CRREL REPORT 95-1

Cold Regions Mobility Models

Paul W. Richmond, Sally A. Shoop and

George L. Blaisdell February 1995
Abstract

This report annotates the cold regions mobility prediction routines included in

the CAMMS/ALBE mobility models. It further explains the development of the

algorithms that are used in these models to describe the interaction of a vehicle

with terrain that has been affected by cold weather. The following terrain

conditions are discussed: undisturbed snow (shallow and deep); disturbed

snow (moderately trafficked and hard packed); ice; and thawing soils. Several

combinations of substrates are also considered. A stand-alone computer

model is included.

For conversion of SI metric units to U.S./British customary units of measurement

consult ASTM Standard E380-89a, Standard Practice for Use of the International

System of Units, published by the American Society for Testing and Materials,

1916 Race St., Philadelphia, Pa. 19103.
CRREL Report 95-1

Cold Regions Mobility Models

Paul W. Richmond, Sally A. Shoop and

George L. Blaisdell February 1995

Prepared for

OFFICE OF THE CHIEF OF ENGINEERS

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was prepared by Paul W. Richmond, Mechanical Engineer; Sally A. Shoop,

Research Civil Engineer; and George L. Blaisdell, Research Civil Engineer, all of the Applied

Research Branch, Experimental Engineering Division, U.S. Army Cold Regions Research

and Engineering Laboratory. Funding for this effort was provided by DA Project

4A762784AT42, Cold Regions Engineering Technology; Work Units M03, Vehicle Snow

Mechanics (Deep Snow), M04, Vehicle Snow Mechanics (Shallow Snow) and M08, Mobility Models

for Thawing Soils.

This report was technically reviewed by Karen Faran and Richard Ahlvin.

The contents of this report are not to be used for advertising or promotional purposes.

Citation of brand names does not constitute an official endorsement or approval of the use

of such commercial products.

ii
CONTENTS

Page

Preface ................................................................................................................................. ii

Nomenclature ..................................................................................................................... v

Introduction ........................................................................................................................ 1

Background ........................................................................................................................ 1

Shallow snow ..................................................................................................................... 2

Undisturbed snow on a firm substrate...................................................................... 2

Undisturbed snow on a soft substrate ....................................................................... 5

Undisturbed snow over ice ......................................................................................... 6

Disturbed, processed and packed snow ................................................................... 6

Deep snow .......................................................................................................................... 7

Ice ......................................................................................................................................... 9

Freezing or thawing ground conditions......................................................................... 9

Bearing capacity of freezing ground ......................................................................... 10

Effect of thawing conditions on vehicle performance ............................................ 11

Speed made good .............................................................................................................. 14

Internal motion resistance ................................................................................................ 15

Slopes ................................................................................................................................... 16

Summary and recommendations .................................................................................... 16

Literature cited ................................................................................................................... 16

Appendix A: Cold Regions Mobility Model CRM-1.F ................................................. 19

Appendix B: FORTRAN code using NRMM/CAMMS variables and format ........ 39

Appendix C: Traction coefficients on packed snow ..................................................... 53

Appendix D: NRMM checkout data ............................................................................... 55

Abstract ............................................................................................................................... 73

ILLUSTRATIONS

Figure

1. Shallow vs. deep snow ............................................................................................ 2

2. Vehicle traction on snow ......................................................................................... 3

3. Snow and vehicle characteristics ............................................................................ 3

4. Vehicle motion resistance in shallow snow .......................................................... 4

5. Prediction of vehicle sinkage in shallow snow .................................................... 4

6. Vehicle sinkage analysis .......................................................................................... 4

7. Vehicle traction for snow over ice .......................................................................... 6

8. Vehicle traction for packed snow ........................................................................... 7

9. Vehicle traction on ice .............................................................................................. 8

10. Vehicle traction on snow and ice ......................................................................... 8

11. Critical conditions for trafficability of freezing or thawing ground ............... 9

12. Vehicle bearing capacity of frozen ground ......................................................... 10

13. Bearing failure modes for a shallow frozen layer over

soft ground ......................................................................................................... 10

14. Traction coefficient and resistance coefficient vs. water content .................... 12

15. Effect of soil thaw depth on net traction and motion resistance

coefficients as a function of soil moisture content ....................................... 13

16. Characteristics of Lebanon sand .......................................................................... 14

17. Idealized traction–slip curve in snow ................................................................. 15

18. Generalized traction–slip curves for different surface materials .................... 15

iii
iv

TABLES Page

Table

1. Bearing strength of frozen peatland ...................................................................... 11

2. Soil wetness descriptions ........................................................................................ 12

3. Internal motion resistance coefficients .................................................................. 16
v

NOMENCLATURE

Symbols

a Length of tire or track in contact with undisturbed snow (m)

Ai Hard surface contact area for element i (m2)

b Width of tire or track (m or in.)

bi Undeflected tire width or track width (in.)

f Traction multiplier for thawing soil

g Resistance multiplier for thawing soil

h Initial snow depth (cm)

hi Tire unloaded section height (in.)

Li Track length (in.)

n Number of wheels on the axle

Ni Normal stress under a wheel or track element i (kPa)

P Maximum load for a given frost depth (MN)

p Contact pressure (same as normal stress) (kPa)

Pfg Fine-grain-soil pressure factor (psi)

r Tire (wheel) radius (cm or in.)

r2 Correlation coefficient

RCI Rating Cone Index

ri Tire radius (in.)

Rinternal Motion resistance due to resistance internal to the vehicle (also called

hard surface resistance) (N)

Rterrain Motion resistance due to terrain (snow, soil, ice, etc.) (N)

Rthaw Motion resistance of thawing soil (N or lb)

S Thaw depth in soil (cm)

s Slip in decimal form

t Frost depth in soil (m)

Tgross Total gross traction available on a specified terrain (N)

Tnet Total net traction (N)

Tthaw Gross traction available on thawing soil (N or lb)

Vs Vehicle speed (mph or kph)

w Weight on axle (lb)

Wi Wheel or track load (lb)

Ws Driven wheel speed (mph or kph)

z Depth that a vehicle sinks into the terrain (sinkage) (cm)

zmax Maximum vehicle sinkage (snow) (cm)

zsoil Vehicle sinkage into soil (cm)

δi Tire loaded deflection (in.)

μice Traction coefficient for ice (ratio of tractive force to normal load)

θ Angle between leading edge of a track and the ground surface

ρ0 Initial snow density (Mg/m3)

ρf Theoretical critical density (Mg/m3)

Abbreviations

ALBE Air Land Battlefield Environment

CAMMS Condensed Army Mobility Model System

CIV CRREL Instrumented Vehicle

HEMTT Heavy Expanded Mobility Tactical Truck

HML Hard Mobile Launcher

HMMWV High Mobility Multipurpose Wheeled Vehicle

LAV Light Armored Vehicle

NRMM NATO Reference Mobility Model

SUSV Small Unit Support Vehicle

USCS Unified Soil Classification System

WES U.S. Army Waterways Experiment Station
• If the vehicle can maneuver or tow a trailer

(tractive reserve); and

• How fast the vehicle can get where it’s going (speed made good).

The first two issues can be determined at the

same time, since a positive value for tractive reserve is required for a “go” condition.

In its simplest form, mobility can be described

by a single equation expressing the balance between traction T and resistance R. Tractive reserve or net traction Tnet can be calculated from

Tnet = Tgross – Rterrain – Rinternal . (1)

In eq 1, Tgross is the maximum tractive force that a

specific vehicle is able to generate on a particular

terrain. Gross traction is generally a function of

• The tire/track contact pressure;

• The ability of the running gear to engage

with the terrain (e.g. the effect of tire tread

and traction aids, or track grousers and

cleats);

• The shear strength of the top layers of the

terrain; and

• The power available to the tire or track.

Motion resistance can be divided into two parts:

that produced by external forces and that produced by internal forces. The external resistance

Rterrain is the resistance attributable to the surface

and is a function of the strength of the terrain and

the vehicle’s running gear characteristics. To obtain Rterrain it is usually necessary to determine

the level to which a vehicle sinks below the terrain surface (sinkage, z). Rinternal is the resistance

caused by friction within the vehicle (tire deformation or track roller resistance, friction in driveline components, etc.).

Speed made good, besides depending on terrain and vehicle characteristics (slip and transmission power curves), is also strongly dependent on

operator skill, visibility, terrain roughness and

other parameters. Although important, speed made

Cold Regions Mobility Models

PAUL W. RICHMOND, SALLY A. SHOOP AND GEORGE L. BLAISDELL

INTRODUCTION

Over the past several years several empirical

and theoretical studies have aimed to predict the

mobility of vehicles over winter terrain and the

trafficability of that terrain. Most of these efforts

were primarily geared toward supporting the U.S.

Army Corps of Engineer’s AirLand Battlefield Environment (ALBE) demonstration program.

Many of these models, or portions thereof, have

also been proposed for incorporation into the

NATO Reference Mobility Model-II (NRMM-II)

(Ahlvin and Haley 1992) and the Condensed Army

Mobility Model System (CAMMS) (Falls et al.

1989). These general mobility models can be used

to estimate the absolute and relative mobility of vehicles traveling over a variety of terrain types. In

addition to being used as military planning and

operational tools, the models can also be used to

compare specific vehicles or to determine specific

vehicle–terrain interactions.

In this report the interaction between winter

terrain surface conditions and wheels (driven or

undriven) or tracks is discussed for snow, ice,

freezing/thawing ground and layered combinations of these conditions. This report brings together supporting documentation, data and theory

for individual segments of the cold regions models. A stand-alone program and the FORTRAN

code for CAMMS/NRMM implementation of the

cold regions models are included as appendices.

BACKGROUND

The term “mobility” is defined as the efficiency

with which a vehicle travels from one point to another. Trafficability refers to the ability of the terrain to support mobility. An effective mobility

model must be able to predict

• If a vehicle can propel itself between two

points (go/no-go);
good has not been fully investigated under winter conditions. Except for an approximation of

speed reduction caused by vehicle slip in snow

(discussed below), it is not addressed by any specific cold regions models. Effects on speed determined for temperate climatic conditions should

apply to winter as a first approximation.

Vehicle mobility in snow depends on snow

depth, snow density, crystal structure of the snow

grains, liquid water content, stratification in the

snowpack and virtually anything that affects the

mechanical characteristics of the snow cover. An

overview of snow characterization measurements

used for vehicle mobility and snow pavements is

given in Shoop (1993b), Shoop and Alger (1993)

and Abele (1990). Snow strength characterization

is reviewed in Shapiro et al. (in prep.). To fully

describe a snowpack in terms of its physical and

mechanical properties is time consuming and requires sophisticated equipment and specialized

techniques. Since the models described in this report were designed for tactical use, it was unrealistic for the models to require as input many of

the traditional scientific measurements. The algorithms we describe here rely solely on the most

basic snow parameters: depth and density.

SHALLOW SNOW

For mobility purposes, snow depth can be categorized as either shallow or deep, the difference

being based on the response of the snowpack to

the load applied by the vehicle. If the region of

disturbed snow under the vehicle’s running gear,

called the pressure bulb, extends to the ground or

pavement under the snow cover, then the snow is

considered shallow. If the pressure bulb is suspended in the snowpack, a deep snow condition exists.

An additional constraint for the shallow snow case

for our models is that the sinkage of the vehicle

be less than the vehicle ground clearance. Interestingly, whether a given snowpack thickness is

deep or shallow depends on the strength of the

snow and the characteristics of the vehicle to be

operated.

Since an assessment of whether a given snow

condition is shallow or deep requires detailed

knowledge of the applied load and snowpack response, we suggest two guidelines for making

this determination. These guidelines are based on

the amount of sinkage calculated in relation to either the tire radius or the undercarriage clearance

as illustrated in Figure 1.

Undisturbed snow on

a firm substrate

We describe undisturbed snow as snow that

has been driven over by less than four vehicles.

We chose this value based on a limited number of

measurements of pressure bulb density, where

we noted that it takes several wheel passes over

the same track to approach the critical density of

snow. (Critical density is generally accepted to be

0.55 Mg/m3, which represents the maximum density that can be attained by snow grain rearrangement. An increase in density beyond this requires

deformation of individual ice grains.) Further, to

be called undisturbed snow it must have a prevehicle-passage density of less than 0.55 Mg/m3.

This is almost always the case for snow, even in

polar regions.

If the terrain underlying the snow has a rating

cone index (RCI) (Shoop 1993a) value high enough

to fully support the vehicle of interest with no sinkage, mobility is assumed to be unaffected by the

substrate. We consider an RCI value of 100 or

greater to be adequate to resist sinkage. Nearly all

paved surfaces and frozen soils have an RCI greater

than 100. For undisturbed snow on a firm substrate,

sinkage will only occur in the snow, and calculation of traction and resistance is straightforward.

Shallow

Deep

z,

z = 2/3 r

Sinkage

Undercarriage Clearance

Pressure Bulb

r

Figure 1. Determining whether a snowpack is considered shallow or deep.

2
where ρ0 = density of the snow immediately in front of the vehicle’s

running gear (Mg/m3)

a = length of the tire or track in

contact with the snow (m)

b = maximum width of the tire or

track (m) (Fig. 3).

This resistance value is applied to up to

four axles or one track set on the vehicles of

interest (including any towed units). For

unknown reasons, predictions of resistance

for the Small Unit Support Vehicle (SUSV)

are most reliable when only the leading

track set is considered (Richmond et al.

1990). Recent analysis by Richmond (in

prep.) indicates that only the first three axles passing through undisturbed snow are important; we apply this equation to the first four axles

since the HEMTT with four axles was included

in development of eq 3. The data forming the basis of eq 3 are displayed in Figure 4. Although

the trend is strong, the r2 value is low (0.39), and

research refining our understanding of vehicle

motion resistance in snow is continuing.*

The length a of a tire or track contact with

snow in eq 3 requires the calculation of vehicle

sinkage z (Fig. 3). This is accomplished by the following equation for sinkage in undisturbed shallow snow:

 

z h max = – 



 

 1  ρ

ρ

0

f

(4)

where zmax = maximum predicted sinkage (cm)

in snow occurring under the tire or

track with maximum contact pressure pmax

h = initial snow depth (cm)

ρ0 and ρf = initial and theoretical final densities

(Mg/m3), respectively (Fig. 5).

The final density ρf is a function of the applied load. In temperate regions with seasonal snow, the following ρf values are used

as estimates; they are based on analysis of

field sinkage measurement, as illustrated in

Figure 6:

120

80

40

0

0 100 200 300

Normal Stress (kPa)

Shear Stress (kPa)

HML


LAV


Challenger


LAV (all tires)


Bradley


M 113


SUSV


HMMWV


HEMTT


5-Ton


CIV

Figure 2. Vehicle traction on snow.

W

r

a z

b

z

b

a

b. Track.

Figure 3. Snow and vehicle characteristics.

a. Wheel.

For shallow, undisturbed snow lying on top of

a strong substrate, we calculate gross traction

(kN) for one driven wheel or track element i

(Blaisdell et al. 1990) as

 

T NA gross i i i = 0 851 0 823 . . (2)

where Ni is the normal stress (kPa) on driving element i and Ai

 is that element’s contact area (m2).

The total gross traction for a vehicle is the sum of

the traction obtained for each driven wheel or

track. This equation is based on data generated

from a wide range of vehicle types and sizes

(both wheeled and tracked, with contact pressures ranging from 10 to 250 kPa) (Fig. 2). The

correlation coefficient for this equation (r2) is

0.97, with data from the standard military vehicles falling within –9 to 16% of the predicted

value.

The equation for motion resistance (N) in undisturbed snow is

Rterrain = 68.083 (ρ0 b a)0.9135 (3)

*A new resistance algorithm presented by Richmond (in prep.) for wheeled vehicles in snow will be

incorporated in an NRMM version newer than 2.5.0.

3
104

103

102

2 4 6 8 10 20 40 60 80

Density . Arc Length . Width (kg/m)

Resistance Per Wheel (N)

Figure 4. Vehicle motion resistance in shallow snow.

300

200

100

0

0 0.1 0.2 0.3 0.4 0.5

h – zmax (m)

ρo . h (kg/m2

)

ρf

 = 0.56 Mg/m3

Figure 6. Vehicle sinkage analysis. (From Richmond et al. 1990.)

Figure 5. Prediction of vehicle sinkage in shallow

snow. 



 





h

z

ρo

ρf

4
analysis that is beyond the scope of our initial

models. Further research may show that these

shortcomings can be accounted for by lowering

the RCI value used to separate firm from soft substrates. We have also ignored the possibility that

shear zones could form between the snow and

the soil (most likely in shallow snow), which

would affect both traction and resistance calculations.

Soil sinkage is calculated separately for wheeled

and tracked vehicles using the sinkage equations

of Willoughby.* The equations for wheeled and

tracked vehicles, respectively, are

 

z

r

r b

W hs

soil

i

i i

i ii

RCI 2

=

( )

















10

1 3 2 1 5

5 3

– / / /

/

δ

 (Wheeled)

zsoil = 0.00443 Li e(5.889 Wi

/RCI bi Li) (Tracked) (9)

zsoil = 0 (If RCI ≥ 100) (10)

where RCI = rating cone index

Li = track length (in.)

bi = undeflected tire width or track

width (in.)

ri = tire radius (in.)

Wi = wheel or track load (lb)

δi = tire loaded deflection (in.)

hi = tire unloaded section height (in.)

s = slip in decimal form (chosen to be

0.05 for Cold Regions Models) for

the running gear element i.

Combined sinkage less than or

equal to the snow depth

For the situation where sinkage occurs in the

soil (RCI < 100) but z is still less than the snow

depth h, we assume that the motion resistance is

only that due to snow. While the combined z from

eq 7 is larger than zmax from the snow, the tire or

track is still contained completely in the snowpack and thus its resistance to motion is caused

primarily by snow deformation. Equations 2 and

3 are used to calculate traction and resistance.

pmax ≤ 210 kPa ρf = 0.50 Mg/m3

pmax > 210 kPa ρf = 0.55 Mg/m3

pmax > 350 kPa ρf = 0.6 Mg/m3

pmax > 700 kPa ρf = 0.65 Mg/m3.

The sinkage calculation is also used to estimate whether the snow is deep or shallow.

Once sinkage z is determined, the value of a

(contact length) for wheeled vehicles is

a = r arccos [(r–z)/r] (5)

where r is the tire radius (cm or in.). For tracked

vehicles the equation is

a = z/sin (θ) (6)

where θ is the angle between the leading edge of

the track and the ground surface (Fig. 3b). Since

the vehicle database defined for CAMMS and

NRMM does not contain this value, we assume

an average value of 26° for θ for all tracked vehicles.

Undisturbed snow on

a soft substrate

For undisturbed snow over a soft soil, additional sinkage occurs as a soil rut is formed. This

increases motion resistance as the wheel or track

sinks deeper in the snow and possibly below the

soil surface.

In this case the total sinkage is estimated to be

the sum of the sinkage of the two materials independently. Soil sinkage is calculated ignoring the

snow cover and is added to the sinkage determined for the snow from eq 4. The arc length a,

and hence the motion resistance Rterrain, is calculated based on the combined sinkage:

z = zsoil + zmax. (7)

This approach may be naive in its assumption

that the snow and soil can each be treated as

separate entities and that their effects can be

added to determine the combined effect on a vehicle. However, this assumption is probably adequate for snow depths greater than about 15 cm

and soil strengths great enough to suffer less than

about 10 cm of sinkage. We also recognize that we

have not accounted for the ability of snow to

spread and attenuate the vehicle’s load. In calculating soil sinkage using this approach, we have

placed the entire running gear load and contact

pressure on the soil. Although this is clearly incorrect, an accurate determination of the actual

load and pressure would involve a sophisticated

(8)

* Personal communication with W. Willoughby, U.S.

Army Waterways Experiment Station, 1992.

5
Figure 7. Vehicle traction for snow over ice. (From Richmond et al.

1990.)

100

80

60

40

20

0

0 100 200 300

Normal Stress (kPa)

Gross Traction (kPa)

SUSV

HMMWV

HEMTT

Combined sinkage greater than

the snow depth

For some situations it is possible that the combined sinkage z is greater than the snow depth. In

this case the motion resistance due to the sinkage

into the soil must be added to that from the snow

to determine the total resistance. Unfortunately

calculating the resistance for a sinkage greater

than the snow depth involves knowing the interaction of the snow and the substrate during deformation and shearing and is far beyond the

scope of current understanding. Thus, we have

no provisions for calculating the additional resistance or the effect on traction when z is greater

than h. The model calculates the resistance based

on the total sinkage considered to be in snow, and

traction is based on the condition specified as if

this case did not occur.

Undisturbed snow over ice

The algorithms above have all assumed that

shear displacement in the terrain as a result of the

tractive demand of the running gear occurs within the snowpack. In this assumption we are

claiming that the internal shear strength of the

snow below a tractive element is less than or

equal to the shear strength of the substrate or the

interface between the substrate and the snow.

This is most likely true for all situations except

when the snow overlies ice. This could occur on a

frozen river or lake or on a road surface where

precipitation started as freezing rain prior to becoming snow. In this case the interfacial shear

strength between the snow and ice is almost

guaranteed to be less than the shear strength within

the snow. Thus, for shallow snow where the pressure bulb is in contact with the ice, we assume

that traction will be governed by the interfacial

properties.

For undisturbed shallow snow deeper than 1

cm lying on top of ice, we use the following traction equation:

 

T NA gross i i i = 0 127 1 06 . . (11)

which was presented by Richmond et al. (1990)

(Fig. 7). The value of 1 cm was chosen to reflect the

point at which the snow/ice interface would have

effectively no strength, and the traction generated

would be the same as that on a clear ice surface.

Rterrain for this case is calculated using eq 3.

Disturbed, processed

and packed snow

The physical and mechanical properties of a

snowpack change significantly when it is driven

over repeatedly. After a large volume of traffic,

the snow’s characteristics cease to change dramatically as the result of tire loads, and the snow

is then considered to be packed.

Vehicle operators tend to follow in the tracks

of preceding vehicles. We assume that after four

passes in the same track, the snow has reached its

critical density, and succeeding vehicles will be

traveling on packed snow. Usually, packed and

disturbed snow conditions can only be formed over

a firm substrate.

In some cases an area of snow is mechanically

processed to produce a snow road that is capable

of supporting wheeled vehicle traffic (Abele 1990).

6
100

80

60

40

20

0

0 100 200 300

Normal Stress (kPa)

Gross Traction (kPa)

SUSV

HMMWV

M60

Bradley

HEMTT

Figure 8. Vehicle traction for packed snow. (From Richmond et al.

1990.)

We assume that disturbed, packed or processed

snow attains a density of at least 0.55 Mg/m3.

Since only vehicles that have a very high ground

pressure are expected to cause any sinkage on

these surfaces, Rterrain for this case becomes zero

for all vehicles.

The equation we use to predict traction on

packed snow is

 

T NA gross i i i = 0 321 0 97 . . (12)

and is shown in Figure 8.

A comparison of measured and predicted traction on shallow, groomed snow is discussed in

Appendix C.

For disturbed snow deeper than 1 cm over an

ice surface, we assume that a bond has developed

between the packed snow and ice; we use eq 12

for traction in this case and again assume that the

Rsnow is zero.

DEEP SNOW

Deep snow occurs when the deformation bulb

under a wheel or track does not extend down

through the snowpack to an underlying surface

(Fig. 1). Since vehicle sinkage depends on ground

pressure, it is apparent that the presence of a deep

snow condition is a function of the snow depth,

bearing capacity (generally reported in the form

of a pressure–sinkage relationship) and vehicle

characteristics. Additionally we include as deep

snow the cases where sinkage is greater than 2/3

of the wheel radius and where sinkage is greater

than the ground clearance for wheeled or tracked

vehicles. This added set of criteria for defining a

deep snow condition recognizes that when a vehicle sinks to the point where the majority of its

running gear is below the snow surface, added

sources of resistance arise beyond simple compaction of the snow in front of the tire or track.

Both traction and resistance are different for

deep snow than for shallow snow. However,

there are few published results for deep snow

mobility with wheeled and tracked vehicles,

making it difficult to write accurate prediction

equations. Thus, we used the shallow snow results as a starting point for the deep snow models. We began by assuming that the deep snow

condition only alters traction to a small degree,

since the majority of the tractive force is generated in the fully compacted portion of the pressure bulb. The tractive force developed in deep

snow is most likely somewhat less than for shallow snow, because the pressure bulb will have a

slightly lower density. The degree of reduction in

density and tractive force is unknown, so we

chose to use the shallow snow traction expression

(eq 2) for deep snow.

Motion resistance generated as the result of

sinkage into the snow exists in deep snow just as

it did for shallow snow. In the vast majority of

cases, sinkage is greater in deep snow, so resistance is higher, since a greater portion of the wheel

or track is involved in compacting and displacing

snow. However, several additional sources of resistance may arise in deep snow. For example, por7
For wheeled vehicles:

ρ0 < 0.15 Mg/m3

1) If sinkage ≥ wheel radius, multiply

resistance by 1.5.

2) If sinkage ≥ ground clearance, add

1.5 to multiplier above.

ρ0 ≥ 0.15 Mg/m3

1) If sinkage ≥ (0.666 × wheel radius)

but less than wheel radius, multiply

resistance by 1.5.

2) If sinkage ≥ wheel radius, multiply

resistance by 2.5.

3) If sinkage ≥ ground clearance, add

1.5 to multipliers above.

For tracked vehicles:

ρ0 < 0.15 Mg/m3

1) If sinkage ≥ ground clearance, multiply resistance by 2.5.

ρ0 ≥ 0.15 Mg/m3

1) If sinkage ≥ ground clearance, multiply resistance by 4.0.

In formulating these guidelines, we took ground

clearance to be the height above ground of the

lowest major component of the undercarriage of

a vehicle, measured while it is parked on a firm

surface. Our experience suggests that small, or a

low number of, protuberances generate little additional resistance (Richmond, in prep.). However, the NRMM/CAMMS database lists ground

clearance as the distance from the lowest component to the ground. Therefore, our model will

yield conservative output (it will err on the side

of overprediction for Rterrain).

0 0.1 0.2 0.3 0.4

Traction Coefficient for Ice

Light snow over smooth ice (Shoop 1993b)


"Rough" ice (Shoop 1993b)


"Rough" ice (Blaisdell 1993b)


Buffed ice at –3°C (Blaisdell & Borland 1992)


Buffed ice at –10°C (Blaisdell & Borland 1992)


μice (SME 1993)


"Rule of thumb"


Highway travel (Clark 1982)

Figure 9. Vehicle traction on ice.

tions of the undercarriage may drag in the snow

as the result of greater sinkage. In very deep snow,

even the front face of a vehicle may be “plowing” snow.

Lacking quantitative data for motion resistance in deep snow, we based our initial model of

resistance in deep snow on a combination of analytical considerations and our collective observations of the behavior of vehicles operating in

deep snow conditions. Our model of resistance

in deep snow uses “multipliers” applied to the

shallow snow resistance expression (eq 3). These

multipliers were chosen to represent the significant increase in resistance experienced when snow

is being pushed forward by the near-vertical face

of the tire when sinkage is large. For tracked vehicles the concern is primarily interference with the

undercarriage. The multipliers are as follows:

100

80

60

40

20

0

0 100 200 300

Normal Stress (kPa)

Gross Traction (kPa)

Undisturbed Snow

Packed Snow

CIV on Ice

Snow Over Ice

Figure 10. Vehicle traction on snow

and ice.

8
When a wet, weak soil begins to freeze (Fig.

11a), the strong frozen layer on top will increase

the bearing capacity of the ground. The bearing

capacity—the ability of the soil to support a vehicle—can be expressed as a function of the frost

depth t and the relative wetness of the frozen

ground surface.

During spring and intermittent thaws, a thawed

layer of soil develops over the frozen soil (Fig.

11b). In the top layer the soil moisture is higher

than normal due to snowmelt, rain and the increased water drawn to the soil layer during the

freezing process. This moisture is trapped in the

shallow thawed layer, creating a wet and weak

layer of soil over the stronger frozen layer. The

reduction in vehicle mobility will be a function of

the strength of the composite soil, which can be

expressed in terms of thaw depth S and the soil

moisture in the thawed layer. As the thaw progresses deeper (Fig. 11c), the frozen layer becomes

too distant to add support to the vehicle or strength

to the effective soil system, but it often continues

to restrict the soil drainage.

Our current state of development of mobility

modeling for freezing ground is limited to go/

no-go predictions based on whether the ground

can support the vehicle. For thawing ground we

can make more quantitative predictions of the

effect on traction and motion resistance. Our

models assume a baseline traction and motion

resistance for the soil of interest in its fully

thawed state. The effects of freezing and thawing are expressed as modifications (multipliers)

to the baseline values for traction and motion

resistance. The effects of other factors (e.g. vegetation and slope) on mobility during freezing

ICE

Ice traction is a function of surface roughness,

temperature, tire compound and vehicle speed

(Blaisdell and Borland 1992). While it may be possible to easily incorporate ice temperature into the

NRMM/CAMMS database, it is unlikely that either tread compound or surface roughness could

be included with any degree of accuracy in the near

term. So, to treat the case of traction on ice, we have

reviewed published data (Fig. 9) (Shoop 1993b) and

taken a conservative value of 0.1. Therefore, we calculate traction on ice as

 

T A gross i i i = 0 1. N . (13)

The traction equations for ice and snow are compared in Figure 10. A model of ice traction utilizing traction aids exists (Blaisdell 1984), but it requires as input geometric features of the devices,

which are not available in the current Army mobility database.

Because of the essentially undeformable nature of ice under a vehicle’s running gear, motion

resistance Rterrain is assumed to be zero.

FREEZING OR THAWING

GROUND CONDITIONS

Freezing ground can often increase vehicle mobility, while thawing ground nearly always reduces

mobility. An additional issue of importance is the

possibility of severe terrain damage when vehicles

operate in areas with thawing conditions. Three

critical conditions for vehicle mobility on freezing

and thawing soils are illustrated in Figure 11.













































 











 















Frozen Soil


Unfrozen Soil

a. Critical depth of frozen soil that will support a

vehicle.

Figure 11. Critical conditions for trafficability of

freezing or thawing ground.

c. Frozen layer too far down to give support. The layer

still impedes drainage. Moisture content and soil properties are critical for trafficability.

b. Critical depth of a thawed wet layer where traction

is too low. If the tires can engage the strength of the

frozen layer, then the ground may be trafficable.

9
P

P

P

P

c. Crushing and compaction of the frozen

material.

d. General shear failure of the underlying

material and tensile failure of the frozen

layer.

Figure 13. Bearing failure modes for a

shallow frozen layer over soft ground.

a. Tensile failure in the lower beam fibers.

b. Punching through the frozen layers.

Figure 12. Vehicle bearing capacity of

frozen ground.

or thawing are assumed to be the same as for unfrozen conditions.

Bearing capacity of

freezing ground

Vehicle operation on freezing ground is characterized by the ability of the ground to fully support the vehicle. For unfrozen soils that are not

extremely difficult to traverse, the presence of 5

cm of frost at the surface will usually allow unlimited cross country operation (Richmond 1991).

Terrain that is normally untrafficable may require

a substantial frost layer before vehicle operations

are possible.

Certainly “soft” terrain stands to gain considerable strength upon freezing. For example, the

compressive strength of frozen peat can be 350–

400 times its unfrozen strength (MacFarlane 1968),

making it possible to operate vehicles in peat areas

as long as they are frozen. We use a definition of

soft terrain based on the Cone Index, where values of 50 or less constitute very weak soils. Although cone penetration is not particularly applicable to measuring the strength of heavily vegetated terrain, it can serve as a gross assessment

of the bearing capacity of the ground, disregarding the strength of root systems. Niemi and Bayer

(1970) have documented Cone Index values of 50

or less for peat or muskeg.

To arrive at predictions of bearing capacity for

frozen ground over a soft substrate, we utilize published guidelines for forestry operations on peatlands (Rummukainen 1984) (Table 1). The equivalent loads are estimates of the gross vehicle weight.

From these guidelines the following equations

were generated to represent the limits for a breakthrough failure of a frozen layer that is less than

0.5 m thick:

P = 0.35 t

2 for dry conditions (14)

P = 0.86 t2 for wet conditions (15)

where P is the maximum recommended load in

MN and t is the frost depth in meters. The wet

condition represents saturated peat. In the dry con0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

Frost Depth (m)

Vehicle Weight (MN)

0

20

40

60

80

100

Vehicle Weight (tons)

Wet Ground

Dry Ground

10
rather than that for the soil alone. However, since

we have no data to confirm this, no algorithm is

implemented to account for this effect.

Effect of thawing conditions on

vehicle performance

Thawing ground causes problems for vehicle

mobility when it is associated with thaw weakening of the soil. During thaw, otherwise freely draining soils can become saturated because drainage

is reduced by the underlying, nearly impermeable frozen layer. Vehicle travel is then restricted

or impossible, and traffic can cause environmental damage (torn vegetation, mass soil flow and

rutting, and subsequent erosion of sediments).

To predict traction and resistance in thawing

soils, we start from either measured or predicted

vehicle performance for the same soil at a temperate state. Adjustments are made to compensate for the significant loss of shear strength in a

wet, thawing soil (resulting in a loss of traction)

and the greater vehicle sinkage in the thaw-weakened soil (causing an increase in motion resistance).

Using established methods for predicting traction

and motion resistance for unfrozen soil (in this case,

models developed by WES), we apply multipliers

to reduce traction and increase motion resistance

as the result of the thawing condition:

Tthaw = f Tgross (16)

Rthaw = g Rterrain (17)

where Tthaw = gross traction in the thawing soil

Rthaw = terrain motion resistance in the

thawing soil

f = traction reduction multiplier

g = motion resistance multiplier

Table 1. Bearing strength of frozen peatland. (After Rummakainen 1984.)

Thickness of frozen peat layer (m)

Dry top Wet top Approx. equiv. load

peat layer peat layer Bearing capacity (MN) (lbf)

0.10 0.05 Will bear a horse 0.00445–0.008 1000–1800

0.15–0.20 0.10 Will bear 6-ton 0.05 12,000

horse-drawn sled traffic

0.20–0.35 0.15–0.25 Will bear empty 0.036 8000

4-ton truck

0.35–0.50 0.25–0.40 Will bear 10-ton truck traffic 0.09 20,000

dition the peat is less than saturated and has usually been drained. (A frost depth of 0.5 m will prevent breakthrough failure of most vehicles.) Equations 14 and 15 are shown schematically in Figure

12 in terms of the frost thickness necessary to support different vehicle classes (vehicle class is approximately the vehicle weight in tons).

Mobility of heavy equipment may be limited

by localized crushing failure of the surface material, particularly for the dry conditions (Fig. 13)

(Shoop, in prep.). Therefore, the prediction equation for dry conditions, where surface crushing is

likely, is not applicable for vehicles with high

ground pressure. We recommend that the dry equation be used for all tracked vehicles and wheeled

vehicles weighing less than 12 tons.

The predictive formulas are based on a best-fit

equation for the wheeled vehicles, and they overestimate the frost thickness necessary for the sled

(Table 1). Thus, our load support predictions will

be conservative for vehicles with running gear

that distributes load uniformly (e.g. tensioned

tracks, numerous road wheels, skis).

These equations can also be applied to frozen

ground other than peat. Once frozen, the strength

of ground depends primarily on its ice content,

its density and its temperature. The time-dependent compressive strength of frozen peat is similar to that of frozen mineral soils (MacFarlane

1968) and falls within the range of frozen silt or

clay (Shoop, in prep.).

Very few data exist for vehicle traction on frozen

ground. In general, frozen ground enhances mobility and traction. Exceptions are if the ground has a

very high ice content or if the temperature is near

melting. In these cases traction may be reduced because of the slipperiness of the surface and may be

closer to the level of traction experienced on ice

11
Figure 14. Traction coefficient and resistance coefficient vs. water content. Below the liquid limit, traction is a function of

applied stress as reflected in tire inflation pressure. The net tractive coefficient decreases and the motion resistance coefficient

increases for soil water contents above the liquid limit.

Table 2. Soil wetness descriptions.

Water content Saturation

Soil wetness (%) (%)

wet* 23–27 83–100

moist 17–21 77–82

dry† 6–13 23–59

* Nearly saturated and above the liquid limit.

† Below the specific retention of the soil.

Tgross = gross traction for the unfrozen soil

Rterrain = terrain resistance for the unfrozen

soil.

The multipliers are defined based on the measurements of vehicle performance on thawing soil

reported in Shoop (1990, 1993c). The experiments

were performed using an instrumented vehicle to

measure traction and motion resistance on a wide

variety of thawing conditions for a fine-grained

sand. The experimental variables were soil thaw

depth, moisture content, density and applied stress

(tire inflation pressure).

The multipliers f and g vary with soil type,

wetness, contact stress and thaw depth. Traction

and motion resistance vary with the wetness of

the thawed soil layer as shown in Figure 14. At

lower water contents the traction coefficient depends on the tire contact stress. At high soil moisture (above the liquid limit), traction drops rapidly, and the contact stress has no noticeable effect. Motion resistance increases considerably at

soil moistures above the liquid limit, and the effect of tire inflation pressure was negligible for

the conditions tested.

The effect of the depth of thaw can be seen

clearly when the data are grouped according to

the wetness of the thawed layer (Fig. 15). The degree of wetness in the thawed layer is defined in

Table 2. For both traction and motion resistance,

the “wet” conditions are the most critical. When

the soil is “moist,” the soil strength is near optimum, and much of its strength is retained during

the thaw cycle. Thus, for moist soils the thawing

layer is strong enough that traction and motion

resistance are nearly constant for all thaw depths

S. For “dry” soils the thawing has a small effect

on the overall soil strength, and traction is a function of both thaw depth and applied stress. Since

this function has not yet been defined, we currently use an interim value of 1. For “dry” soils

the effect of thawing on motion resistance is negligible.

The following expressions define the multipliers f and g in eq 16 and 17:

Traction:

Wet soils

f = 1.0 S ≤ 2.5 cm (18)

f = 2.379 (1/S2) + 0.619 2.5 < S < 15(19)

f = 0.63 15 ≤ S (20)

12
0.3

0.4

0.5

0.6

0.7

0 4 8 12 16

Traction Coefficient

Water Content
 ––––––––––––––– 6-13% (dry)


17-21% (moist)


23-27% (wet)

Figure 15. Effect of soil thaw depth on net traction and motion resistance coefficients as a function of soil

moisture content.

b. Resistance coefficient vs. thaw depth.

Moist soils

f = 1.0 (21)

Dry soils

f = 1.0. (22)

Motion resistance:

Wet soils

g = 1.0 S ≤ 2.5 cm (23)

g = 2.883 S – 6.056 2.5 < S < 4 (24)

g = –0.22 S2 + 3.54 S – 5.24 4 ≤ S ≤ 8 (25)

g = 0.225 S + 7.2167 8 < S < 12 (26)

g = 10.00 12 ≤ S (27)

Moist or dry soils

g = 1.0. (28)

These equations are based on data obtained using an instrumented Jeep Cherokee (gross vehicle

weight of 5600 lb.) equipped with light-truck, allseason, radial tires at a variety of tire inflation pressures (Shoop et al. 1993). For very heavy vehicles

and for tracked vehicles, the critical thaw depth

will change because of the larger and deeper volume affected by the applied stress. Because of the

lack of effect of tire inflation pressure (contact pressure) for the most critical conditions (wet), the proposed relationships can be applied to a wide variety of vehicles with the understanding that there

are no experimental data to validate the results.

This aspect will be addressed in future studies.

The traction relationships are based on the optimum available traction, obtained by taking an

average of the top 20% of the traction curve. The

relative slip values and traction curve shapes were

not evaluated.

0.04

0.06

0.08

0.10

0.02

0

0 4 8 12 16

Thaw Depth (cm)

Resistance Coefficient

Water Content
 ––––––––––––––– 6-13% (dry)


17-21% (moist)


23-27% (wet)

a. Traction coefficient vs. thaw depth.

13
Because these relationships were derived from

tests on a non-plastic fine sand (unified soil classification SM) (Fig. 16), and limited tests on other

sandy soils indicate the same general trends, we

feel confident applying them to the following soil

types:

SW: Well-graded sands, gravely sands, little

or no fines

SP: Poorly graded sands, gravely sands, little

or no fines

SM: Silty sands, sand and silt mixtures.

It is also reasonable to extrapolate beyond the range

of test soils to other soils of similar mechanical

behavior, such as other sands (SC), gravels (GW,

GP, GM, GC) and silts (ML). We don’t advise that

they be applied to clayey soils or highly plastic

soils since the behavior of the soil, and therefore its influence on traction and motion resistance, is likely to be quite different. When thawing conditions are encountered in clays and medium- or high-plasticity soils, we recommend that

algorithms designed to treat surface slipperiness

(Willoughby et al. 1991) be implemented in future versions of NRMM/CAMMS. Continuing

research is aimed at completing the definition of

f and g for more soil types and wetness conditions.

SPEED MADE GOOD

The time to get from one point to another, or

speed made good, is a function of many vehicle/

operator and terrain/environment variables. Some

reduction in speed occurs as a wheel or track slips.

Making the assumptions that

• For a vehicle moving at a constant velocity

on level terrain the traction generated must

equal the total motion resistance,

2.0

1.8

1.6

8 10 12 14 16 18

Water Content (%)

CE-55

Modified Proctor

Dry Unit Weight (g/cm ) 3

b. Soil compaction curve.

a. Grain size distribution.

6" 4" 2" 1" 10 40 200 3/8"

U.S. Standard Sieve Numbers Hydrometer

100

80

60

40

20

0 100

80

60

40

20

0

Percent Finer by Weight

Percent Coarser by Weight

100 10 1 0.1 0.01 0.001

Grain Size (mm)

Cobbles

Gravel

Coarse Fine C'rse Medium Fine

Sand

Silt or Clay

Lebanon Sand (SM)

Liquid Limit: 20

Specific Retention Water Content: 12 - 14%

Specific Gravity: 2.71

Figure 16. Characteristics of

Lebanon sand.

14
R

Tgross

0.1 0.2

Slip

R = Rterrain + Rinternal


Slip = ws – vs ––––––


 vs

1.0

0.8

0.6

0.4

0.2

0

Dense Sandy Soils

Shallow Snow

Ice

Traction

0 20 40 60 80 100

Slip (%)

Loose Sandy Soils

Figure 17. Idealized traction–slip curve in snow.

Figure 18. Generalized traction–slip curves for

different surface materials.

• The maximum traction in snow occurs at

about 20% slip, and

• The traction–slip curve is nearly linear between 0 and 20% slip (Fig. 17),

we claim that the slip when operating in snow

can be calculated from the following equation:

 

 

Slip R R

T snow terrain internal

gross

= 0 2. ( ) + (29)

for Tgross ≥ Rterrain + Rinternal.

Once the slip has been calculated, the estimated

vehicle velocity can be calculated using the definition for slip:

 

V W

Slip s s

1

snow 1 = +

 (30)

where Vs and Ws are the vehicle and wheel speeds,

respectively. We recommend that this velocity correction be applied before other effects are taken into

account. Generalized traction–slip curves for different materials are shown in Figure 18. These variations will need to be considered when or if the full

traction curves are incorporated into future mobility models.

INTERNAL MOTION

RESISTANCE

Internal motion resistance, as mentioned earlier, is the force caused by friction within the vehicle (tire deformation, friction in driveline components, etc.). We use the values for Rinternal of

wheeled and tracked vehicles as tabulated by

Ahlvin and Haley (1992). These values (Table 3) are

in coefficient form (the ratio of resistance force to

wheel or track weight).

15
Because this is an empirically based model, and

because mobility is a continuing area of interest

to the U.S. Army, improvements and expansion

of the model are to be expected. In the process of

preparing this report a number of areas needing

improvement were identified. For mobility/trafficability analysis over snow-covered areas, the following need further research: motion resistance

in shallow snow, deep snow trafficability, and snow

over a soft soil with large sinkage values. For operations on ice the effects of temperature and traction aids needs further study. In freezing/thawing

soils further tests with heavy vehicles are required,

the types of soils investigated need to be expanded,

and tracked vehicles need to be evaluated.

LITERATURE CITED

Abele, G. (1990) Snow roads and runways. USA

Cold Regions Research and Engineering Laboratory, Monograph 90-3.

Ahlvin, R. and P. Haley (1992) NATO reference

mobility model edition II, User’s guide, Volume I

(NRMM II). USA Waterways Experiment Station,

Technical Report GL-92-19.

Blaisdell, G.L. (1984) Winter traction aids for

wheeled vehicles. In Proceedings of the 1984 Army

Science Conference, 19-21 June 1984, West Point, New

York.

Blaisdell, G.L. and S. Borland (1992) Braking traction on sanded ice at low slip rates. Report prepared

for Federal Aviation Administration, Washington D.C., by USA Cold Regions Research and Engineering Laboratory.

Blaisdell, G.L., P.W. Richmond, S.A. Shoop, C.

Green and R.G. Alger (1990) Wheels and tracks

in snow: Validation study of the CRREL shallow

snow mobility model. USA Cold Regions Research

and Engineering Laboratory, CRREL Report 90-9.

Clark, S.K. (1982) Mechanics of pneumatic tires.

U.S. Department of Transportation. Washington,

D.C.: U.S. Government Printing Office.

Falls, T.C., C.D. Butler, B.T. Webb, J.L. Williamson

and A. Chase (1989) A User’s Guide for CAMMS

Version 2.0.

MacFarlane, I.C. (1968) Strength and deformation

tests on frozen peat. In Proceedings of the Third International Peat Congress, Quebec, Canada, August

18–23, 1968, p. 143–149.

Niemi, E.W. and R. Bayer (1970) Analytical prediction of vehicle mobility on muskeg. U.S. Army

Tank Automotive Command, Warren, Michigan,

Table 3. Internal motion resistance coefficients.

Rinternal

Wheeled Tracked Surface

0.0150 0.0375 Superhighways and primary roads and ice

0.0250 0.0450 Secondary roads

0.0175 0.0525 Trails and cross country (Pfg* ≥ 4.0)

0.0150 0.0525 Trails and cross country (Pfg < 4.0)

* Pfg = w/(nbr), in psi, where, w is the weight on an axle, n is the

number of wheels on an axle, b is the wheel width and r is the

wheel radius.

SLOPES

The main effect of slopes is the redistribution

of the force of gravity on the vehicle body forces

(Yong et al. 1984). This redistribution is seen as an

additional resistance term due to gravity and a reduction of the normal load on each wheel or track

assembly. Richmond (1993) examined this approach using the traction and resistance equations

for snow presented earlier and obtained good

results when compared with go/no-go tests on

slopes. The effect of slopes on traction is implemented by multiplying the normal load on a wheel

or track by the cosine of the slope angle. The effect

on resistance is implemented by adding a resistance

term due to gravity, which is equal to the gross vehicle weight times the sine of the slope angle, to

Rterrain.

SUMMARY AND

RECOMMENDATIONS

The algorithms, rationale and data sources for

what we call the Cold Regions Mobility Model

have been presented. These algorithms are primarily empirical in nature and rely on relatively

simple terrain measurements. Appendix A contains a stand-alone FORTRAN code of the Cold

Regions Mobility Model (CRM-1.F); sample data

files and output are presented.

We did not address the accuracy of the algorithms in this report; the reports in which these

algorithms were initially developed discuss this

issue somewhat. Future work will examine improvements in the algorithms and the overall accuracy with regard to speed made good and go/

no-go predictions.

16
TACOM Technical Report No. 11108 (LL 140) (AD

730792).

Richmond, P.W . (1991) Notes for cold weather

military operations. USA Cold Regions Research

and Engineering Laboratory, Special Report 19-30

(with excerpts from US Army Field Manual FM

90-13/FM 7-26, Ice Bridging, p. B-20).

Richmond, P.W . (1993) Predicting vehicle mobility on snow covered slopes. In Proceedings of the

First International Conference on Winter Vehicle Mobility, June 1991, Santa Barbara, California (G.L. Blaisdell, Ed.). USA Cold Regions Research and Engineering Laboratory, Special Report 93-17.

Richmond, P.W. (in prep.) The motion resistance

of wheeled vehicles in snow. USA Cold Regions

Research and Engineering Laboratory, CRREL Report.

Richmond, P.W., G.L. Blaisdell and C.E. Green

(1990) Wheels and tracks in snow: Second validation study of the CRREL shallow snow mobility

model. USA Cold Regions Research and Engineering Laboratory, CRREL Report 90-13.

Rummukainen, A. (1984) Peatland properties and

their evaluation for wood harvesting. Final Report

for “Harvesting on Peatlands,” a research project of

the Nordic Research Council on Forest Operations

(NSR), 1977–1983, University of Helsinki, Department of Logging and Utilization of Forest Products, Research Notes No. 45.

Shapiro, L.H., J.B. Johnson, M. Sturm and G.L

Blaisdell (in prep.) Snow mechanics: Review of

the state of knowledge and applications. USA Cold

Regions Research and Engineering Laboratory,

CRREL Report.

Shoop, S.A. (1990) Mechanisms controlling vehicle

mobility on a thawing soil. In Proceedings of the 10th

International Conference of the International Society

of Terrain Vehicle Systems, August 1990, Kobe, Japan,

vol. I, p. 301–312.

Shoop, S.A. (1993a) Three approaches to winter

traction testing. USA Cold Regions Research and

Engineering Laboratory, CRREL Report 93-9.

Shoop, S.A. (1993b) Terrain characterization for

trafficability. USA Cold Regions Research and Engineering Laboratory, CRREL Report 93-6.

Shoop, S.A. (1993c) Effect of soil thawing on offroad vehicle traction. In Proceedings, 6th International

Permafrost Conference, July 1993, Beijing, China., vol.

1, p. 559–563. Submitted to Journal of Terramechanics.

Shoop, S.A. (in press) Vehicle bearing capacity of

frozen ground. Canadian Geotechnical Journal, accepted for publication in June 1995.

Shoop, S.A. and R. Alger (1993) Snow characterization for traction testing: A survey of techniques

used. In Proceedings of the First International Conference on Winter Vehicle Mobility, June 1991, Santa Barbara, California (G.L. Blaisdell, Ed.). USA Cold Regions Research and Engineering Laboratory, Special Report 93-17.

Shoop, S.A., E. Berliner and S. Decato (1993) An

experimental method for vehicle mobility testing

on freezing/thawing soil. In Proceedings of the First

International Conference on Winter Vehicle Mobility,

June 1991, Santa Barbara, California (G.L. Blaisdell,

Ed.). USA Cold Regions Research and Engineering Laboratory, Special Report 93-17.

Society of Mining Engineers (1973) SME Mining

Engineering Handbook. New York: Society of Mining Engineering of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.

Yong, R.N., E.A. Fattahand and N. Skiadas (1984)

Vehicle Traction Mechanics. New York: Elsevier.

Willoughby, W.E., R.A. Jones, C.D. Cothren, D.W.

Moore, D.M. Rogillio, R.F. Unger and T.L. Prickett

(1991) Mobility in slippery soils and across gaps,

Volume 1: Program summary. USA Waterways Experiment Station, Technical Report GL-91-2.

17
Line Value Data FORTRAN format code

1 Vehicle name HMMWV 2a4

2 Vehicle type 0 10i2

3 No. of axles 2 i2

4 Ground clearance, inches 15.75 f8.2

5 No. wheels per axle 2 2 10i2

6 Axle power 1 1 10i2

7 Radius of each wheel (in.) 16.90 16.90 10f7.2

8 Width of each wheel (in.) 12.60 13.00 10f7.2

9 Load on each axle divided 1625.00 2135.00 10f7.2

by the number of wheels (lb)

10 Tire contact area (in.2) 115.00 115.00 10f7.2

11 Unloaded section height 9.0 1.2 *

and loaded tire deflection (in.)

APPENDIX A: COLD REGIONS MOBILITY MODEL CRM-1.F

GENERAL

The program CRM-1.F is a FORTRAN code that calculates mobility parameters and factors that can be

used to determine go/no-go conditions, drawbar pull, drawbar coefficient, gross traction, total resistance

and slip due to traction on snow. For calculations on snow the required data are snow depth and density,

slope, RCI if there is a soft soil underlying the snow, and vehicle data (described below). If the analysis

involves only thawing or freezing soils, the model requires soil type, soil wetness (Table 2) and the frost or

thaw depth. To calculate the frost depth needed to support a vehicle, the vehicle weight or class is needed.

The code consists of a main program and the following subroutines:

For snow calculations:

vehdata – reads the vehicle data files for snow modeling

snow – reads the snow and terrain data (interactively)

pressure – calculates vehicle contact pressures

density – calculates ρf and the vehicle sinkage

rterrain – calculates the resistance due to the terrain

hard – determines the internal resistance coefficient

traction – calculates the gross traction

totalsnow – calculates the ratio of vehicle to wheel speed, net traction and drawbar coefficients.

For thawing and freezing soil:

soil – reads USCS soil type and soil wetness (interactively)

trmult – calculates traction multipliers for thawing soils

mrmult – calculates resistance multipliers for thawing soils

thaw – writes traction and resistance multipliers to the screen

freeze – models frozen soil bearing capacities for wet or dry soils.

VEHICLE DATA FILES

CRM-1.F reads vehicle data files developed specifically for the Cold Regions Mobility Model to determine the mobility parameters of a specified vehicle operating in snow. No vehicle data file is required for

the freezing–thawing soils subroutines. The program reads two types of data files: wheeled and tracked

vehicle files. The data below are for the HMMWV, a wheeled vehicle.

The second line represents the type of vehicle. Wheeled vehicles are labeled as type 0, and tracked

vehicles are type 1. Line 3 lists the number of axles. The number of wheels per axle is in line 5; as indicated, the HMMWV has two wheels for each axle. The axles are powered if the value for the axle power

is 1; if the value is 0, the axle is not powered. Line 7 is the radius of each wheel. Line 8 is the maximum

19
Table A1. Codes for different soil and

terrain surface types used in CRM-1.

These are the same surface codes

used in CAMMS and NRMM.

1 SW 11 OL

2 SP 12 OH

3 SM 13 WATER

4 SC 14 PAVEMENT

5 SMSC 15 ROCK

6 CL 16 GW

7 ML 17 GP

8 CLML 18 GM

9 CH 19 GC

10 MH 20 PT (peat)

deflected tire width. The contact area, line 10, is the hard surface contact area for a single tire on each

axle. The unloaded section height is determined by the height of the tire without any load placed on it to

cause a deflection. The loaded tire deflection is determined by calculating the deflection of the tire when

a load is placed on it. Note that lines 8, 10 and 11 are functions of the tire inflation pressure.

For the tracked vehicles the data files are set up a little differently. The example below is for the M113.

Line Value Data FORTRAN format code

1 Vehicle name M113 2a4

2 Vehicle type 1 10i2

3 No. of track sets 1 i2

4 Width of the track (in.) 15.00 10f7.2

5 Length of the track (in.) 105.00 10f7.2

6 Gross vehicle weight (lb) 23401.00 f8.2

7 Ground clearance (in.) 16.93 f8.2

8 Entry angle (degrees) 21.00 10f7.2

The third line gives the number of track sets for the vehicle (the SUSV, a two-unit articulated vehicle has

two track sets). The number of tracks per set is set to 2 in the program. The entry angle, although required, is not used; an average value of 26° for all tracked vehicles is specified in CRM-1.

TERRAIN INPUT

Terrain data are input interactively through a series of menus. For a soils analysis the codes in Table

A1 and Table 2 (wetness definitions) are used. Table A2 contains the input data and associated output for

a freezing–thawing soils analysis. Sample input data and the resulting output are shown in Table A3 and

A4 for thawing and freezing soils, respectively. For snow analysis the input data and corresponding

output are in Table A5. Table A6 is a set of results for an analysis of oversnow mobility of the M113 and

HMMWV (using the vehicle parameters stated in describing the vehicle data files), comparing each of

the underlying surfaces and snow types.

Table A2. Input and output of CRM-1 (Soils).

Input Output

Thawing Soils

Soil type (Table A1) Traction multiplier

Wetness (dry, moist, or wet) Resistance multiplier

Wheeled or tracked vehicle

Thaw depth (cm)

Freezing Soils

Wet or dry ground, plus

Frost depth (cm) yields Max. vehicle weight and class supported

Vehicle class yields Min. frost depth required

Vehicle weight (lb) yields Min. frost depth required

Frost depth and vehicle yields Go/no-go

yields

20
Table A3. Traction and motion resistance multipliers for wheeled vehicles on thawing sandy soils.*

Soil Type: SW Wetness: Wet Vehicle: Wheeled

Thaw depth (cm) Traction multiplier Resistance multiplier

1 1.0 1.0

2 1.0 1.0

3 0.88 2.6

4 0.77 5.4

5 0.73 6.96

6 0.68 8.1

8 0.66 9.0

10 0.64 9.5

12 0.636 9.9

15 0.63 10.0

20 0.63 10.0

*The same multipliers are obtained (with warnings) for

clayey soils and tracked vehicles. A multiplier of 1.0 is

specified for rock, water and pavement and for all dry

(with warning) or moist soils.

Table A4. Vehicle weights supported by various frost

depths.

Weight on wet ground Weight on dry ground

Frost depth (cm) (MN) (lb) (MN) (lb)

2 0.0003 77 0.0001 31

5 0.0022 483 0.0008 197

10 0.0086 1933 0.0035 787

15 0.0194 4350 0.0079 1770

20 0.0344 7734 0.0140 3147

30 0.0774 17401 0.0315 7082

40 0.1376 30935 0.0560 12590

50 0.2150 48336 0.0875 19672

Table A5. Sample input and output of CRM-1 (snow).

Example

12 3 45

Input

Modeling option* 1 1 1 3 4

Vehicle† M113 M113 M113 M113 M113

Snow Base Code** 1 1 1 3 4

Snow depth (cm) 15 15 15 15 12

Snow type†† 77 6 67

RCI —*** — — — —

Snow density (g/cm3) 0.2 0.2 — — 0.2

Slope (degrees) 0.0 30.0 0.0 0.0 0.0

Output

Vehicle speed/wheel speed 0.975 0 0.974 0.964 0.941

Rut depth††† (cm) 9.0 9.0 0.0 0.0 7.2

Gross traction (N) 44134.3 39207.1 29692.1 29692.1 16741.3

Total resistance (N) 5585.4 57631.6 3903.5 5464.8 5275.1

Drawbar (N) 38548.9 –18424.5 25788.6 24227.2 11466.2

Drawbar coefficient 0.370 –0.177 0.248 0.233 0.110

Notes

*Modeling option 1 is snow analysis, 2 is freezing/thawing soils.

†Requires a vehicle data file name.

**Snow base codes (the material underlying the snow):

1—superhighways/primary roads.

2—secondary roads.

3—off-road terrain/trails/strong frozen ground.

4—ice (if snow depth is <1.0 cm, then ice only).

5—unfrozen soil (requires RCI). ††Snow type:

6—disturbed (more than four vehicle passes or a prepared snow road).

7—undisturbed snow.

***Input not required with the previous specified input.

†††Total vehicle sinkage.

21
Table A6. Terrain/vehicle data sets from CRM-1.

Vehicle: M113

Gross Total Drawbar

IBASE Vs/Ws Rut depth (cm) traction (N) resistance (N) Drawbar (N) coefficient

Snow Type: Undisturbed

Snow Depth: 15 cm Density: 0.2 Mg/m3 Slope: 0.0°

1 0.975 9.0 44134.3 5585.5 38548.9 0.370

2 0.972 9.0 44134.3 6366.1 37768.2 0.362

3 0.968 9.0 44134.3 7146.8 36987.5 0.355

4 0.937 9.0 16741.3 5585.5 11155.9 0.107

5 (RCI=30) 0.965 14.1 44134.3 7996.6 36137.7 0.347

Snow Depth: 20 cm Density: 0.15 Mg/m3 Slope: 10.0°

1 0.901 14.0 43581.8 23915.4 19666.4 0.188

Snow Depth: 0.0 Density: — Slope: 0.0°

4 0.930 0.0 10409.2 3903.5 6505.8 0.063

Snow Type: Disturbed

Snow Depth: 15 cm Density: — Slope: 0.0°

1 0.974 0.0 29692.1 3903.5 25788.6 0.248.

2 0.969 0.0 29692.1 4684.2 25007.9 0.240

3 0.964 0.0 29692.1 5464.8 24227.2 0.234

4 0.974 0.0 29692.1 3903.5 25788.6 0.248

5 (RCI=20) 0.935 10.5 29692.1 10359.0 19333.0 0.186

Snow Depth: 15 cm Density: — Slope: 15.0°

1 0.0 0.0 28710.2 30844.5 –2134.4 –0.021

Snow type: Undisturbed

Snow depth: 15 cm Density: 0.2 Mg/m3 Slope: 0.0°

1 0.934 9.0 12318.2 4348.9 7969.3 0.238

2 0.929 9.0 12318.2 4683.4 7634.8 0.228

3 0.933 9.0 12318.2 4432.5 7885.7 0.236

4 0.866 9.0 5643.9 4348.9 1295.0 0.039

5 (RCI=30) 0.924 12.6 12318.2 5096.3 7221.9 0.216

Snow Depth: 20 cm Density: 0.15 Mg/m3 Slope: 10.0°

1 0.859 14.0 12163.9 9965.6 2198.4 0.068

Snow Depth: 0.0 Density: — Slope: 0.0°

4 0.971 0.0 3345.0 501.8 2843.3 0.085

Snow Type: Disturbed

Snow Depth: 15 cm Density: — Slope: 0.0°

1 0.989 0.0 9316.0 501.8 8814.3 0.264.

2 0.982 0.0 9316.0 836.3 8479.8 0.254

3 0.986 0.0 9316.0 858.4 8730.7 0.261

4 0.989 0.0 9316.0 501.8 8814.3 0.264

5 (RCI=20) 0.835 7.0 9316.0 9193.4 122.6 0.004

Snow Depth: 15 cm Density: — Slope: 15.0°

1 0.0 0.0 9008.0 9159.4 –151.4 –0.005

22
C CRM-1.f

C 7 MARCH 1994

C THIS PROGRAM CALCULATES THE TRACTION AND MOTION RESISTANCE

C OF WHEELED AND TRACKED VEHICLES OPERATING ON ICE, OR IN DEEP OR

C SHALLOW SNOW OVER VARIOUS BASE MATERIALS AND THAWING SOILS

C PROGRAM BY:

C HEATHER BANKER

C GEORGE BLAISDELL

C PAUL RICHMOND

C SALLY SHOOP

C KAREN FARAN

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

common/m7/ibase,rci,idist,slope

1000 write(*,*)’choose an option:’

write(*,*)’1 = snow modeling (snow or ice covered)’

write(*,*)’2 = soils modeling (frozen or thawing soils)’

read(*,*)input

C INITIALIZE VARIABLES

sumz=0.

zmax=0.

gvw=0.

rsnow=0.0

trsnow=0.

totalr=0.

totaldb=0.

if(input.eq.1)then

call vehdata

call snow(hsnow,sigma0)

call pressure

call density(hsnow,sigma0,sigmaf,zmax)

call rterrain(hsnow,sigma0,sigmaf,zmax,sumz,rsnow)

call hard(reshard)

call traction(hsnow,trsnow)

call totalsnow(rsnow,trsnow,reshard,hsnow,sigma0,sumz)

else

write(*,*)’what type of soil problem is this’

write(*,*)’1 = thawing soil’

write(*,*)’2 = frozen soil’

read(*,*)iput

if(iput.eq.1)then

call soil(isoil,iwet)

call trmult(isoil,iwet,trmlt,zthaw,ivehs)

call mrtmult(zthaw,svalid,isoil,iwet,rmult,ivehs)

23
call thaw(trmlt,rmult,zsnow)

else

call freeze(isoil)

end if

end if

write (*,*)’enter y to run another condition’

read(*,300)ans

300 format (a1)

if ((ans.eq.”Y”) .or. (ans.eq.”y”)) then

goto 1000

end if

c call exit(0)

end

C ########################################################################

subroutine vehdata

C THIS SUBROUTINE READS DATA FROM THE VEHICLE DATA FILE

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

character*12 mfile

write(*,*)’enter the vehicle data file name’

read(*,10) mfile

open(21,status=’old’,file=mfile,form=’formatted’)

C READ IN VEHICLE DATA

read(21,100)title

read(21,110)iveh !WHEELED=0, TRACKED=1

if(iveh.eq.0) then

C READ WHEEL VEHICLE DATA - ENGLISH UNITS

read(21,115)nunits !NO. AXLES,

read(21,220)gclear !GROUND CLEARANCE

read(21,110)(nwhls(i),i=1,nunits) !NUMBER OF WHEELS PER AXLE

read(21,110)(ip(i),i=1,nunits) !AXLE, O=NO POWER ,1=POWERED

read(21,120)(rads(i),i=1,nunits) !RADIUS OF EACH WHEEL, IN.

read(21,120)(width(i),i=1,nunits) !WIDTH OF EACH WHEEL, IN.

read(21,120)(pload(i),i=1,nunits) !LOAD ON EACH WHEEL, LBS.

read(21,120)(area(i),i=1,nunits) !TIRE CONTACT AREA, SQ. IN.

read(21,*)sec,def !UNLOADED SECTION HEIGHT, LOADED

TIRE DEFLECTION

24
C CALCULATE GVW FOR WHEELED VEHICLES

do i=1,nunits

gvw=gvw+(pload(i)*nwhls(i))

end do

write(*,115)nunits

write(*,220)gclear

write(*,110)(nwhls(i),i=1,nunits)

write(*,110)(ip(i),i=1,nunits)

write(*,120)(rads(i),i=1,nunits)

write(*,120)(width(i),i=1,nunits)

write(*,120)(pload(i),i=1,nunits)

write(*,120)(area(i),i=1,nunits)

write(*,*)sec,def

write (*,*)gvw

else

C READ TRACK VEHICLE DATA - ENGLISH UNITS

read(21,215)nunits

read(21,120)(width(i),i=1,nunits) !TRACK WIDTH

read(21,120)(tlength(i),i=1,nunits) !TRACK LENGTH

read(21,220)gvw !GROSS VEHICLE WEIGHT

read(21,220)gclear !GROUND CLEARANCE

read(21,120)(aa(i),i=1,nunits) !ENTRY ANGLE

write(*,215)nunits

write(*,120)(width(i),i=1,nunits)

write(*,120)(tlength(i),i=1,nunits)

write(*,220)gvw

write(*,220)gclear

write(*,120)(aa(i),i=1,nunits)

end if

10 format(a12)

100 format(2a4)

110 format(10i2)

115 format(i2)

120 format(10f7.2)

130 format(f6.2,f6.3)

215 format(i2)

220 format(f10.2)

close(21)

return

end

C *******************************************************************

subroutine snow(hsnow,sigma0)

C THIS SUBROUTINE READS IN SNOW AND TERRAIN DATA

25
common/m7/ibase,rci,idist,slope

C ENTER TERRAIN DATA

write(*,*)’enter snow base code:’

write(*,*)’1 = super highways/primary roads’

write(*,*)’2 = secondary roads’

write(*,*)’3 = off-road terrain/trails/strong frozen soil’

write(*,*)’4 = ice (if snow depth is < 1.0cm then ice only)’

write(*,*)’5 = unfrozen soil’

read(*,*) ibase

write(*,*)’input the snow depth (cm)’

read(*,*)hsnow

if ((ibase.ne.4).or.(hsnow .ge. 1.0)) then

write(*,*)’enter the type of snow’

write(*,*)’6 = disturbed snow (more than 4 vehicle passes)’

write(*,*)’7 = undisturbed snow’

read(*,*)idist

end if

if (ibase.eq.5) then

write(*,*)’input rating cone index of the soil’

write(*,*)’20 < RCI < 100'

read(*,*) rci

end if

if (idist.eq.6) then

if (sigma0.le.0.55) then

sigma0 = 0.55

end if

else

if ((ibase.ne. 4).or.(hsnow .ge. 1.0)) then

write(*,*)’input the snow density (g/cm**3)’

read(*,*)sigma0

end if

end if

write(*,*)’enter the angle of the slope (degrees)’

read(*,*)slope

return

end

C **************************************************************************

subroutine pressure

C THIS SUBROUTINE CALCULATES THE CONTACT PRESSURE

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

26
common/m5/iveh,nunits,pmax,gclear,gvw

if (iveh.eq.1) then

C CALCULATE VALUES FOR TRACKED VEHICLES

do i=1,nunits

nwhls(i)=2 !ALL TRACKED VEHICLES HAVE 2 TRACKS PER AXLE

ip(i)=1 !ALL TRACKS ARE DRIVEN

area(i)=width(i)*tlength(i)

pload(i)=gvw/nunits/nwhls(i)

pres1(i)=pload(i)/area(i)

c write(*,*)’pressure’,pres1(i)

end do

else

C CALCULATE GROUND CONTACT PRESSURES FOR WHEELED VEHICLES

do i=1,nunits

pres1(i)=pload(i)/area(i)

c write(*,*)’pressure1',pres1(i)

end do

end if

C CALCULATE THE MAXIMUM PRESSURE

pmax=pres1(1)

do i=1,nunits

if (pres1(i).gt.pmax) pmax=pres1(i)

end do

return

end

C **********************************************************************

subroutine density(hsnow,sigma0,sigmaf,zmax)

C THIS SUBROUTINE CALCULATES THE FINAL DENSITY AND SINKAGE

common/m5/iveh,nunits,pmax,gclear,gvw

C COMPUTE FINAL DENSITY DATA

sigmaf=.5

if(pmax.gt.30.5) sigmaf=.55

if(pmax.gt.50.8) sigmaf=.60

if(pmax.gt.101.5) sigmaf=.65

C COMPUTE SINKAGE

zmax= hsnow * (1. - (sigma0/sigmaf))

if(zmax.lt.0.)zmax=0.

return

end

C *******************************************************************

subroutine rterrain(hsnow,sigma0,sigmaf,zmax,sumz,rsnow)

27
C THIS SUBROUTINE CALCULATES TERRAIN RESISTANCE OF THE VEHCILE

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

common/m7/ibase,rci,idist,slope

dimension xl2(10),rres1(10)

C START LOOP FOR RESISTANCE

flag = 1.0

rsnow = 0.0

soilz = 0.0

do i=1,10

xl2(i)=0.0

rres1(i)=0.0

end do

i=1 !ALL RESISTANCE CALCULATIONS ARE BASED ON FIRST !

UNIT CHARACTERISTICS AND PMAX

C WHEELED VEHICLES

if (iveh.eq.0) then

C ACCT FOR WEAK SOIL BASE

if(ibase.eq.5) then

pn = 1. !IS THE NUMBER OF PASSES THE VEHICLE MAKES

s = 0.05 !SLIP ASSUMMED CONSTANT FOR THIS CALC

C def IS THE LOADED TIRE DEFLECTION

C sec IS THE UNLOADED TIRE SECTION HEIGHT

soilz=(10.*rads(i)*pn**.5)/((rci*2.*rads(i)*width(i))/

&(pload(i)*(1.-def/sec)**(3./2.)*s**0.2))**(5./3.)

if (soilz.lt.0.0) soilz=0.0

soilz = soilz*2.54

end if

sumz=zmax+soilz !sumz IS IN cm

C RESISTANCE PARAMETER, WHEELED VEHICLES IN SNOW

xl2(i)=rads(i)*acos((rads(i)-(sumz/2.54))/rads(i)) !INCHES

xl2(i)=xl2(i)*2.54 !cm

c write(*,*)’xl2',xl2,’rads’,rads(i)

C ACCOUNT FOR TIRE CURVATURE/DEEP SNOW FLAG

radscm = rads(i)*2.54

28
if((sigma0.lt.0.15).and.(sumz.ge.radscm))flag = 1.5

if((sigma0.ge.0.15).and.(sumz.ge.(radscm*2./3.)))flag = 1.5

if((sigma0.ge.0.15).and.(sumz.ge.(radscm)))flag = 2.5

C GROUND CLEARANCE FLAG

if (sumz.ge. (gclear*2.54)) flag = flag+1.5

else

C TRACKED VEHICLE RESISTANCE

C ACCOUNT FOR WEAK SOIL BASE

if(ibase.eq.5) then

pn = 1. !IS THE NUMBER OF PASSES THE VEHICLE MAKES

soilz=tlength(i)*pn**.5*0.00443*

&exp((5.889*pload(i))/(rci*width(i)*tlength(i)))

soilz = soilz*2.54

end if

sumz=zmax+soilz !cm

C RESISTANCE PARAMETER, TRACKED VEHICLES IN SNOW

aa(i)=26.0 !AN AVERAGE VALUE FOR NRMM

xl2(i)=(sumz/sin(aa(i)*3.14159265/180.)) !cm

C GROUND CLEARANCE, LOW (FLAG=2.0) OR HIGH (FLAG=4.0) DENSITY SNOW

if((sigma0.lt.0.15).and.(sumz.ge.(gclear*2.54))) flag = 2.5

if((sigma0.ge.0.15).and.(sumz.ge.(gclear*2.54))) flag = 4.0

end if

if (flag.gt.1.0) then

C DEEP SNOW WARNING

write(*,*)’*************************************************’

write(*,*)

write(*,*)’A DEEP SNOW FLAG HAS BEEN SET,’

write(*,*)’CALCULATIONS ARE NOT VALIDATED.’

write(*,*)’FLAG = ‘, flag

write(*,*)

write(*,*)’*************************************************’

end if

c print *, rads(i)

print *, xl2(i),sumz

xl=xl2(i)

w=width(i)*2.54 !CONVERT TO cm

rres1(i)=(68.1*(0.10*sigma0*xl*w)**0.914)*flag !KG/M IN PARATHESISES

c write(*,*)’flag’,flag,’rres1',rres1,’sigma0',sigma0

c write(*,*)(0.10*sigma0*xl*w),xl,w,sigma0

29
rres1(i)=rres1(i)/4.4482 !CONVERT TO lbs

C ADD SLOPE TO RESISTANCE AND SUM RESISTANCE FOR WHOLE VEHICLE

C UP TO 4 UNITS ONLY FOR WHEELED VEHICLE SNOW RESISTANCE,

C 1 UNIT LIMIT FOR TRACKS

sloper=slope*3.14159265/180. !SLOPE IN RADIANS

if(iveh.eq.0)then

do j=1,nunits

rres1(j)=rres1(1)

if (j.gt.4) then

rres1(j)=0.0

end if

rsnow= rsnow+((rres1(j)+pload(j)*sin(sloper))*nwhls(j))

end do

else

rsnow=rres1(1)*nwhls(1)+gvw*sin(sloper)

end if

return

end

C ****************************************************************

subroutine hard(reshard)

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

common/m7/ibase,rci,idist,slope

dimension cpffg(10)

C CPFFG = F-G CONTACT PRESSURE FACTOR FOR EACH ELEMENT

C W = WEIGHT BENEATH SUSPENSION ASSEMBLY (TRACK PAIR OR AXLE) IN LBS

C RHARD = HARD SURFACE RESISTANCE COEFFICIENT

reshard = 0.0

C WHEELED VEHICLES

if(iveh.eq.0)then

do i = 1,nunits

w = pload(i)*nwhls(i)

cpffg(i) = w/(nwhls(i)*width(i)*rads(i))

if((ibase.eq.3).or.(ibase.eq.5))then

if(cpffg(i).ge.4.0)then

30
rhard = 0.0175

else

rhard = 0.015

end if

else if((ibase.eq.1).or.(ibase.eq.4))then

rhard = 0.015

else

rhard = 0.025

end if

reshard = reshard +rhard*w

end do

C TRACKED VEHICLES

else

if((ibase.eq.3).or.(ibase.eq.5))then

rhard = 0.0525

else if((ibase.eq.1).or.(ibase.eq.4))then

rhard = 0.0375

else

rhard = 0.045

end if

reshard = rhard*gvw !TOTAL HARD SURFACE RESISTANCE FOR TRACK

end if

return

end

C *************************************************************************

subroutine traction(hsnow,trsnow)

C THIS ROUTINE CALCULATES THE TRACTION OF THE VEHICLE

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

common/m7/ibase,rci,idist,slope

dimension trcn1(10)

C TRACTION CALCULATION

trsnow = 0.0

do i = 1,nunits

pr=pres1(i)*6.8948 ! KPA

pr=pr*cos(slope*3.14159265/180.) ! ACCOUNT FOR SLOPE

C UNDISTURBED SNOW

if(((ibase.eq.1).or.(ibase.eq.2).or.(ibase.eq.3).or.(ibase.eq.5))

&.and.(idist.eq.7))then

trcn1(i)=0.851*((pr)**0.823)

c write(*,*)’area’,area(i),’load’,pload(i)

c write(*,*)’pressure’,pres1(i)

31
c write(*,*)’pressure in kPa’,pr

c write (*,*)trcn1(i)

end if

C HARD PACKED SNOW

if (idist.eq.6) then

if((ibase.eq.1).or.(ibase.eq.2).or.(ibase.eq.3))then

trcn1(i)=0.321*(pr)**0.97

end if

if(ibase.eq.5)then

trcn1(i)=0.321*(pr)**0.97

end if

end if

C SNOW ON ICE BASE

if((ibase.eq.4).and.(idist.eq.7))then

trcn1(i)=0.127*(pr)**1.06

else if((ibase.eq.4).and.(idist.eq.6))then

trcn1(i)=0.321*(pr)**0.97

end if

C ICE SURFACE

if ((ibase.eq.4).and.(hsnow.le.1.0))then

trcn1(i)=0.1*pr

end if

trcn1(i)=(trcn1(i)/6.8948)*area(i) !CONVERT TO lbs

C NON-DRIVEN WHEEL

if(ip(i).eq.0) trcn1(i)=0.0

C SUM TRACTION FOR EACH ELEMENT

trsnow = trsnow + trcn1(i)*nwhls(i)

end do

return

end

C ******************************************************************

subroutine totalsnow(rsnow,trsnow,reshard,hsnow,sigma0,sumz)

common/m1/nwhls(10),rads(10),width(10),pload(10),area(10),aa(10)

common/m2/ip(10),pres1(10),tlength(10)

common/m3/xl2(10),cpffg(10)

common/m5/iveh,nunits,pmax,gclear,gvw

common/m6/def,sec

common/m7/ibase,rci,idist,slope

C TOTAL VEHICLE TRACTION AND RESISTANCE

totalr = reshard + rsnow

totaldb = trsnow - totalr

32
C SLIP DUE TO TRACTION

if (totalr.le.trsnow) then

slipt = .2*totalr / trsnow

slipw = 1./(slipt + 1.) !RATIO OF VEHICLE SPEED TO WHEEL SPEED

else

slipw=0.0

end if

C WRITE TOTAL VEHICLE TRACTION AND RESISTANCE

write(*,210)hsnow,sigma0,slope

write(*,*)’ratio of vehicle speed to wheel speed: ‘,slipw

write(*,*)’ units are lbs:’

write(*,260)sumz,trsnow,totalr,totaldb

write(*,*)’ units are N:’

write(*,260)sumz,trsnow*4.4482,totalr*4.4482,totaldb*4.4482

write (*,*)’drawbar coefficient = ;(totaldb/gvw)

200 format(1x,a12)

210 format(/1x,”snow depth, cm.= “,f5.2,2x,”density, g/cc= “,f5.4,

& “ slope= “,f6.2)

260 format(1x,”rut,cm.= “,f4.1,2x,”tr =”,f8.1,2x,”rr= “,f8.1,

& 2x,”db= “,f8.1)

return

end

C ***************************************************************

subroutine thaw(trmlt,rmult,zsnow)

C if(layer.eq.1.and.zsnow.lt.1.0/xcm2in)then

do i = 1, nunits

c trmltn = (dowpb(i) + rtowpb(i))*trmlt

c rtowpb(i) = rtowpb(i)*rmult

c rtowt(i) = rtowt(i)*rmult

c dowpb(i) = trmltn - rtowpb(i)

end do

C else

C write(*,*)’routine thaw is not implemented for:’

C if(layer.ne.1.)then

C write(*,*)’critical depth > 6 in.’

C else

C write(*,*)’snow cover > 1 cm’

C end if

C end if

write(*,*)’traction multiplier’,trmlt

write(*,*)’motion resistance multiplier’,rmult

C

return

end

C********************************************************************

subroutine trmult(isoil,iwet,trmlt,zthaw,ivehs)

c this subroutine calculates the traction multiplier

33
write(*,*)’are you using wheeled (0) or a tracked vehicle (1)’

read(*,*)ivehs

write(*,*)’input the thaw depth (cm)’

read(*,*)zthaw

trmlt = 1.

if((iwet.eq.3).and.((isoil.lt.13).or.(isoil.gt.15)))then

if(zthaw.le.2.5)then

trmlt = trmlt

else if((zthaw.gt.2.5).and.(zthaw.lt.15.))then

trmlt = trmlt*(2.379*(1/zthaw**2.)+0.619)

else if(zthaw.ge.15.)then

trmlt = 0.63*trmlt

end if

else if(iwet.eq.2) then

trmlt = 1.

else if(iwet.eq.1)then

write(*,*)’*********************************************************’

write(*,*)’for dry soils, the effect of thawing on traction is a’

write(*,*)’function of applied stress; these functions have not

write(*,*)yet been developed so a multiplier of 1.0 is used’

write(*,*)’*********************************************************’

end if

if((isoil.ge.13).and.(isoil.le.15))then

trmlt = 1.

write(*,*)’********************************************************’

write(*,*)’A multiplier of 1.0 is used for water, rock, or pavement’

write(*,*)’********************************************************’

end if

if(((isoil.ge.6).and.(isoil.le.12)).or.(isoil.eq.20))then

write(*,*)’*******************************************************’

write(*,*)’calculations are based on sandy soils’

write(*,*)’*******************************************************’

end if

if(ivehs.eq.1)then

write(*,*)’*******************************************’

write(*,*)’calculations are based on wheeled vehicles ‘

write(*,*)’*******************************************’

end if

return

end

C ************************************************************************

subroutine mrtmult(zthaw,svalid,isoil,iwet,rmult,ivehs)

c this subroutine calculates the motion resistance multipler

rmult = 1.

c if(iwet.eq.3)then

if((iwet.eq.3).and.((isoil.lt.13).or.(isoil.gt.15)))then

if(zthaw.le.2.5)then

rmult = 1.

else if((zthaw.gt.2.5).and.(zthaw.lt.4.))then

34
rmult = rmult*(2.883*zthaw - 6.056)

else if((zthaw.ge.4.).and.(zthaw.le.8.))then

rmult = rmult*(-0.22*zthaw**2. + 3.54*zthaw - 5.24)

else if((zthaw.gt.8.).and.(zthaw.lt.12.))then

rmult = rmult*(0.225*zthaw + 7.2167)

else if(zthaw.ge.12)then

rmult = rmult*10.0

end if

end if

return

end

C ****************************************************************************

subroutine soil(isoil,iwet)

c this subroutine asks the USCS soil type and wetness

write(*,*)’choose an USCS soil type code:’

write(*,*)’ 1 = SW’

write(*,*)’ 2 = SP’

write(*,*)’ 3 = SM’

write(*,*)’ 4 = SC’

write(*,*)’ 5 = SMSC’

write(*,*)’ 6 = CL’

write(*,*)’ 7 = ML’

write(*,*)’ 8 = CLML’

write(*,*)’ 9 = CH’

write(*,*)’10 = MH’

write(*,*)’11 = OL’

write(*,*)’12 = OH’

write(*,*)’13 = WATER’

write(*,*)’14 = PAVEMENT’

write(*,*)’15 = ROCK’

write(*,*)’16 = GW’

write(*,*)’17 = GP’

write(*,*)’18 = GM’

write(*,*)’19 = GC’

write(*,*)’20 = PT’

read(*,*)isoil

write(*,*)’input the soil wetness’

write(*,*)’ 1 = dry’

write(*,*)’ 2 = moist’

write(*,*)’ 3 = wet (water content is above liquid limit)’

read(*,*)iwet

return

end

C **************************************************************************

subroutine freeze

write(*,*)’FROZEN GROUND MENU’

write(*,*)’1 = input the frost depth’

write(*,*)’2 = input the vehicle class’

35
write(*,*)’3 = input the vehicle weight (lb.)’

write(*,*)’4 = input frost depth and vehicle class or weight’

read(*,*)nput

write(*,*)’choose a soil condition’

write(*,*)’1 = wet’

write(*,*)’2 = dry’

read(*,*)cond

if(nput.eq.1)then

write(*,*)’input the frost depth (cm)’

read(*,*)fdepth

fdepth = fdepth/100. !CONVERT TO METERS

C CALCULATE THE MAXIMUM LOAD THAT A SPECIFIED FROST DEPTH WILL HOLD

if(cond.eq.1)then

p = 0.86*fdepth**2.

else if(cond.eq.2)then

p = 0.35*fdepth**2.

end if

write(*,*)’maximum load that can travel on’,fdepth,’m =’,p,’MN’

c convert dimensions of p from MN to pounds

p=p/(4.448222e-6)

write(*,*)’maximum load that can travel on’,fdepth,’m =’,p,’pounds’

else if(nput.eq.2)then

write(*,*)’input the vehicle class’

read(*,*)vclass

C CALCULATE THE MINIMUM FROST DEPTH THAT WILL HOLD A SPECIFIED VEHICLE

if(cond.eq.1)then

fdepth = 10*(vclass)**.5

else if(cond.eq.2)then

fdepth = 16*(vclass)**.5

end if

fdepth = fdepth/100 !convert from cm to m

write(*,*)’minimum frost depth that can hold class’,vclass,’=’,

& fdepth,’m’

else if(nput.eq.3)then

c write(*,*)’input the vehicle weight (MN)’

 write(*,*)’input the vehicle weight (pounds)’

 read(*,*)vwght

 vwght=vwght*4.448222e-6 !convert to MN

C CALCULATE THE MINIMUM FROST DEPTH THAT WILL HOLD A SPECIFIED LOAD

if(cond.eq.1)then

c fdepth = (0.86/p)**.5

fdepth = (vwght/0.86)**.5

else if(cond.eq.2)then

c fdepth = (0.35/p)**.5

fdepth = (vwght/0.35)**.5

end if

write(*,*)’minimum frost depth that can hold’,vwght,’MN =’,fdepth,’m’

36
vwght=vwght/4.448222e-6 !convert to pounds

write(*,*)’minimum frost depth that can hold’,vwght,’pounds =’,

& fdepth,’m’

C CALCULATE THE GO/NO GO SITUATION OF BOTH VALUES INPUTTED

C EITHER THE WEIGHT OR THE CLASS WILL BE READ

else if(nput.eq.4)then

write(*,*)’input the frost depth (cm)’

read(*,*)fdepth

fdepth = fdepth/100. !CONVERT TO METERS

write(*,*)’are you using vehicle weight (1) or class (2)’

read(*,*)ans

if(ans.eq.1)then

c write(*,*)’input the vehicle weight (MN)’

write(*,*)’input the vehicle weight in pounds’

read(*,*)vwght

vwght=vwght*4.448222e-6

if(cond.eq.1)then

if(vwght.le.0.86*fdepth**2.)then

write(*,*)’****************************************’

write(*,*)’the ground can support this vehicle!’

write(*,*)’****************************************’

else

write(*,*)’****************************************’

write(*,*)’the ground can not support this vehicle!’

write(*,*)’****************************************’

end if

else if(cond.eq.2)then

if(vwght.le.0.35*fdepth**2.)then

write(*,*)’****************************************’

write(*,*)’the ground can support this vehicle!’

write(*,*)’****************************************’

else

write(*,*)’****************************************’

write(*,*)’the ground can not support this vehicle!’

write(*,*)’****************************************’

end if

end if

else if(ans.eq.2)then

write(*,*)’input the vehicle class (tons)’

read(*,*)vclass

if(cond.eq.1)then

if(fdepth.ge.10.*(vclass)**.5)then

write(*,*)’****************************************’

write(*,*)’the ground can support this vehicle!’

write(*,*)’****************************************’

else

write(*,*)’****************************************’

write(*,*)’the ground can not support this vehicle!’

write(*,*)’****************************************’

end if

else if(cond.eq.2)then

if(fdepth.ge.16.*(vclass)**.5)then

37
write(*,*)’****************************************’

write(*,*)’the ground can support this vehicle!’

write(*,*)’****************************************’

else

write(*,*)’****************************************’

write(*,*)’the ground can not support this vehicle!’

write(*,*)’****************************************’

end if

end if

end if

end if

if(fdepth.ge.0.5)then

write(*,*)’**************************************************’

write(*,*)’0.5m frost will prevent breakthrough of most heavy’

write(*,*)’equipement but mobility may be limited by crushing’

write(*,*)’failure of the surface material.’

write(*,*)’**************************************************’

end if

return

end

38
APPENDIX B. FORTRAN CODE USING NRMM/CAMMS VARIABLES AND FORMAT

Scenario variable


ISMODL

Yes

No

Yes

Yes

Yes

Yes

No

Yes

No

No

Go to snow subroutines

Normal soil conditions

Normal soil conditions

Normal soil conditions

Snow or


 ice present?

Is any of


the soil frozen?


 DTHAW <

 DFREEZE

Is RCInormal

< VCI?

Complete ZTEST

Is


frozen thickness


< ZTEST?

Use slippery


soils algorithms Is soil clayey?

Is DTHAW = 0? Set RCI = RCI300

P. RIC

P

Figure B2. Logic in the cold regions

module of NRMM II ver. 2.5.0.



















Surface: 

ZTHAW (DTHAW)


SMOIST (TMOIST)

KUSCS


CI/RCI


WETNESS INDEX

Road Type: 

Soil or


Pavement

Variables
 ––––––––––––––––

Freeze Depth: 

SCENARIO (TERRAIN)

Soil Data: 

IROAD

ZFREEZ (DFREEZ)

Freeze Depth: 

ISCOND

ZSNOW (DSNOW)


GAMMA (SIGMA)

Surface Cover Depth: 

Figure B1. Cold regions variable

description for NRMM II ver. 2.5.0.

39
C CRLSNOW COLD REGIONS MODEL 28 March 94

C***************************

C *

C C R L S N O W *

C *

C****************

 LOGICAL FUNCTION CRLSNOW()

C

C 18 Jun 92 Implemented in CAMMS/NRMM by R.B.Ahlvin

C 15 Mar 94 Paul Richmond

C 28 Mar 94 Karen Faran

C

C Inputs:

C Common /DERIVE/

C JPSI Current deflection scenario index

C Common /PREP/

C GCA(NAMBLY,NJPSI) Ground contact area for each traction element

C Common /TERRAN/

P. RICHMOND


PR 54

Dry Average Wet

Clayey?

Is there soil


moisture input for


thawed layer?

Dry, average,


or wet

Use normal soil conditions Use normal soil conditions Normal soil conditions

Normal soil conditions

Set:


Fmax, WI = 3 < M.C. < Fmax, WI = 5 = Wet


Fmax, WI = 2 ≤ M.C. ≤ Fmax, WI = 3 = Average


Fmax, WI = 2 ≤ M.C. < Fmax, WI = 2 = Dry

Set:


WI0, 1 = Dry


WI2, 3 = Average


WI4, 5 = Wet

Set:


TR = TRRCI 300 × TRMULT


MR = MRRCI 300 × MRMULT


Is DTHAW < 15 cm? Is sinkage < DTHAW?

Set RCI for


sinkage = DTHAW

No

No

Yes

Yes

No Yes

Figure B2 (cont’d). Logic in the cold regions module of NRMM II ver. 2.5.0.

40
C DSNOW Depth of snow cover (0=no snow) [in]

C DTHAW Depth of thawing [in]

C ITSURF Hard surface condition: [1]=dry, 2=wet, 3=ice-covered

C SIGMA Density of snow [gm/cm^3)

C Common /VEHICL/

C CL Minimum ground clearance [in]

C DIAW(NAMBLY) Undeflected tire diameter, each assembly [in]

C NAMBLY #traction element assemblies (axles and tracks)

C NVEH(NAMBLY) Vehicle traction assembly type: 0=tracked, 1=wheeled

C NWHL(NAMBLY) #tires on each wheeled assembly

C SECTW(NAMBLY) Tire nominal section width [in]

C TRAKLN(NAMBLY) Length of track on ground [in]

C TRAKWD(NAMBLY) Track width (one side) for each tracked assembly [in]

C WGHT(NAMBLY) Weight on each vehicle assembly [lbs]

C WT(NAMBLY) Tread widths, each assembly (center to center) [in]

C WTE(NAMBLY) Min. width between traction elements [in]

C

C Outputs:

C Common /DERIVE/

C DOWPB(NAMBLY) Drawbar coefficient for each assembly

C RTOWPB(NAMBLY) Motion res. coef., powered or braked, each element

C RTOWT(NAMBLY)Motion res. coef., towed, each element

C Common /TPREP/

C IBASE CRREL model base code:

C 0 = unassigned

C 1 = super-highway, primary road

C 2 = secondary road

C 3 = off-road & trail

C 4 = Ice

C 5 = soft soil

C

C External:

C RHARD Function to return hard surface resistance for snow

C

C Internal:

C AATrack approach angle (rad)

C AREA1 Contact area single traction element (in^2)

C DEFSEC 1 minus-the deflected radius divided by the section width (in)

C FACT Conversion factor for N/cm^2 to psi

C FLAG Deep snow multiplier

C I Traction assembly index

C IBASE Terrain type flag as follows:

C 1 = road

C 2 = frozen or strong soil

C 3 = unfrozen soil (RCI<100)

C 4 = ice

C PMAX Maximum suspension element contact pressure (psi)

C PN Number of vehicle passes

C PR1KPA Contact pressure of single traction element Kilo-Pascals

C PRES1 Contact pressure of single traction element (psi)

C RADSI Radius of current wheeled traction element (in)

C RRES1 Motion resistance from snow (lb)

C RTOW Temporary resistance coefficient

41
C SIGMA0 Input snow specific gravity

C SIGMAF Final snow specific gravity

C SLIP Vehicle wheel slip

C SOILZ Sinkage in soil of current traction element (in)

C SUMZ Total vehicle sinkage

C TFOW Temporary traction coefficient

C TRCN1 Maximum traction for i-th tire (lb)

C XL2 Snow contact length for i-th suspension element (in)

C XNWORT Number of wheels or tracks on suspension assembly

C XWID1 Width of one traction element (in)

C WGHT1 Weight on single traction element (wheel or track) (lb)

C X2KPA Conversion factor from psi to KPA

C ZMAX Maximum sinkage in snow (in)

C

 IMPLICIT NONE

 INCLUDE ‘nrmmdefs.inc’

 INCLUDE ‘nrmmdrvc.inc’

 INCLUDE ‘nrmmcntc.inc’

 INCLUDE ‘nrmmvehc.inc’

 INCLUDE ‘nrmmvppc.inc’

 INCLUDE ‘nrmmscnc.inc’

 INCLUDE ‘nrmmterc.inc’

 INCLUDE ‘nrmmtppc.inc’

C

 INTEGER I

 REAL ACOS

 REAL AA, AREA1, DEFSEC, FLAG

 REAL PMAX, PN, PRES1, RADSI, RRES1, RTOW

 REAL SIGMA0, SIGMAF, SLIP, SOILZ, SUMZ

 REAL TFOW, TRCN1, WGHT1, X2KPA, XL2

 REAL XNWORT, XWID1, ZMAX

C

 REAL RHARD

 EXTERNAL RHARD

C

C Conversion factor for psi to KPA

 PARAMETER ( X2KPA = XM2IN * XM2IN / 1000.0 / XN2LB )

C

C Diagnostic printout of input data:

 IF( KIV(3) .GT. YES )THEN

CALL DIAGIN(‘!0***Routine CRLSNOW(IV3) ‘// ‘CRREL snow model’)

CALL DIAG( ‘CL DIAW DSNOW DTHAW GCA’ )

CALL DIAG( ‘ITSURF ITUT NAMBLY NVEH NWHL’ )

CALL DIAG( ‘SECTW SIGMA TRAKLN TRAKWD WGHT’ )

CALL DIAG( ‘WT WTE’ )

 END IF

C

 CRLSNOW = .TRUE.

C

C ... Set Snow model flag, IBASE

 IF( ITSURF.EQ.3 )THEN

C Ice

 IBASE = 4

 ELSE IF( ITUT.GE.11.AND.ITUT.LE.13 )THEN

42
C Hard surface

 IBASE = 1

C ELSE IF( DTHAW .LE. 0.0 )THEN

 ELSE IF( DFREEZ .GT. 0.0 .AND. DTHAW .LE. 0.0 )THEN

C Frozen soil surface

 IBASE = 2

 ELSE

C Unfrozen soil

 IBASE = 3

 END IF

C

 SIGMA0 = SIGMA

C

C ... Find maximum contact pressure

 PMAX = 0.0

 DO 10 I=1, NAMBLY

 IF( NVEH(I) .EQ. WHEEL )THEN

 AREA1 = GCA(I,JPSI)

 XNWORT = NWHL(I)

 ELSE

 AREA1 = GCA(I,JPSI) / 2.0

 XNWORT = 2.0

 END IF

C Weight on single traction element

WGHT1 = WGHT(I) / XNWORT

C Maximum contact pressure of all traction elements

PMAX = AMAX1( PMAX, WGHT1/AREA1 )

C

 10 CONTINUE

C

C ... Compute final density sigmaf

 IF( PMAX .GT. 101.5 ) THEN

 SIGMAF = 0.65

 ELSE IF( PMAX .GT. 50.8 ) THEN

 SIGMAF = 0.60

 ELSE IF( PMAX .GT. 30.5 ) THEN

 SIGMAF = 0.55

 ELSE

 SIGMAF = 0.5

 END IF

C

 FLAG = 1.0

 SUMZ = 0.0

C

C Initial density and final density information

 ZMAX = AMAX1( 0.0, DSNOW * (1. - (SIGMA0/SIGMAF)) )

 IF(KIV(3).GT.YES)WRITE(LUN1,601)PMAX,SIGMA0,SIGMAF,ZMAX

 601 FORMAT(‘ Max elmnt cntct pres PMAX =’,F8.4/

 & ‘ Inp snow density SIGMA0 =’,F8.4/

 & ‘ Final snow density SIGMAF =’,F8.4/

 & ‘ Max avail sinkage ZMAX =’,F8.4)

C

 DO 20 I = 1, NAMBLY

43
C

C Compute terrain rolling resistance

C (based on first assembly characteristics)

C

 IF( NVEH(1) .EQ. WHEEL )THEN

 RADSI = DIAW(1)/2.0

 XWID1 = SECTW(1)

 DEFSEC = (1.0-(DFLCT(1,NJPSI)/SECTW(1)))

 ELSE

 XWID1 = TRAKWD(1)

 END IF

C Weight on a single traction element

 WGHT1 = WGHT(1) / XNWORT

 PRES1 = WGHT1/AREA1

C

C Account for weak soil base

C number of passes and slip assumed constant for following eqns.

C Number of vehicle passes made

PN = 1.0

C Wheel slip

SLIP = 0.05

C

 IF( NVEH(I) .EQ. WHEEL ) THEN

C

 IF (IBASE .EQ. 3) THEN

C Unfrozen soil

 SOILZ = (10.* RADSI*pn**0.5)/((CIRCI*XWID1*RADSI*2.0)/

 & (WGHT1 * DEFSEC**(3./2.) *

 & SLIP**(1./5.)))**(5.0/3.0)

C

 IF (SOILZ .LT. 0.0) SOILZ = 0.0

 ELSE

 SOILZ = 0.0

 END IF

C

 SUMZ = ZMAX + SOILZ

 XL2 = RADSI * ACOS((RADSI-SUMZ)/RADSI)

C

C Account for tire curvature/deep snow flag

 IF( (SIGMA0.LT.0.15) .AND. (SUMZ.GE.RADSI) ) FLAG=1.5

 IF( SIGMA0 .GE. 0.15 ) THEN

 IF( SUMZ .GE. (RADSI*2.0/3.0) ) FLAG = 1.5

 IF( SUMZ .GE. RADSI ) FLAG = 2.5

 END IF

C Belly Drag

 IF( SUMZ .GE. CL) FLAG = FLAG + 1.5

 ELSE

C

C Tracked

C

 IF (IBASE .EQ. 3) THEN

 SOILZ = TRAKLN(1) * pn**0.5 * 0.00443 *

 & EXP((5.889 * WGHT1) / (CIRCI * XWID1 * TRAKLN(1)))

 ELSE

44
 SOILZ = 0.0

 END IF

C

 SUMZ = ZMAX + SOILZ

 IF(KIV(3).GT.YES)WRITE(LUN1,602)SOILZ

 602 FORMAT(‘ Sinkage in soil SOILZ =’,F8.4)

C

C Since NRMM does not have the approach angle of a track available

C in the input data, is assumed to be about 26 deg. for

C all tracked vehicles.

 AA = 26.0 * DEGRAD

 XL2 = ( SUMZ) / SIN( AA )

C

C Belly drag , low (flag=2.0) or high (flag=4.0) density

C

 IF( SUMZ .GE. CL ) THEN

 IF( SIGMA0 .LT. 0.15) THEN

 FLAG = 2.5

 ELSE

 FLAG = 4.0

 END IF

 END IF

 END IF

C

C Warning for deep snow

 CALL ERROR( ‘CRLSNO(IV3)’,

 & ‘***Warning*** Vehicle belly dragging in deep snow’)

C

C ..... Calculate terrain resistance for up to 4 units for wheeled vehicles

C

IF (NVEH(I).EQ. WHEEL) THEN

 IF (I.LE.4) THEN

 RRES1 = ( ( 68.1 * ( 0.10* SIGMA0 * (XL2/XCM2IN) *

 & (XWID1/XCM2IN) )**0.914) * FLAG ) * XN2LB

 ELSE

 RRES1 = 0.0

 END IF

END IF

C

C 1-unit limit for tracks

C

IF (NVEH(I).EQ. TRACK) THEN

 IF (I.LT.2) THEN

 RRES1 = ( ( 157.54 * ( 0.10* SIGMA0 * (XL2/XCM2IN) *

 & (XWID1/XCM2IN) )**0.833) * FLAG ) * XN2LB

 ELSE

 RRES1 = 0.0

 END IF

END IF

C

C Terrain resistance on packed snow is zero

IF (SIGMA0 .GE. 0.55) RRES1 = 0.0

C Terrain resistance on ice is zero

45
IF ((IBASE.EQ.4) .AND. ( DSNOW .LE. (1.0/XCM2IN))) RRES1 = 0.0

C

C ..... Traction calculation

C

IF( NVEH(I) .EQ. WHEEL )THEN

 AREA1 = GCA(I,JPSI)

 XNWORT = NWHL(I)

 XWID1 = SECTW(I)

 ELSE

 AREA1 = GCA(I,JPSI) / 2.0

 XNWORT = 2.0

 XWID1 = TRAKWD(I)

 END IF

C Weight on a single traction element

 WGHT1 = WGHT(I) / XNWORT

 PRES1 = WGHT1/AREA1

C

 IF( IBASE .NE. 4 )THEN

C Snow on road (IBASE=1)

C Snow on frozen or strong (RCI>100) soil (IBASE=2)

C Snow on unfrozen soil (RCI<=100) (IBASE=3)

 IF (SIGMA0.GE.0.55) THEN

C hard packed snow

 TRCN1 = 0.321 * (PRES1*X2KPA)**0.97

 ELSE

 TRCN1 = 0.851 * (PRES1*X2KPA)**0.823

 END IF

 ELSE

C Snow on ice base (IBASE=4)

 IF ( DSNOW .LE. (1.0/XCM2IN)) THEN

 TRCN1 = 0.1 * (PRES1*X2KPA)

 ELSE

 IF (SIGMA0.GE.0.55) THEN

C Disturbed snow

 TRCN1 = 0.321 * (PRES1*X2KPA)**0.97

 ELSE

C Undisturbed snow

 TRCN1 = 0.127 * (PRES1*X2KPA)**1.06

 END IF

 END IF

 END IF

C

C TRCN1 is a stress at this point

 TRCN1 = (TRCN1/X2KPA) * AREA1

C

 TFOW(I) = TRCN1 * XNWORT / WGHT(I)

 RTOW = RRES1 * XNWORT / WGHT(I) + RHARD(I)

C

 RTOWPB(I)= RTOW

 RTOWT(I) = RTOW

 DOWPB(I) = TFOW(I) - RTOW

C

 20 CONTINUE

C

46
 99 RETURN

 END

C RHARD Hard surface resistance for snow 19 Jun 92

C***************************************

C *

C R H A R D *

C *

C************

 REAL FUNCTION RHARD(I)

C

C This routine computes the motion resistance for the hard surfaces

C to be added to the resistance computed for snow.

C

C 19 Jun 92 Origional edit (taken from part of origional NRMM snow model)

C

C Inputs:

C I Suspension assembly index

C Common /PREP/

C CPFFG(NAMBLY) F-G contact pressure factor for each element

C Common /TPREP/

C ITUT Terrain type code:

C 1 = off-road (areal)terrain

C 2 = water-covered terrain

C 11 = on-road super-highway

C 12 = on-road primary road

C 13 = on-road secondary road

C 14 = on-road trail

C Common /VEHICL/

C NVEH(NAMBLY) Vehicle traction assembly type: 0=tracked, 1=wheeled

C

C Outputs:

C RHARD Hard surface resistance coefficient

C

 IMPLICIT NONE

 INCLUDE ‘nrmmdefs.inc’

 INCLUDE ‘nrmmcntc.inc’

 INCLUDE ‘nrmmvehc.inc’

 INCLUDE ‘nrmmvppc.inc’

 INCLUDE ‘nrmmtppc.inc’

C

 INTEGER I

C

 IF( NVEH(I) .EQ. WHEEL )THEN

C Hard surface resistance coefficients (wheeled)

 IF( ITUT.EQ.1 .OR. ITUT.EQ.14 )THEN

C Off-road and trails (no ice)

 IF( CPFFG(I).GE.4.0 )THEN

 RHARD = 0.0175

 ELSE

 RHARD = 0.015

 END IF

 ELSE IF (ITUT.EQ.11 .OR. ITUT.EQ.12 )THEN

C Super-highways & primry roads or ice

 RHARD = 0.015

47
 ELSE

C Secondary roads & all others

 RHARD = 0.025

 END IF

 ELSE

C Hard surface resistance coefficients (tracked)

 IF( ITUT.EQ.1 .OR. ITUT.EQ.14 )THEN

C Off-road and trails

 RHARD = 0.0525

 ELSE IF (ITUT.EQ.11 .OR. ITUT.EQ.12 )THEN

C Super-highways & primry roads

 RHARD = 0.0375

 ELSE

C Secondary roads & all others

 RHARD = 0.045

 END IF

 END IF

C

 IF(KIV(3).GT.YES)WRITE(LUN1,601)RHARD

 601 FORMAT(‘ Hard Sfc Resist. Coef. RHARD =’,F8.4)

C

 RETURN

 END

C THAW CRREL Thawing ground traction model 6 Jan 94

C*****************************************

C *

C T H A W *

C *

C**********

 LOGICAL FUNCTION THAW()

C

C 6 May 94 Implemented in NRMM II

C

C Inputs:

C Common /DERIVE/

C DOWPB(NAMBLY) Drawbar coefficient for each assembly

C LAYER Soil layer index (Critical layer): 1=0"-6", 2=6"-12"

C RTOWPB(NAMBLY) Motion res. coef., powered or braked, each element

C RTOWT(NAMBLY) Motion res. coef., towed, each element

C Common /TERRAN/

C DTHAW Ground thawing depth [in]

C DSNOW Snow depTH [in]

C Common /VEHICL/

C NAMBLY #traction element assemblies (axles and tracks)

C

C Outputs:

C THAW Return status .TRUE. = O-K

C Common /DERIVE/

C DOWPB(NAMBLY) Drawbar coefficient for each assembly

C MRMUL(NAMBLY) Winter model soil resistance multiplier, each element

C RTOWPB(NAMBLY) Motion res. coef., powered or braked, each element

C RTOWT(NAMBLY) Motion res. coef., towed, each element

C TFMUL(NAMBLY) Winter model traction multiplier, each element

C TFOW(NAMBLY) Traction coefficient from soil, each element

48
C

C External:

C MRMULT Soil motion coefficient multiplier for thawing soils

C TRMULT Soil traction coefficient multiplier for thawing soils

C

C Internal:

C I Suspension assembly index

C STATOK Temporary status flag

C

 IMPLICIT NONE

 INCLUDE ‘nrmmdefs.inc’

 INCLUDE ‘nrmmdrvc.inc’

 INCLUDE ‘nrmmcntc.inc’

 INCLUDE ‘nrmmvehc.inc’

 INCLUDE ‘nrmmvppc.inc’

 INCLUDE ‘nrmmterc.inc’

 INCLUDE ‘nrmmtppc.inc’

C

 LOGICAL STATOK

 INTEGER I

 REAL MRMULT, TRMULT

 EXTERNAL MRMULT, TRMULT

C

C Diagnostic printout of input data:

 IF( KIV(3) .GT. YES )THEN

CALL DIAGIN(‘!0***Routine THAW(IV3) ‘//

 & ‘CRREL Thawing soil traction model’)

CALL DIAG( ‘DOWPB DTHAW DSNOW LAYER NAMBLY’ )

CALL DIAG( ‘RTOWPB RTOWT’ )

 END IF

C

 STATOK=.TRUE.

 DO 10 I=1, NAMBLY

TFMUL(I) = TRMULT()

IF(STATOK)STATOK = TFMUL(I).GT.0

TFOW(I) = (DOWPB(I)+RTOWPB(I))*TFMUL(I)

MRMUL(I) = MRMULT(I)

IF(STATOK)STATOK = MRMUL(I).LT.999.

RTOWPB(I) = RTOWPB(I)*MRMUL(I)

RTOWT(I) = RTOWT(I)*MRMUL(I)

DOWPB(I) = TFOW(I) - RTOWPB(I)

 10 CONTINUE

 THAW = STATOK

C

C Check for validity

 IF( LAYER .EQ. 2 )

 & CALL ERROR( ‘THAW’,’Critical depth > 6"’ )

 IF( DSNOW .GT. 1./XCM2IN)

 & CALL ERROR( ‘THAW’,’Snow cover > 1 cm.’ )

C

 RETURN

 END

C TRMULT Traction multiplier for thawing soils 6 Jan 94

C*********************************************

49
C *

C T R M U L T *

C *

C**************

 REAL FUNCTION TRMULT()

C

C May 92 Model based on US ARMY CRREL research done by Sally Shoop

C Coded by Jim Slota, OptiMetrics for CRREL. (SSM 6.2)

C 23 Jun 92 Implemented in CAMMS by R. B. Ahlvin, WES

C 6 Jan 94 Implemented in NRMM II by R.B.Ahlvin

C

C This function returns a multiplier value to modify drawbar-pull

C in lbs. Traction is reduced for travel over a thawing soil layer

C that overlays a frozen soil layer. Calculations are applicable

C only for sandy soils with little or no snow cover, and for

C vehicles with a critical depth of less than 6 inches. The wetness

C index, as calculated by the SMSP model, is also required.

C

C Inputs:

C Common /TERRAN/

C DTHAW Depth of thawing is soil [in]

C KUSCS USCS soil type code: 1=SW, 2=SP, 3=SM, 4=SC, 5=SMSC,

C 6=CL, 7=ML, 8=CLML, 9=CH, 10=MH, 11=OL, 12=OH, 13=WATER,

C 14=PAVEMENT, 15=ROCK, 16=GW, 17=GP, 18=GM, 19=GC, 20=Pt

C KWI SMSP wetness index: 0=arid, 1=dry, 2=average, 3=wet,

C 4=saturated, 5=waterlogged

C Output:

C TRMULT Tractio multiplier

C

 IMPLICIT NONE

 INCLUDE ‘nrmmdefs.inc’

 INCLUDE ‘nrmmcntc.inc’

 INCLUDE ‘nrmmterc.inc’

 INCLUDE ‘nrmmvehc.inc’

C

 INTEGER I,J, LENSTR

 REAL MRMULT, THAWCM

 LOGICAL SVALID(20)

 CHARACTER *4 ZUSCS(20)

 CHARACTER *5 ZVTYPE

 EXTERNAL LENSTR

 DATA ZUSCS/’SW’,’SP’,’SM ‘,’SC ‘,’SMSC’,

 & ‘CL’,’ML’,’CLML’,’CH ‘,’MH ‘,

 & ‘OL’,’OH’,’WATR’,’PVMT’,’ROCK’,

 & ‘GW’,’GP’,’GM ‘,’GC ‘,’Pt ‘/

C

 DATA (SVALID(J),J= 1, 5)

 & /.TRUE. ,.TRUE. ,.TRUE., .TRUE., .TRUE./

C SW SP SM SC SMSC

 DATA (SVALID(J),J= 6,10)

 & /.TRUE. ,.FALSE.,.FALSE.,.FALSE.,.FALSE./

C CL ML CLML CH MH

 DATA (SVALID(J),J=11,15)

 & /.FALSE.,.FALSE.,.FALSE.,.FALSE.,.FALSE./

50
C OL OH WATR PVMT ROCK

 DATA (SVALID(J),J=16,20)

 & /.TRUE. ,.TRUE. ,.TRUE. ,.TRUE. ,.TRUE./

C GW GP GM GC Pt

C

 THAWCM = DTHAW / XCM2IN

 IF( (THAWCM .GT. 2.5) .AND. (THAWCM .LT. 15.0)) THEN

 TRMULT = 2.379 * (1.0/(THAWCM*THAWCM)) + 0.619

 ELSE IF (THAWCM .GE. 15.0) THEN

 TRMULT = 0.63

 ELSE

 TRMULT = 1.0

 END IF

 IF( .NOT.SVALID(KUSCS) ) THEN

WRITE(ERRMSG,9901)KUSCS,ZUSCS(KUSCS)(1:LENSTR(ZUSCS(KUSCS)))

 9901 FORMAT(‘Relations not implemented for ‘,

 & ‘soil type KUSCS=’,I2,’ (‘,A,’)’:

 & ‘ NVEH(I)=’,I1,’ (‘,A,’)’)

CALL ERROR( ‘TRMULT’, ERRMSG )

 END IF

C

 RETURN

C

C MRMULT Motion resistance multiplier for thawing soils 23 Jun 92

C******************************************************

C *

C M R M U L T *

C *

C**************

 ENTRY MRMULT(I)

C

C May 92 Model based on US ARMY CRREL research done by Sally Shoop

C Coded by Jim Slota, OptiMetrics for CRREL. (SSM 6.2)

C 6 May 94 Implemented in NRMM II by R.B.Ahlvin

C

C This function returns a multiplier value to motion resistance

C values. This applies to travel over a thawing soil layer

C overlaying a frozen layer. Calculations are applicable only for

C wheeled vehicles on sandy soils with little or no sno cover,

C and for vehicles with a critical depth of less than 6 inches. The

C wetness index, as calculated by the SMSP model, is also required.

C

C Inputs:

C I Suspension assembly index

C Common /TERRAN/

C DTHAW Depth of thawing is soil [in]

C KUSCS USCS soil type code: 1=SW, 2=SP, 3=SM, 4=SC, 5=SMSC,

C 6=CL, 7=ML, 8=CLML, 9=CH, 10=MH, 11=OL, 12=OH, 13=WATER,

C 14=PAVEMENT, 15=ROCK, 16=GW, 17=GP, 18=GM, 19=GC, 20=Pt

C KWI SMSP wetness index: 0=arid, 1=dry, 2=average, 3=wet,

C 4=saturated, 5=waterlogged

C Common /VEHICL/

C NVEH(NAMBLY) Vehicle traction assembly type: 0=tracked, 1=wheeled

C

51
C Output:

C MRMULT Motion resistance multiplier

C

MRMULT = 1.0

C

THAWCM = DTHAW / XCM2IN

C The following 3 lines handle cases for which THAWCM < 2.5 cm

IF( THAWCM .LE. 2.5 )THEN

 MRMULT = 1.0

ELSE IF( (THAWCM .GT. 2.5) .AND. (THAWCM .LT. 4.0)) THEN

 MRMULT = 2.883 * THAWCM - 6.056

ELSE IF( (THAWCM .GE. 4.0) .AND. (THAWCM .LT. 8.0)) THEN

 MRMULT = -0.22*THAWCM*THAWCM + 3.54*THAWCM - 5.24

ELSE IF( (THAWCM .GE. 8.) .AND. (THAWCM .LT. 12.0)) THEN

 MRMULT = 0.225*THAWCM + 7.2167

ELSE

 MRMULT = 10.0

END IF

IF( NVEH(I).EQ. TRACK )

 & CALL ERROR( ‘MRMULT’,

 & ‘Multiplier may not be valid for TRACKED elements’ )

 IF( .NOT.SVALID(KUSCS) ) THEN

WRITE(ERRMSG,9901)KUSCS,ZUSCS(KUSCS)(1:LENSTR(ZUSCS(KUSCS))),

 & NVEH(I),ZVTYPE

CALL ERROR( ‘MRMULT’, ERRMSG )

 END IF

C

 RETURN

 END

52
0 0.2 0.4 0.6

Traction Coefficient (μ)

μ CIV 12% Slip

μ CIV SAE

μ CIV Ave. Peak (gross)

μSaab Predicted, Undisturbed Snow

μ CIV Predicted, Undisturbed Snow

μ Packed Snow (SME, 1973)

μSaab 12% Slip

μ CIV Ave. Peak (gross)

μ U - G Max

μSaab 12% Slip

μ U - G SAE

μ CIV Ave. Peak

μ CIV Ave. Peak (gross)

μ CIV Predicted, Hard Packed Snow

Snow Road


2.5 cm, 0.25 g/cm3

Snow over Hard Pack

Snow Test Section '92


10 cm, 0.54 g/cm3

Snow over Hard Pack


(Tair = – 2° C, Tsnow = – 1° C)

Snow Test Section '93


2 cm, 0.59 g/cm3

Snow over Hard Pack


(Tair = – 0.6° C, Tsnow = – 2.8° C)

Snow


–––––

μ U - G SAE

μ CIV Max

μ CIV Max

μ CIV Ave. Peak

μ CIV 12% Slip

μ CIV SAE

μ U - G Max

μ CIV Ave. Peak (net)

μSaab Predicted, Hard Packed Snow

Data from Shoop 1993


Data from Richmond et al. 1990, SME 1977


Predicted Gross Traction

6 cm,0.59 g/cm3 Groomed


and Packed Snow


(Richmond et al., 1990).

Figure C1. Comparison of measured, published and predicted values of traction on shallow

groomed snow.

APPENDIX C. TRACTION COEFFICIENTS ON PACKED SNOW

Traction on groomed, shallow snow was measured with three different vehicles— the CRREL Instrumented Vehicle (CIV), the Saab Friction Tester and the Uniroyal-Goodrich Traction Tester (U-G)—in Shoop

(1993a). Several methods of reporting the traction coefficient (μ) were used:

• The maximum value (μmax);

• An average peak value (μpeak);

• The value at 12% slip (μ12%slip); and

• The SAE-specified μ (μSAE).

These measurements are compared to other published traction coefficients on groomed snow in Figure

C1. The predicted traction values, using CRREL’s Cold Regions Mobility Models, is expressed in coefficient form and is shown by the open circles at the bottom of the figure.

53
APPENDIX D: NRMM CHECKOUT DATA

TERRAIN UNIT INPUT

 38 8 Checkout terrain for CRREL winter effects model 6 May 94

!

! 1) Best possible on-road terrain

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA EANG RADC

 1 ‘BstON’ 1.00 1 1 0 0.0 999 0 5000

!

! 2) Best possible off-road terrain

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 2 ‘BstCC’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

!

! 3) Soft soil effects, Soil strength = 100

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 3 ‘CI100’ 1.00 0 1 0 0.0 999 SM 2 100 100 99

!

! 4) Soft soil effects, Soil strength = 50

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 4 ‘CI50’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

!

! 5) Soft soil effects, Soil strength = 20

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 5 ‘CI20’ 1.00 0 1 0 0.0 999 SM 4 20 20 99

!

! 6) Frozen ground, w/Ice base

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 6 ‘Ice’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 99.9 0.0 0.0 1

!

! 7) 1-in snow on frozen ground, w/Ice base

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 7 ‘1in/I’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 1.0 0.2 99.9 0.0 0.0 1

!

! 8) 10-in snow on frozen ground, w/Ice base

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 8 ’10inI’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 99.9 0.0 0.0 1

!

! 9) 1-in snow on frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 9 ‘1in’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 1.0 0.2 99.9 0.0 0.0 0

!

! 10) 10-in snow on frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 10 ’10in’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 99.9 0.0 0.0 0

!

! 11) 20-in snow on frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 11 ’20in’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 20.0 0.2 99.9 0.0 0.0 0

!

! 12) 10-in snow on frozen ground, density= 0.1

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 12 ’10".1' 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.1 99.9 0.0 0.0 0

!

55
! 13) 10-in snow on frozen ground, density= 0.3

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 13 ’10".3' 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.3 99.9 0.0 0.0 0

! 14) 10-in snow on frozen ground, density= 0.4

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 14 ’10".4I’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.4 99.9 0.0 0.0 0

!

! 15) 10-in snow on road

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA EANG RADC

 15 ’10"ON’ 1.00 1 5 0 0.0 999 0 5000

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 0.0 0.0 0.0 0

!

! 16) 10-in snow on unfrozen ground, CI=150

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 16 ’10CI150' 1.00 0 1 0 0.0 999 SM 1 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 0.0 0.0 0.0 0

!

! 17) 10-in snow on unfrozen ground, CI=50

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 17 ’10CI50' 1.00 0 1 0 0.0 999 SM 2 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 0.0 0.0 0.0 0

!

! 18) 10-in snow on unfrozen ground, CI=20

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 18 ’10CI20' 1.00 0 1 0 0.0 999 SM 3 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 0.0 0.0 0.0 0

!

! 19) 10-in snow on 2-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 19 ‘2frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 2.0 0.0 0.0 0

!

! 20) 10-in snow on 4-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 20 ‘4frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 4.0 0.0 0.0 0

!

! 21) 10-in snow on 6-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 21 i’6frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 6.0 0.0 0.0 0

!

! 22) 10-in snow on 12-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 22 ’12frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 0.0 0.0 0

!

! 23) 10-in snow on 2-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 23 ‘2thaw’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 2.0 0.0 0

! 56
! 24) 10-in snow on 4-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 24 ‘4thaw’ 1.00 0 1 0 0.0 999 SM 4 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 4.0 0.0 0

!

! 25) 10-in snow on 8-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 25 ‘8thaw’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 8.0 0.0 0

!! 26) 10-in snow on 8-in thawing ground, 10% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 26 ‘8thM10’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 8.0 10.0 0

!

! 27) 10-in snow on 8-in thawing ground, 30% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 27 ‘8thM30’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 8.0 30.0 0

!

! 28) 10-in snow on 8-in thawing ground, 50% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 28 ‘8thM30’ 1.00 0 1 0 0.0 999 SM 4 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 10.0 0.2 12.0 8.0 50.0 0

!

! 29) 0-in snow on 2-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 29 ‘2frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 30) 0-in snow on 4-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 30 ‘4frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 4.0 0.0 0.0 0

!

! 31) 0-in snow on 6-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 31 i’6frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 6.0 0.0 0.0 0

!

! 32) 0-in snow on 12-in frozen ground

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 32 ’12frez’ 1.00 0 1 0 0.0 999 SM 1 300 300 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 0.0 0.0 0

!

! 33) 0-in snow on 2-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 33 ‘2thaw’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 34) 0-in snow on 4-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 34 ‘4thaw’ 1.00 0 1 0 0.0 999 SM 4 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 4.0 0.0 0

!

57
! 35) 0-in snow on 8-in thawing ground (using WI)

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 35 ‘8thaw’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 8.0 0.0 0

!

! 36) 0-in snow on 8-in thawing ground, 5% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 36 ‘8thM10’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 8.0 5.0 0

!

! 37) 0-in snow on 8-in thawing ground, 10% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 37 ‘8thM30’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 8.0 10.0 0

!

! 38) 0-in snow on 8-in thawing ground, 30% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 38 ‘8thM30’ 1.00 0 1 0 0.0 999 SM 4 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 8.0 30.0 0

54 8 Checkout terrain for CRREL winter effects model 6 May 94

!

! 39) ZTEST #1:2" frozen ground,RCI1,2=5,5;KWI=1

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 39 ‘zt-1’ 1.00 0 1 0 0.0 999 SM 1 5 5 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 40) ZTEST #2:2" frozen ground,RCI1,2=20,20;KWI=1

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 40 ‘zt-2’ 1.00 0 1 0 0.0 999 SM 1 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 41) ZTEST #3:2" frozen ground,RCI1,2=100,100;KWI=1

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 41 ‘zt-3’ 1.00 0 1 0 0.0 999 SM 1 100 100 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 42) ZTEST #4:2" frozen ground,RCI1,2=5,5; KWI=5

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 42 ‘zt-4’ 1.00 0 1 0 0.0 999 SM 5 5 5 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 43) ZTEST #5:2" frozen ground,RCI1,2=20,20;KWI=5

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 43 ‘zt-5’ 1.00 0 1 0 0.0 999 SM 5 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 44) ZTEST #6:2" frozen ground,RCI1,2=100,100;KWI=5

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 44 ‘zt-6’ 1.00 0 1 0 0.0 999 SM 5 100 100 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 2.0 0.0 0.0 0

!

! 45) 0-in snow on 2-in thawing ground (using WI), wet conditions

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 45 ‘2thaw’ 1.00 0 1 0 0.0 999 SM 5 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

58
! 46) SOIL TEST#1: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 46 ‘st-1’ 1.00 0 1 0 0.0 999 SW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 47) SOIL TEST#2: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 47 ‘st-2’ 1.00 0 1 0 0.0 999 SP 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 48) SOIL TEST#3: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 48 ‘st-3’ 1.00 0 1 0 0.0 999 SW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 49) SOIL TEST#4: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 49 ‘st-4’ 1.00 0 1 0 0.0 999 SC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 50) SOIL TEST#5: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SMSC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 50 ‘st-5’ 1.00 0 1 0 0.0 999 SMSC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 51) SOIL TEST#6: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 51 ‘st-6’ 1.00 0 1 0 0.0 999 CL 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 52) SOIL TEST#7: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 52 ‘st-7’ 1.00 0 1 0 0.0 999 ML 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 53) SOIL TEST#8: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CLML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 53 ‘st-8’ 1.00 0 1 0 0.0 999 CLML 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 54) SOIL TEST#9: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 54 ‘st-9’ 1.00 0 1 0 0.0 999 CH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 55) SOIL TEST#10: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; MH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 55 ‘st-10’ 1.00 0 1 0 0.0 999 MH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 56) SOIL TEST#11: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 56 ‘st-3’ 1.00 0 1 0 0.0 999 OL 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

59
! 57) SOIL TEST#12: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 57 ‘st-12’ 1.00 0 1 0 0.0 999 OH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 58) SOIL TEST#13: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; WATR

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 58 ‘st-13’ 1.00 0 1 0 0.0 999 WATR 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 59) SOIL TEST#14: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; PAVE

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 59 ‘st-14’ 1.00 0 1 0 0.0 999 PAVE 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 60) SOIL TEST#15: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ROCK

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 60 ‘st-15’ 1.00 0 1 0 0.0 999 ROCK 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!! 61) SOIL TEST#16: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 61 ‘st-16’ 1.00 0 1 0 0.0 999 GW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 62) SOIL TEST#17: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 62 ‘st-17’ 1.00 0 1 0 0.0 999 GP 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 63) SOIL TEST#18: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 63 ‘st-18’ 1.00 0 1 0 0.0 999 GM 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 64) SOIL TEST#19: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 64 ‘st-19’ 1.00 0 1 0 0.0 999 GC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 65) SOIL TEST#20: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; Pt

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 65 ‘st-20’ 1.00 0 1 0 0.0 999 Pt 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 66) #2SOIL TEST#1: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 66 ‘2st-1’ 1.00 0 1 0 0.0 999 SW 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 67) #2SOIL TEST#2: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 67 ‘2st-2’ 1.00 0 1 0 0.0 999 SP 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

60
! 68) #2SOIL TEST#3: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 68 ‘2st-3’ 1.00 0 1 0 0.0 999 SW 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 69) #2SOIL TEST#4: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 69 ‘2st-4’ 1.00 0 1 0 0.0 999 SC 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 70) #2SOIL TEST#5: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SMSC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 70 ‘2st-5’ 1.00 0 1 0 0.0 999 SMSC 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 71) #2SOIL TEST#6: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 71 ‘2st-6’ 1.00 0 1 0 0.0 999 CL 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 72) #2SOIL TEST#7: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 72 ‘2st-7’ 1.00 0 1 0 0.0 999 ML 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!! 73) #2SOIL TEST#8: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CLML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 73 ‘2st-8’ 1.00 0 1 0 0.0 999 CLML 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 74) #2SOIL TEST#9: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 74 ‘2st-9’ 1.00 0 1 0 0.0 999 CH 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 75) #2SOIL TEST#10: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; MH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 75 ‘2st-10’ 1.00 0 1 0 0.0 999 MH 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 76) #2SOIL TEST#11: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 76 ‘2st-3’ 1.00 0 1 0 0.0 999 OL 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 77) #2SOIL TEST#12: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 77 ‘2st-12’ 1.00 0 1 0 0.0 999 OH 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 78) #2SOIL TEST#13: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; WATR

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 78 ‘2st-13’ 1.00 0 1 0 0.0 999 WATR 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

61
! 79) #2SOIL TEST#14: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; PAVE

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 79 ‘2st-14’ 1.00 0 1 0 0.0 999 PAVE 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 80) #2SOIL TEST#15: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ROCK

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 80 ‘2st-15’ 1.00 0 1 0 0.0 999 ROCK 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 81) #2SOIL TEST#16: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 81 ‘2st-16’ 1.00 0 1 0 0.0 999 GW 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 82) #2SOIL TEST#17: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 82 ‘2st-17’ 1.00 0 1 0 0.0 999 GP 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 83) #2SOIL TEST#18: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 83 ‘2st-18’ 1.00 0 1 0 0.0 999 GM 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 84) #2SOIL TEST#19: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 84 ‘2st-19’ 1.00 0 1 0 0.0 999 GC 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!! 85) #2SOIL TEST#20: KWI=0, RCI1,2=150, DFREEZE=12in;DTHAW=2in; Pt

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 85 ‘2st-20’ 1.00 0 1 0 0.0 999 Pt 0 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 40.0 0

!

! 86) 0-in snow on 4-in thawing ground, 5% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 86 ‘4thM5’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 4.0 5.0 0

!

! 87) 0-in snow on 4-in thawing ground, 10% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 87 ‘4thM10’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 4.0 10.0 0

!

! 88) 0-in snow on 4-in thawing ground, 30% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 88 ‘4thM30’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 4.0 30.0 0

!

! 89) 0-in snow on 4-in thawing ground, 50% moisture content

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 89 ‘4thM10’ 1.00 0 1 0 0.0 999 SM 3 50 50 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 4.0 50.0 0

!

62
! 90) 0-in snow on 2-in thawing ground, RCI1,2=5

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 90 ‘2thR5’ 1.00 0 1 0 0.0 999 SM 3 5 5 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 91) 0-in snow on 2-in thawing ground, RCI1,2=20

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 91 ‘2thR20’ 1.00 0 1 0 0.0 999 SM 3 20 20 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

! 92) 0-in snow on 2-in thawing ground, RCI1,2=150

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 92 ‘2thR150’ 1.00 0 1 0 0.0 999 SM 3 150 10 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 12.0 2.0 0.0 0

!

20 8 Checkout terrain for CRREL winter effects model 22 July 94

!

! 93) SOIL TEST#1: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 93 ‘st-1’ 1.00 0 1 0 0.0 999 SW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

! 94) SOIL TEST#2: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 94 ‘st-2’ 1.00 0 1 0 0.0 999 SP 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

! 95) SOIL TEST#3: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 95 ‘st-3’ 1.00 0 1 0 0.0 999 SW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

! 96) SOIL TEST#4: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 96 ‘st-4’ 1.00 0 1 0 0.0 999 SC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

! 97) SOIL TEST#5: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; SMSC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 97 ‘st-5’ 1.00 0 1 0 0.0 999 SMSC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

! 98) SOIL TEST#6: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 98 ‘st-6’ 1.00 0 1 0 0.0 999 CL 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

! 99) SOIL TEST#7: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 99 ‘st-7’ 1.00 0 1 0 0.0 999 ML 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

63
!100) SOIL TEST#8: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CLML

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 100 ‘st-8’ 1.00 0 1 0 0.0 999 CLML 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!101) SOIL TEST#9: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; CH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 101 ‘st-9’ 1.00 0 1 0 0.0 999 CH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!102) SOIL TEST#10: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; MH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 102 ‘st-10’ 1.00 0 1 0 0.0 999 MH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!103) SOIL TEST#11: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OL

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 103 ‘st-3’ 1.00 0 1 0 0.0 999 OL 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!104) SOIL TEST#12: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; OH

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 104 ‘st-12’ 1.00 0 1 0 0.0 999 OH 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!105) SOIL TEST#13: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; WATR

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 105 ‘st-13’ 1.00 0 1 0 0.0 999 WATR 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!106) SOIL TEST#14: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; PAVE

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 106 ‘st-14’ 1.00 0 1 0 0.0 999 PAVE 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!107) SOIL TEST#15: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; ROCK

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 107 ‘st-15’ 1.00 0 1 0 0.0 999 ROCK 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!108) SOIL TEST#16: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GW

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 108 ‘st-16’ 1.00 0 1 0 0.0 999 GW 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!109) SOIL TEST#17: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GP

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 109 ‘st-17’ 1.00 0 1 0 0.0 999 GP 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!110) SOIL TEST#18: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GM

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 110 ‘st-18’ 1.00 0 1 0 0.0 999 GM 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

64
!111) SOIL TEST#19: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; GC

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 111 ‘st-19’ 1.00 0 1 0 0.0 999 GC 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

!

!112) SOIL TEST#20: KWI=5, RCI1,2=150, DFREEZE=12in;DTHAW=2in; Pt

! NTU TUID AREA IROAD ISCOND GRADE ACTRMS RDA USCS KWI RCI1 RCI2 DBROCK

 112 ‘st-20’ 1.00 0 1 0 0.0 999 Pt 5 150 150 99

! DSNOW SIGMA DFREEZ DTHAW TMOIST ICE

WIN 0.0 0.2 0.0 0.0 0.0 0

65
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February 1995

Cold Regions Mobility Models PE:6.27.84A

PR: 4A762784AT42

TA: CS

WU: M03, M04 & M08

Paul W. Richmond, Sally A. Shoop and George L. Blaisdell

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road CRREL Report 95-1

Hanover, New Hampshire 03755-1290

Office of the Chief of Engineers

Washington, D.C. 20314-1000

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161

79

Cold regions Models

Mobility Vehicle mobility

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

This report annotates the cold regions mobility prediction routines included in the CAMMS/ALBE mobility

models. It further explains the development of the algorithms that are used in these models to describe the

interaction of a vehicle with terrain that has been affected by cold weather. The following terrain conditions are

discussed: undisturbed snow (shallow and deep); disturbed snow (moderately trafficked and hard packed); ice;

and thawing soils. Several combinations of substrates are also considered. A stand-alone computer model is

included.