Relationship of Mean Stress, Volumetric Strain and Dynamic Loads in Soil

The changes in soil consolidation resulting from externally applied forces and the effect of these changes on the physical properties of the soil have been studied by many individuals. Unfortunately their results have not produced an adequate agricultural soil mechanics. The development of soil stress-strain relationships which will permit the prediction of the changes in the state of compaction caused by various implements and power units will be a major contribution toward controlling soil compaction. Disciplines Agriculture | Bioresource and Agricultural Engineering Comments This article is published as Harris, W. L., W. F. Buchele, and L. E. Malvern. "Relationship of Mean Stress, Volumetric Strain and Dynamic Loads in Soil." Transactions of the ASAE Vol. 7, no. 4 (1964): 362. DOI: 10.13031/2013.40781. Posted with permission. This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/abe_eng_pubs/984 Relationship of Mean Stress, Volumetric Strain and Dynamic Loads in Soil W. L. Harris, W. F. Buchele, and L. E. Malvern MEMBER ASAE MEMBER ASAE T changes in soil consolidation resulting from externally applied forces and the effect of these changes on the physical properties of the soil have been studied by many individ­ uals. Unfortunately their results have not produced an adequate agricultural soil mechanics. The development of soil stress-strain relationships which will permit the prediction of the changes in the state of compaction caused by various implements and power units will be a major contribution toward controlling soil compaction. An investigation by V a n d e n B e r g (5)* revealed that the concept of con­ tinuum mechanics could be used as a mathematical model for studying the soil-compaction problem. W i t h this model the forces acting on a volume element may be described by a set of quantities in the form of a stress tensor. He found that the volumetric strain, which is the change in compaction, can be expressed by the change in bulk density or the change in percentage of total pore space. To define the state of stress at a point requires the de­ termination of six independent values. The hypothesis that volume strain is governed by the mean normal stress acting on the element was proposed by VandenBerg (5) . The purpose of the investigation re­ ported in this paper was to use con­ tinuum mechanics in the study of vari­ ous soil stress-strain relationships. The hypothesis that changes in the mean normal stress control changes in volu­ metric strain was tested by measuring the components of the stress tensor and changes in bulk density while the soil was subjected to dynamic loads of vari­ ous magnitudes. Presented as Paper No. 61-604 at the Winter Meeting of the American Society of Agricultural Engineers at Chicago, 111., December 1961, on a program arranged by the Power and Machinery Division. Authorized for publication as Journal Article No. 2987 of the Michigan Agricultural Experiment Station. The authors—W. L. HARRIS, W. F. BUCHELE, and L. E. MALVERN—are, respec­ tively, former graduate research assistant, Mich­ igan State University. East Lansing (now assis­ tant professor of agricultural engineering, Uni­ versity of Maryland, College Park); former associate professor of agricultural engineering, Michigan State University, East Lansing (now professor of agricultural engineering, Iowa State University, Ames); and professor of applied me­ chanics, Michigan State University, East Lansing. Acknowledgment: The authors express their appreciation to the Land Locomotion Laboratory, Ordnance Tank-Automotive C o m m a n d , U.S. Army, Detroit, Mich., for assistance and co­ operation in connection with the research study reported in this paper. * Numbers in parentheses refer to the ap­ pended references. 362 FIG. 1 Six-directional stress transducer used to measure components of stress ten­ sor. A series of 27 laboratory tests of five replications composed of three depths below the loading surface, three mois­ ture contents, and three rates of load­ ing were conducted using a Brookston sandy loam. A description of the tests is given in Table 1. Electrical s t r a i n g a g e transducers, Type A, developed by Cooper (1) and a six-directional s t r e s s t r a n s d u c e r (6DST) developed by Harris (2) Fig. 1, were used to measure and record the normal stresses necessary to calcu­ late the components of the stress ten­ sor. A strain-gage force transducer was used to measure the total vertical force applied to the loading plate. Recording volumetric transducers similar to the one developed by Hovanesian (3) were used to measure changes in bulk den­ sity. Procedure The controlled variables in this in­ vestigation were moisture content, rate of loading and state of stress. Each series of tests was conducted by filling a 55-gal drum (soil tank) to the de­ sired level below the loading surface. A circle 12 in. in diameter was located in the center of the tank. The stress trans­ ducers and b a l l o o n s for measuring changes in bulk density were placed on the periphery of the circle as shown in Fig. 2. The tank was then filled to the operating level and the surface leveled. The loading plate was properly positioned and the recording instru­ ments activated. The surface load was then applied hydraulically. TABLE 1. DESCRIPTION OF THE LABORATORY TESTS Test no. Depth, in. Rate of loading, in ./sec Moisture Initial bulk content, density, percent gm/cc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 10 5 15 10 5 15 5 15 10 15 10 5 10 5 15 10 5 15 10 5 15 10 5 15 10 5 15 0.62 0.62 0.62 0.38 0.38 0.38 0.38 0.38 0.38 0.62 0.62 0.62 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.62 0.62 0.62 0.38 0.38 0.38 1.00 8.63 9.89 11.59 11.56 8.89 7.97 11.35 11.39 11.38 12.63 12.43 12.46 17.41 17.41 14.85 14.85 14.34 12.31 10.95 10.79 17.93 17.52 17.67 16.16 15.78 16.05 16.54 1.08 1.08 1.06 1.06 1.07 1.08 1.08 1.09 1.06 1.06 1.08 1.09 0.94 0.94 1.01 1.02 1.03 1.08 1.06 1.06 0.93 0.91 0.95 1.00 0.98 0.98 0.96 FIG. 2 Stress transducers used to obtain data. and balloons Upon completion of a test the soil and instruments were removed from the tank. The soil was passed through a % X 2-in. screen to remove large blocks of soil formed during the compaction process. Results and Discussion In order to verify the hypothesis that the changes in soil compaction developed under dynamic conditions are controlled by the changes in mean normal stress, two things must be dem­ onstrated : (a) That mean normal stress does correlate with changes in bulk density (b) That the deviator stress tensor does not correlate with changes in bulk density. The only measure of the spherical stress tensor is mean normal stress. Many expressions can be used as a measure of the deviator tensor. Since earlier investigations had indicated a TRANSACTIONS OF THE ASAE • 1964 relationship between maximum shear stress (an invariant of the deviator ten­ sor) or maximum normal stress (which depends on the deviator tensor as well as on the mean stress) and bulk density, these relationships were investigated. The values of mean normal stress (am), the m a x i m u m s h e a r stress, the maximum normal stress and the second invariant of the stress deviator tensor were computed from four meas­ ured normal stress values obtained with Type A cells using the appropriate formulas as reported by VandenBerg (5) . The values for the 6DST were computed from six measured normal stresses using the formulas reported by Harris (2) . Mistic, an electronic digital computer at Michigan State Univer­ sity, was used to make the lengthy cal­ culations involved in evaluating the equations and the statistical analysis of the data. The sum of least squares method was used to determine the best predicting relationship for the data plotted on semilogarithmic paper. The regression equa­ tions, estimates of standard error (bXy) and confidence limits for both the Type A and 6DST data are given in Table 2. The Type A data is designated by an A following the test number and the 6DST data by only the test number. The calculated values of t were com­ pared with the distribution of t using the degrees of freedom (DF) shown. All calculated values were highly sig­ nificant, which means that the regres­ sion coefficients or slopes are different than zero. The true regression coef­ ficient is within the limits presented for each relationship. Assuming a normal distribution of error, one standard er­ ror (Sxy) would include 68.3 percent of the values used to determine the regression equation. The data obtained with the six directional transducer are consistently more varied than the data TABLE 2. Test no. STATISTICAL ANALYSIS FOR MEAN NORMAL STRESS VERSUS BULK DENSITY Regression equation Syx DF t Confidence limits 15 DEPTH TEST 7 210" DEPTH TEST 9 315" DEPTH TEST 8 1.20 1.25 BULK DENSITY GM/CC FIG. 3 Mean stress vs bulk density re­ lationship. 1964 • TRANSACTIONS OF THE ASAE 1 1A