-situ

measurement, (b) laboratory testing, (c) theoretical analysis, and(d) empirical methods.

Ideally, the coefficient of permeability should be determined byin-situ measurements, and it is recommended that this practice be fol-lowed whenever possible. There are a variety of reliable techniquesthat have been developed for making determinations of this type innatural soils and rock (51,52). In addition, procedures have beendeveloped for evaluating the in-situ coefficient of permeability inbases, subbases, and drainage layers (52,53). However, obtainingthe coefficient of permeability of compacted drainage layers after theyare in place cannot be considered a design function. It is rather, aninspection or control function designed to assure that the coefficientof permeability falls within l imi ts established by some other means asbeing desirable for the particular subsurface drainage system underconsideration.

When field evaluation of the coefficient of permeability is notfeasible, then the use of laboratory determinations is highly recom-mended, particularly for fil l materials, bases, subbases and otherdrainage layers. The laboratory methods are well known and are con-sidered to be reliable (27,28,34,54,55). Commonly, the materials arecompacted to the anticipated field moisture and density conditions fortesting. There is, however, a problem associated with determining thecoefficient of permeability for coarse granular materials. As notedin Section 1.3.3, the flow in these materials may become nonlaminar,even at low hydraulic gradients, invalidating Darcy's Law. Underthese circumstances, there are two procedures that can be used toallow for the reduced efficiency caused by turbulence. One procedureis to estimate the range of hydraulic gradients to be experienced inthe field and to perform the laboratory tests at these hydraulic gra-dients. When this is done, errors from turbulence are largely eli-minated because the measured coefficient, although not a true Darcycoefficient, should have the correct magnitude for estimating theseepage quantities and velocity at the test gradient. An alterna-

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tive procedure is to establish the true Darcy permeability by per-forming the laboratory tests under small hydraulic gradients thatensure laminar flow and then to apply a correction factor to accountfor the reduced efficiency caused by turbulence at greate r hydraulicgradients than used in the tests. The details of this procedure andtypical correction factors have been presented by Cedergren (SeeReference 11, pp. 139-145 and pp. 195-196).

Throughout the years, many theoretical and empirical equationshave been devised for estimating the coefficient of permeability ofporous media (28,56,57). The most reliable of these, however, seemto have been developed by empirical modification of purely theoreticalequations (57). For the most part, these equations are not suitablefor use in the practical analysis and design of highway subdrainageand, therefore, they will not be given further consideration.Although field or laboratory evaluation of the coefficient of per-meability is considered desirable, in practice it is often necessaryfor the designer to estimate the coefficient of permeability empirical-ly without the benefit of these refinements. Several appraoches areavailable for doing this, but they all depend upon some kind of correla-tion between the coefficient of permeability and such properties asgrain size characteristics, dry density, and porosity or void ratio.One method that reportedly has been used with some success utilizes arelationship between permeability, specific surface and porosity (58).One typical set of values of the coefficient of permeability anda general indication of the degree of permeability is given in Table 1

Table 1. Typical values of soil permeabilitySoil Description Coefficient of Permeabilityk(ft./day)l Degree ofPermeability

Medium and CoarseCrave1 >30.0Fine gravel; coarse,medium and finesand; dune sand.Very fine sand; siltysand; loose silt;

loess; rock flour.Dense silt; denseloess; clayey silt;silty clay.Homogeneous clays

30.0 to 3.0

3.0 to 0.030.03 to 0.0003


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as a function of the grain size characterist ics of the material. InTable 2, ranges of values of coefficient of permeability are given asa function of the Unified Soi l Classification and the relative degreeof permeability (59). In Table 3, average values of the coefficient

Table 2. Approximate correlation between permeabilityUnified Soil

ClassificationGWGPGMGCSWSPSMSCMLCLOLMHCH

and Unified So il Classification (59)lRelative Coefficient of PermeabilityPermeability k(ft./day)

PerviousPervious to Very Pervious

SemiperviousImpervious

PerviousSemipervious to Pervious

Impervious to SemiperviousImperviousImperviousImperviousImpervious

Very ImperviousVery Impervious

2.7 to 27413.7 to 27,400

2.7~10-~ to 272.7x10 -5 to 2.7x10 -2

1.4 to 1370.14 to 1.4

2.7x10 -4 to 1.42.7~10-~ to 0.142.7x10 -5 to 0.142.7x10 -5 to 2.7x10 -32.7~10-~ to 2.7~10-~2.7x10 -6 to 2.7x10 -42.7x10 -7 to 2.7x10 -5

of permeability are given as a function of the Unified Soi l Class ifi-cation void ratio and dry density (50).In using Table 1,2 and 3, the general manner in which the coeffi-cient of permeability varies with the controlling soil properties shouldbe understood. With respect to grain size, finer soils can, in general

be expected to have lower permeabilities, and well graded soils can beexpected to be less permeable than more uniform soils. With respectto density, a decrease in permeability should be expected with in-creased dry density. Furthermore, it should also be recognized thatthe permeabilities given in Tables 1,2 and 3 are typica l values forhomogeneous and isotropic soil or aggregate masses, and that aniso-

1When placed as well-constructed rolled-earth embankment withmoisture-density control.

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Table 3. Average values of soil permeabilities (50)Unified Soil Dry DensityClassification lbs/cu.ft. Void Ratio*e Coefficient of Permeabilityk(ft./day)

GwGPGMGCSWspSM

SM-SCSCML

ML-CLCLMHCH

119110114115

119 + 5110 + 2114 + 1119 + 1-115 + 1-103 + 1-109 rfr 2108 f 1-

82 + 494 + 2

0.37 + -0.50 2 0.030.48 + 0.020.41 Ifi 0.020,48 f- 0.010.63 + 0.020.54 + 0.030.56 + 0.011.15 5 0.120.80 2 0.04

73.973 2 35.616175.242 5 93.151

8.219 x 10 48.219 x 10 -4

4,110 x lo-22.055 + 1.315 x 10 2-2.192 21.644 x lO-38.219 + 5.479 x 10 41.616 + 0.630 x lO-33.5612 1.917 x lO-42.191 + 0,821 x 10 44.343 2 2.739 x lo-41.369 + 1.369 x 10 4

*Average values were obtained from more than 1500 soil samples compacted to the Standard Proctormaximum dry density. The 5 entry indicates 90 percent confidence limits for the averag e values.


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tropy , stratification, naturally occuring cracks and fissues, etc.,can have a dramatic effect on the in-situ permeability.It is of particular importance in the analysis of subsurface drain-age systems to be able to estimate the coefficient of permeability ofgranular drainage and filter materials. Figure 28 has been preparedto help in this regard. It was developed by correlating stat istica llythe measured coefficients of permeability for a large number of samples(26,27,34,60,61) with those properties known to exert an influence on

permeability. The results showed that the most significant proper-ties were the effective grain size, DlO, the porosity, n, and the per-cent passing the No. 200 sieve, ~200. These three parameters explain-ed over 91 percent of the variation in the coefficient of permeability.For convenience, a conversion has been made, so that dry density isused in the chart instead of porosity. It is particularly importantto note that the amount of fines (P200) exerts a marked influence onthe coefficient of permeability for granular materials. Thus, a smallincrease in the amount of fines can cause a large decrease in thecoefficient of permeability (5,16,27). Since Figure 28 was developedfrom data on granular bases and subbases, its applicability is neces-sari ly limited to these types of materials. An additional aid toestimating the coefficient of permeability is given in Figure 29,which shows typical gradations and permeabilities of open gradedbases and filter materials (5,16).

Although the effective porosity, or yield capacity, n', commonlyappears in the literature in the solutions to problems involving time-dependent drainage, criteria for estimating numerical values of thisparameter are not generally given (5,6,7,10,12). However, as notedearlier, there does appear to be some evidence (26,27,62) to supportthe belief that some kind of relationship should exist between theeffective porosity, n', and the coefficient of permeability, k. Onthis basis, Figure 30 was developed by correlating stat istica lly themeasured values of effective porosity with the measured coefficient ofpermeability for soi ls of varying gradations and densities (27,32).While Figure 30 does provide the designer with a simple and reasonablyreliable way to estimate effective porosity, it should be used withcaution, particu larly at the extremities where data were lacking(high vales) or were quite scattered (low values).

A knowledge of the frost susceptibility of subgrade soils and thedepth of frost penetration (see Section 2.4.2) can provide the de-signer with .some insight into the extent of the subsurface drainagerequired to control frost action and the amount of water that must beremoved by suitable drainage layers during periods of thawing in orderto prevent the saturation of the pavement structural section. Rapidremoval of the melt water from thawing ice masses (19,20) is consideredto be an essential factor in limiting both the duration and magnitudeof the reduction in supporting power of the subgrade, base and subbaseduring periods of spring thaw (5,16,20,63). Although many differenttest methods and criteria for evaluating frost susceptibility have

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1.478 6.654k = 6.214x105(D10) (4(p200)O*597 (ft./day)

'dXI = Porosity * (1 - -62.4GG - Specific Gravity

(Assumed =I 2.70)

-- -. - --

I: 0.005

-f0.01

?E

10.0

- ---- --b

Example:P200 = 2%D10 = 0.6 lmn'd = 117 lb./cu.ft.Read:k = 65 ft./day

105

10

103

10*

10

1

-110

-2?O

Figure 28. Chart For Estimating Coefficient of Permeabi lityof Granular Drainage and Filter Materials


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I FINE SAND I IEDIUMSAND ki%:Ei GRAVEL

+&~-GRADED -I+ a

908070605040302010n200 80 50 302016 108 I4 3A, I1z

U.S. STANDARD SIEVE SIZES

Figure 29. Typical Gradations and Permeabilities ofOpen Graded Bases and Filter Materials (5,lfj)

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-- 0.01 0.02 0.05 0.10 0.20 0.50Yield Capacity -nt

Figure 30. Chart For Determining Yield Capacity(Effective Porosity)53


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P~rctnlopc by weight f iner than 0.02 myGravelly Sollr ,, FlL--e-- FI 1 i2 1 F3SAN DS IExcrpl very f ine s il ly S ANDS ] Fi I FSVery f ina s1lIy SANDS F4i l l S ILTS F4CLAYS (P112) - :?ICLA YS (PI~lZl,v~rv~d CLA YS and olhrr f ins-groined bonded redimenlr-F4

Figure 31, Summary of Results of Al l Standard LaboratoryFreezing Tests Performed by The Corps ofEngineers Between 1950 and 1970 (64)

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been considered (19,20), there does not appear to be, as yet, a singleproven, simple and reliable test or criterion for frost susceptibilityadaptable to general highway design use (20). However, some relativeindication of frost susceptibility can be obtained from Figure 31,which summarizes the results of standard laboratory freezing testsmade by the Corps of Engineers from 1950 to 1970 (64). Th.e Fl to F4frost design classification groups (65), used by the Corps of Engi-neers for pavement design purposes, are also shown in Figure 31.2.4 -' Climatological Data

2.4.1 Precipitation. Although a precise understanding of thefrequency, intensity and duration of precipitation in an area is notgenerally necessary for the detailed design of highway subsurface drain-age, it can be helpful in defining the seriousness of the problem andin devising solutions. Generally, groundwater problems occur morefrequently and are more serious in areas of high rainfall. Underthese circumstances fluctuations in groundwater level may correlatereasonably well with amount of precipitation. On the other hand, thereis some evidence that the infiltration of rainfall into pavementsections is dependent more upon duration of rainfall than intensityor frequency (29). Thus, there may be areas in the United Stateswhere there are no signifieant problems with respect to groundwater.However, this does not necessarily mean that no water will ever in-filtrate into the pavement structural section (see Section 3.2.1).The United States National Weather Service publishes records ofprecipitation in a variety of forms. Of particular interest and valueare the maps which show rainfall intensity as a function of frequencyand duration (66). A typical map of this type, giving the 1 hour/l yearfrequency precipitation rates, is shown in Figure 32. The rainfallrates shown on this map were recommended by Cedergren (5,161 as thebasis for computing infiltration rates into pavement structural sec-tions. This will be discussed in greater detail in Section 3.2.1.2.4.2 Depth of Frost Penetration. Some indication of the depthto which freezing temperatures may penetrate into the pavement orunderlying subgrade can be helpful in assessing the seriousness ofpossible frost action. A number of theoretical relationships havebeen developed over the years which permit a reasonably reliableprediction of frost depth based upon air or pavement freezing in-dices and the thermal properties of the pavement elements andthe subgrade (19,20,67,68). The most reliable of these formulasappears to be the modified Berggren equation (67,68). While mapsgiving average or maximum depths of frost penetration (69,70,71,72) may be very helpful (e.g. see Figure 33,) they should be usedwith caution, because of the extreme variations in frost depththat can occur as a function of elevation and latitude (68). Ideally,well kept records of accurately measured depths of frost penetrationwould provide th

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