deformation characterization of subgrade soils for...

Deformation Characterization of Subgrade Soils for Highways and Runways in Northern Environments1

D. G. FREDLUND, A. T. BERGAN, AND E. K. SAUER Deprrrttnent of Civil Engirzeering, University of Saskorcl~ewatr, Saskatoorz, Snskatche~vnn T6G 2G7

Received August 23, 1974 Accepted January 21, 1975

Roads and runways in Northern Canada often must carry exceptionally heavy loads. In order to design for these loads, a procedure has been developed which enables the prediction of fatique life of pavements. Experimental evidence indicates that the definition of resilient deformation, which controls fatigue life of pavements, can be resolved in terms of stress state variables. The resilient modulus is defined in terms of ( a , - a,), (a3 - rr,), and (11, - 11,) which is applied in a theoretical analysis. Typical forms of the constitutive relationships are presented. The effect of freeze-thaw cycles does not appear to produce significant hysteresis in the constitutive relationships.

Les routes et pistes d'atterissage doivent souvent supporter des charges exceptionnellement tlevtes dans le nord canadien. Pour aider au dimensionnement des pavages soumis B de telles charges, une proctdure a Ctb dtveloppte qui permet la prtvision de la durte de vie des pavages compte tenu du phtnomkne de fatique. Les observations exptrimentales indiquent que la dtfinition de la deformation de rtsilience, qui contr6le le ddveloppement de la fatigue des pavages, peut &tre exprimbe en terme de paramktres de l'etat de contraintes. Le module de rtsilience est dtfini en fonction de (UI - a3), (a3 - u,) et (11, - 11,) et utilist dans une analyse thtorique. Les formes types des lois constitutives sont prtsenttes. L'effet de cycle gel-dtgel ne semble pas produire de phtnomkne notable d'hystirtsis dans les lois constitutives.

Introduction Rapid development in Northern Canada has

required the construction of roads and runways to transport raw resources out of the region. As a result, there is a necessity to be able to design facilities for heavier loads than is possible with existing conventional design pro- cedures. During the past 6 years, the Univer- sity of Saskatchewan in cooperation with the Saskatchewan Department of Highways has carried out an extensive research and development program to formulate a design procedure which will make it possible to design asphalt pavement structures for heavy axle loads and in addition be able to consider the economic consequences of increased axle loads. This procedure is now developed and is being used in the design of resource haul roads in North- ern Saskatchewan.

In order to satisfactorily carry out the design, considerable knowledge is required on the deformation characteristics of subgrade soils and changes that occur throughout the

'Presented to the 27th Canadian Geotechnical Con- ference, Edmonton, Alberta, November 7-8, 1974.

Can. Geotech. J . , 12,213 (1975)

[Traduit par la Revue]

year. Figure 1 illustrates the seasonal variation in Benkelman beam deflections of a section of highway between Regina and Lumsden in Sas- katchewan, Canada. Bergan ( 1972) was able to predict the seasonal changes in the subgrade deformation characteristics of this highway by 'backing-in' on the results of Benkelman beam measurements with a theoretical stress analysis. However, this type of data is not always avail-

- X = MEAN DEFLECTION

S = STANDARD DEVIATION

PlPRlL MAY JUNE JULY AUG. SEPT. OCT.

TIME OF YEAR

FIG. 1. Typical Benkelman beam deflections versus time of year for the Regina to Lumsden highway (from Bergan 1972).

214 CAN. GEOTECH. J. VOL. 12, 1975

able, therefore, it would be advantageous to be able to predict the subgrade behavior from a knowledge of expected changes in the stress state variables throughout the seasons. In turn, the stress state variables would be predicted from the microclimatic environment and the geometric boundary conditions of the cross section under consideration.

The freezing and thawing of the subgrade also has an effect on its response to dynamic loading and must be given consideration in the cold environment of Canada. This paper deals with the prediction of the deformation characteristics of an unsaturated subgrade soil in terms of the associated stress state variables, giving consideration to the effects of freeze- thaw cycles.

Theory One of the principal modes of failure in

pavements is fatigue cracking from repeated flexure under dynamic loads produced by moving vehicles. During the past decade, increasing use has been made of the repeated load laboratory test for the prediction of pavement deflections (Seed et al. 1965). The tests measure the resilient (or elastic) strain when a sample is subjected to repeated loadings under triaxial conditions. The soil parameter evaluated is the resilient modulus.

where M I , = modulus of resilient deformation (analogous to an elastic modulus), r = resilient axial strain in the major principal stress direc- tion, a,, = repeatedly applied deviator stress, crl = major principal stress, and a:% = minor principal stress.

In order to describe the resilient modulus in terms of stresses only, it is necessary to know the stress state variables associated with the prediction of strain in an unsaturated soil. Fredlund ( 1973) used the superposition of coincident equilibrium stress fields for each phase of an unsaturated soil in order to predict the stress state variables. The predicted stress state variables were experimentally verified by means of null-type tests. The analysis indicated that one possible set of stress state variables, in matrix form, is:

ox - uw Tyx

'x, 'Jy - -w T7,y

Tx2 7,z " z - uw and

u - u 0 O 1

0 u, - uw I where a,, a,, o, = total normal stress in the x, y, and z directions respectively, T,,, T,,, T,,, T,,, rZy, T,, = total shear stress, and ua, uw = the air and water pressures, respectively.

The stress analysis further indicates that any two of three possible forms of the stress state variables can be used.

If we assume that an unsaturated soil behaves as an isotropic linear elastic continua, the strain can be written in terms of the stress state variables (Fredlund 1973) :

where E, = the elastic modulus associated with a change in (al - u,,.), p2 = the corresponding Poisson's ratio, and H, = the elastic modulus associated with a change in (u, - u,,.).

Equation [2] is of essentially the same form as that proposed by Biot ( 1941 ) and Coleman (1962).

An examination of Eqs. [2] and [ I ] gives an indication of the stress state variables in- volved. However, it must be emphasized that the combination of these equations does not uniquely describe the resilient modulus under repeated loading conditions. The dimensional- type analysis shows that:

The proper form of the constitutive relationship between resilient modulus and. the stress

FREDLUND ET AL.: DEFORMATION CHARACTERIZATION 215

state variables must be obtained through experimental analysis. Another form of Eq. [3] is :

The form in Eq. [4] is advantageous when considering the field problem since the air pressure tends to equilibrium with the atmosphere. In other words, the air is either open to atmosphere in nature or else it diffuses through the water in order to come to equilibrium with the atmosphere.

Since (ol - u,) is equal to [(ol - 53) + (03 - u,)], we can also write

In some analyses, it is sufficient to use a constant (ol - c3) stress. In this case,

and can graphically be represented as shown in Fig. 2. -

There are serious technical problems with respect to measuring air and water pressures under dynamic loading conditions. All attempts to measure these pressures at the University of Saskatchewan have been unsuccessful due to the slow response of the measuring system (Fredlund and Morgenstern 1973). For this reason, it appears necessary to revert to a total

FIG. 2. Form of the constitutive surface for resilient modulus.

stress type of approximation during repeated loading.

Dehlen (1969) found that 1000 initial stress repetitions were sufficient to avoid changes in axial deflection because of sample end imperfections. MacLeod ( 1971 ) found that 50 to 100 repetitions were sufficient to establish the resilient modulus after a change in deviator stress on a sample. Culley (1971 ) presented typical results for the variation of resilient modulus versus the number of load repetitions (Fig. 3 ) . On the basis of this evidence, it would appear satisfactory to use the resilient modulus computed after approximately 1000 repetitions, and relate it to the stress state variables just prior to loading the sample.

Effect of Freeze-Thaw Cycles Hamilton (1966) found that samples com-

pacted below a 90% degree of saturation shrank upon freezing while those compacted at higher water contents increased in volume. The greatest amount of shrinkage on freezing was observed for samples between 60 and 70% saturation. Upon thawing, a net increase in volume was observed. Similar observations have been reported by Mickleborough ( 1969) and Lidgren (1970). This indicates that a basic change is taking place as a result of freezing and thawing.

If the freezing and thawing of a soil were a nonhysteretic process, the stress state variables should be the same before and after freezing.

W IL I I I I

10 1 0 0 1000 IOOOO IOOOOO

NUMBER OF LOADINGS

FIG. 3. Effect of water content and degree of saturation on resilient modulus versus number of loadings (after Culley 1971 ) .

216 CAN. GEOTECH. J . VOL. 12. 1975

Since the total and air pressures are essentially the same before and after freezing, only the changes in water pressure need to be observed. Mickleborough ( 1970) and Bergan ( 1972) reported significant decreases in matric suction (u;, - u , ~ ) as a result of freezing and thawing. In addition, the structure of the soil is modified as a result of freezing and thawing. Although the matric suction changes as a result of freezing and thawing, the question relevant to this paper involves the adequacy of the stress state variables to define the resilient modulus before and after freezing and thawing.

Prediction of Stress State Variable Changes The diffusivity of air through water is such

that the air phase of a soil should equalize with the atmosphere in a relatively short period of time. Therefore a knowledge of changes in the water pressure is the key to determining the changes in the stress state variables throughout the year.

A transient flow analysis such as that proposed by Richards ( 1965) and Nachlinger and Lytton (1969) is being considered to relate microclimatic changes with pore water pressures. As well, consideration is being given to simpler microclimatic evapotranspiration cal- culations to define soil moisture deficiency (Thornthwaite 1948).

Laboratory Equipment The triaxial loading systems are designed to

repeatedly apply a load to the soil, thereby attempting to simulate the stresses produced by a moving vehicle. Bergan (1972) has dcm- onstrated that the test results do give a realistic simulation of the field case.

The loading system is operated by com- pressed air which applies a pneumatic pressure to a bellofram located above the main piston2 (Fig. 4 ) . The frequency of the loading is gov- erned by a control timer. The loading frequency is 20 repetitions per minute with a load duration of 0.1 s, similar to that used by Seed et al. ( 1965).

The load applied to the sample is measured by a load cell in the base plate. The vertical

'University of Saskatchewan Soils Laboratory, Saskatoon, Saskatchewan.

and lateral strains are measured by linear variable differential transformers (LVDT's) .

The data presented in this paper was obtained over a period of several years and during this time the equipment has undergone numerous modifications. The equipment shown in Fig. 4 is presently operating at the Univer- sity of Saskatchewan.

Soil Samples Two types of soil have been used in the

investigation: (i) a glacial till taken from the Qu7Appelle moraine in the southeast part of the Province of Saskatchewan and (ii) a highly plastic lacustrine clay from Regina, Saskatch- ewan. The properties are summarized in Table 1. These are the most common types of materials in this region.

Presentation of Test Results The relationship between resilient modulus

and each of the stress state variables will be examined separately. In each case it would be desirable to have all samples initially prepared to the same water content and density. How- ever, most of the test programs were set up independent of this study and, therefore, different molding densities and water contents were used. Krahn and Fredlund (1972) showed that the effect of varying density had only a small effect on the suctions for both the till and Regina clay. These results are in agreement with the findings of Olson and Langfeldcr ( 1965) and suggest that samples with varying initial densities can be used to test the proposed hypothesis.

(a ) Effect of Deviator Stress (crl - ad) Seed et al. (1965) showed that the magni-

tude of the deviator stress has a significant effect on the resilient modulus for plastic soils.

TABLE 1. Properties of soils tested

Property Glacial till Regina clay

Liquid limit 38.5% 78.4% Plastic limit 16.8% 30.6% % sand 26.8 5.6 % silt 40.0 27.2 % clay 33.3 67.2 Specific gravity 2.77 2.83 Max. std. density 106.8 p.c.f. 91.8 p.c.f. Opt. water content 19.0% 27.8%

FREDLUND ET AL.: DEFORMATION CHARACTERIZATION

FIG. 4. Repeated loading triaxial system (University of Saskatchewan, Saskatoon).

As seen in Fig. 5, the resilient modulus decreases with increasing deviator stress in the low deviator stress range. At higher deviator stresses, the resilient modulus increases. However, the results are not too meaningful at high deviator stresses since failure conditions are ap- proached.

Weimer (1972) and Bergan (1972) demonstrated a similar behavior for glacial till and Regina clay in the low deviator stress range (Fig. 6) . The relationships are only slightly nonlinear in the stress range considered.

A deviator stress of 10 p.s.i. (0.7 kg/cm2) has generally been used when evaluating the resilient modulus. However, a deviator stress range should be evaluated in order to duplicate the actual stress conditions that occur at the subgrade covered by a pavement structure.

(6) Effect of Confining Pressure (u3 - u,) For sands and gravels, Seed et al. (1965)

have shown that there is a unique relationship between the resilient modulus and the confining pressure provided the applied stresses are not

CAN. GEOTECH. J . VOL. 12, 1975

, 1 1 1 1 1 1 1 1 1

RESILIENT MODULI AFTER 200 LOAOINGS

DEVIATOR STRESS ( FISJ.)

FIG. 5. Effect of stress intensity on resilience characteristics-AASHO road test subgrade soil (after Seed et al. 1967).

GLACIAL TILL

'b d = 106.8 R E S = 85.1 %

I I I I 5 10 15 2 0

DEVIATOR STRESS , (Td (P.S.1.)

FIG. 6. Effect of deviator stress on resilient modulus for glacial till and Regina clay.

sufficiently large to cause failure (Fig. 7 ) . The logarithm of resilient modulus is linear with the logarithm of confining pressure giving rise to an equation of the form:

MR = K x m7'

where K and n = material constants determined experimentally.

Very little data is available on the effect of confining pressure for plastic soils. A series of tests performed by Weimer (1972) showed an insignificant dependence on confining pressure (Fig. 8 ) .

In the past, it has been assumed in the fatigue analysis that the resilient modulus for a cohesive subgrade soil is independent of the confining pressure. Further testing is required to ensure that the confining pressure has been allowed sufficient time to equalize after its application.

(c) Eflect of Matric Suction (u, - u,) The relationship between resilient modulus

and matric suction has been established in two steps. That is, the relationship of matric suction to water content has been determined and the relationship of resilient modulus to water content has been established.

The uniqueness of the relationship between water content and matric suction for glacial till is demonstrated by plotting the results obtained by Sauer ( 1968), Krahn and Fredlund ( 1972), and Weimer (1972) on remoulded

0 - TOTAL VERTICAL STRESS : 6 0 RSJ.

A - TOTAL VERTICAL STRESS : 3 0 PS.1.

0 - TOTAL VERTICAL STRESS : 5 PSI. 100

7 0

CONFINING PRESSURE ( PSI . )

FIG. 7. Effect of confining pressures on the resilient moduli of sand measured in repetitive load triaxial tests (from Seed et al. 1967).

FREDLUND ET AL.: DEFORMATION CHARACTERIZATION

3 000 I I I I I I I I I 0 5 10 15 20 25 30 35 40

CONFINING PRESSURE ( RS.1.)

FIG. 8. Effect of confining pressure on resilient modulus for glacial till (from Weimer 1972).

180, I I I I I

\ * SAUER (1967

+ WEIMER (1972)

A KRAHN A N D FREOLUND (1972

120 \. 100

linear from a water content of 10 to 14% where it breaks into a parabolic shape.

Figure 10 shows the relationship for glacial till between resilient modulus and water content for 10 000 and 1000 repetitions of loading (Sauer 1968). On the basis of the data available, the relationship is essentially linear. Cross- plotting (Fig. 1 1 ) demonstrates a second-order relationship between matric suction and resilient modulus.

Figure 12 shows the water content versus matric suction relationship for Regina clay (Mickleborough 1970; Krahn and Fredlund 1972; Bergan 1972). Although there is some scatter when all the data is combined, the relationship tends toward uniqueness for each set of samplcs tested. The scatter is related to slight variations in the material properties since the materials tested by each investigator were from different sources.

There is only a limited amount of data available on the relationship between resilient modulus and water content for Regina clay (Bergan 1972). However, the available data gives an indication of the relationship between resilient modulus and matric suction for that material (Fig. 13). WATER CONTENT ( % I

FIG. 9. Water content versus matric suction for glacial till. (d) Eflect of Freeze-Thaw Cycles

A well-defined secondary structure and def- inite ice segregation is evident in compacted samples subjected to freeze-thaw cycles (Ber- gan and Fredlund 1973). About three freeze- thaw cvcles amear necessarv to establish a new

samples prcpared from the Qu'Appelle moraine (Fig. 9 ) . All matric suction measurements were made on a pressure plate apparatus using the null technique. The relationship is essentially

CAN. GEOTECH. J. VOL. 12, 1975

+ - 1 0 0 0 0 REPETITIONS \ ' A - 100 REPETITIONS) SAUER (1967) ~4

- 10 REPETITIONS . - 1 0 0 0 REPETITION - WEIMER ( I 9 7 2 1

L

10 12 14 16 18 20

WATER CONTENT ( % )

FIG. 10. Water content versus resilient modulus for glacial till.

I I I I I I I 0 2 0 4 0 6 0 8 0 100 120 140

MATRlC SUCTION ( RSJ.)

FIG. 11. Matric suction versus resilient modulus for glacial till.

MICKLEBORWGH 11970)

160 A KRAHN AND FREOLUND 11972)

+ BERGAN 11972 )

0 1 I I I I I I 2 4 2 6 28 3 0 32 3 4

WATER CONTENT (%)

FIG. 12. Water content versus rnat;ic suction for Regina clay.

I I I I I I

MATRlC SUCTION ( P.S.I.)

FIG. 13. Matric suction versus resilient modulus for Regina clay (data from Bergan 1972).

equilibrium in the soil. Associated with the freezing and thawing phenomena is a significant reduction in the matric suction of the soil.

Weimer ( 1972) measured the matric suction on compacted glacial till after five freeze-thaw cycles (Fig. 14). The reduction in suction was


WATER CONTENT ( % )

FIG. 14. Reduction in matric suction for glacial ti l l subjected to freeze-thaw cycles.

substantial below optimum water content, diminishing above optimum water content. A similar reduction (Mickleborough 1970) in matric suction has been observed for Regina clay (Fig. 15). Bergan (1972) found that similar reductions in matric suction occur in undisturbed subgrade samples during the spring of the year. Figure 1 demonstrates the increase in deflections during the spring of the year and it is pertinent to ask whether the increased deflections are a unique function of matric suction.

Test results on glacial till (Weimer 1972) showed a reduction in resilient modulus of approximately 4000 p.s.i. (280 kg/cm2) after five freeze-thaw cycles. The sample was at the optimum water content of 19% and was tested with a confining pressure of 10 p.s.i. (0.7 kg/cm" and a deviator stress of 10 p.s.i. (0.7 kg/cm2). The reduction in matric suction after five freeze-thaw cycles was approximately 7 p.s.i. (0.5 kg/cm2). Referring to Fig. 11, the predicted reduction in resilient modulus would be approximately 3000 p.s.i. (210 kg/cm2) if the relationship (i.e. M , versus (u,, - u,,.)) was unique through freezing and thawing.

Cullev ( 197 1 ) also showed that substantial

glacial till as a result of freezing and thawing (Fig. 16). The glacial till tested was of lower plasticity than that tested by Sauer (1968), Weimer (1972), and Krahn and Fredlund ( l972), and since no corresponding matric suction relationship is presented, it is not possible to get an indication if the resilient modulus versus water content relationship is unique. Table 2 shows the reductions in resilient modulus as a result of freeze-thaw cycles on Regina clay.

Due to the limited amount of data, it is not possible to definitely confirm the uniqueness of the suction versus resilient modulus relationship during freezing and thawing. The limited results appear to support uniqueness.

Summary In spite of extensive complications induced

by freeze-thaw and other variables, the evidence indicates that the definition of resilient deformation of the subgrade can be resolved in terms of stress state variables. For example, the resilient modulus can be defined as a function of: (i) (ul - a3), (ii) (03 - u,), and (iii) (u,, - u,,.).

This gives rise to a practical, but theoretical, basis for predicting fatigue failure.

MICKLEBOROUGH ( AFTER 4 FREEZE - THAW CYCLES 1

+ BERGAN

(AFTER 2 FREEZE- THAW CYCLES 1

+ ;; 0

24 26 28 30 32 34

WATER CONTENT ( % )

FIG. 15. Reduction in matric suction for Regina , . - reductions in resilient modulus occurred in clay subjected to freeze-thaw cycles.

CAN. GEOTECH. J. VOL. 12, 1975

TABLE 2. Effect of freeze-thaw cycles on resilient modulus of Regina clay

Resilient modulus (p.s.i.)*

Prior to After freeze-thaw freeze-thaw w (%> Y d Remarks

Undisturbed samples 6100 3700 33.7 82.2 Regained original M,

after 10 000 repetitions 5800 3800 34.8 83.1 Regained original MR

after 10 000 repetitions Remolded samples

15 000 6500 33.0 - Average of five tests

*For all tests, a3 = 2 p s i . (0.14 kg/crnz) and od = 5 p.s.i. (0.35 kglcrn2).

STANDARD AASHO \ \ MAX. rd * 114.0 RCF \ \ OPT. W U = 14.9 X \ + t LlOUlD LIMIT 33.0 \ PLASTIC LIMIT I58

I t I00 % STANDARD

AASHO

WATER CONTENT ( % )

FIG. 16. Effect of freeze-thaw on the resilient modulus of glacial till (after Culley 1971).

constitutive relationships. Therefore it may be possible to account for the effects of freezing and thawing by a drop in matric suction. Fur- ther verification is required on this aspect.

BERGAN, A. T. 1972. Some considerations in the design of asphalt concrete pavements in cold regions. Ph.D. Dissertation, University of California, Berkeley, California.

BERGAN, A. T., and FREDLUND, D. G. 1973. Characteriza- tion of freeze-thaw effects on subgrade soils. Pre- sented to the Symposium on Frost Action on Roads, Organization for Economic Cooperation and De- velopment, Oslo, Norway.

BIOT, M. A. 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12, pp. 155-163.

COLEMAN, J. D. 1962. Stresslstrain relations for partly saturated soils. Geotechnique, 12(4), pp. 348-350.

CULLEY, R. W. 1971. Effect of freeze-thaw cycling on stress-strain characteristics and volume change of a till subiected to reuetitive loading. Can. Geotech. J.

The resilient modulus can be linked with the stress state variables by observing the behavior of samples under repeated loading conditions. Typical forms of constitutive relationships are presented; however, further research is required to completely verify their uniqueness and form for various soils.

The objective of the analysis is to be able '

to predict seasonal changes in resilient modulus, which in turn are estimated from microclimatic conditions.

The effect of freeze-thaw cycles does not appear to produce significant hysteresis in the

DEHLEN, G. L. 1969. The effect of non-linear material response on behavior of pavements subjected to traffic loads. Ph.D. Thesis, University of California, Ber- keley, California.

FREDLUND, D. G. 1973. Volume change behavior of unsaturated soils. Ph.D. Thesis, University of Alberta, Edmonton, Alberta.

FREDLUND, D. G., and MORGENSTERN, N. R. 1973. Pres- sure response below high air entry discs. Third inter- national conference on expansive soils, Vol. 1, Jerusalem Academic Press, Israel.

HAMILTON, A. B. 1966. Freezing shrinkage in compacted soils. Can. Geotech. J. 3(1), pp. 1-17.

KRAHN, J., and FREDLUND, D. G. 1972. On total, matric and osmotic suction. Soil Sci. 114(5), pp. 339-348.

LIDGREN, R. A. 1970. Volume change characteristics of compacted till. M.Sc. Thesis, University of Saskatch- ewan, Saskatoon, Saskatchewan.

MCLEOD, D. R. 1971. Some fatigue considerations in the design of thin pavements. M.Sc. Thesis, University of Saskatchewan, Saskatoon, Saskatchewan.

MICKLEBOROUGH, B. W. 1970. An experimental study of the effects of freezing on clay subgrades. M.Sc.


Thesis, University of Saskatchewan, Saskatoon, Sas- katchewan.

NACHLINGER, R. R . , and L y n o ~ , R. L. 1969. continuum theory of moisture movement and swell in expansive clays. Res. Rep. 118-2, project 3-8-68-118, Centre for highway research, the University of Texas at Au- stin, Texas.

OLSON, R. E., and LANGFELDER, L. J. 1955. Pore water pressures in unsaturated soils. Roc. Am. Soc. Civ. Eng. 91, pp. 127-150.

RICHARDS, B. G. 1965. An analysis of subgrade conditions at the Horsham experimental road site using the two- dimensional diffusion equation on a high-speed digital computer. I n Moisture equilibria and moisture changes in soils beneath covered areas. Edited by Aitchison, G. D. Butterworths, Australia.

SAUER, E. K. 1967. Application of geotechnical principles to road design problems. Doctor of engineering thesis, University of California, Berkeley, California.

SEED, H. B., MITRY, F. G., MONISMITH, C. L., ~ ~ ~ C H A N , C. K. 1965. Prediction of pavement deflections from laboratory repeated load tests. Rep. No. TE-65-6, Eng.: Office of Research Services, University of California, Berkeley, California.

THORNWAITE, C. W. 1948. An approach toward a rational classification of climate. Geogr. Rev. 38, pp. 55-94. . WEIMER, H . F. 1972. The strength, resilience, and frost durability characteristics of a lime-stabilized till. M.Sc. Thesis, University of Saskatchewan, Saska- toon, Saskatchewan.

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