INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING
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A Method of Estimating Seulement by Roller Compaction Méthode de Calcul du Tassement à Attendre d’un Compactage au Rouleau
by G. Kuno, Japan Highway Public Corporation, Tokyo, Jap an an d T. Mogami, University of Tokyo, Tokyo, Japan
Summary Sommaire A method of estimation of seulement in field compaction is pre- Cette communication présente une méthode de calcul des tasse sented. It depends upon the performance of confined compression ments à attendre du compactage sur un chantier. EUe comporte tests in the laboratory which give the compression characteristics of tout d’abord l’exécution en laboratoire de l’essai de compression du soil. Calculation, by Frôhlich’s équation, of the stress distribution sol dans une enceinte rigide; on en déduit les caractéristiques de com in a fill induced by a roller combined with these results gives the pression des sols. wanted estimation of the settlement. The settlement which has En combinant ces résultats, avec le calcul des contraintes produites already been attained by N passages can be estimated by Sasaki’s lors du compactage, que l’on déduit de la formule de Frohlich, on formula. peut évaluer le tassement. Le tassement atteint après N passages de rouleau est donné par la formule de Sasaki. Introduction Since Proctor published his first report in 1933, work in this The relationships of void ratio e0 and dry density yd0 when field has been developed to the stage where the use of laboratory Fundamental Considérations From équation 1 the compressive strain of the specimen is Compressibility characteristics o f soils—Equation 1 expressing written the relationship between compressive stress cr and void ratio e of compressed soil was proposed by Terzaghi and others. e = T = r h l {ei ~ eo) + Cc lo g l° 3 • • • • (2) e = e0 — Cc log10 cr/oo ----- (1) where e,- is the initial void ratio of soil. Putting the pressure affects the value of Cc if the loading velocity is high enough not to dissipate the pore pressure during its acting Earth pressure induced by a roller—The earth pressure in period. duced by a roller is usually estimated by the formula due to Soils for constructing earthworks are not always in the Boussinesq, Frohlich, etc. In these computations the total saturated state, and moreover the loading velocity of common- weight of equipment is distributed uniformly on the contact type rollers is not so high, therefore the effect of pore pressure area between the equipment and the ground surface. on Cc can be neglected. Much larger maximum vertical earth pressures were observed The results of the confined compression tests with the in our laboratory and in the field than those computed by the apparatus illustrated in Fig. 1 are shown in Figs. 2 and 3. above said procédure. Therefore, it may be considered that 134 the load distribution on the contact area is not uniform but If we assume that the p is W/B, équation 6 becomes concentrated at the centre of the loaded strip. W After the actual measurements of earth pressure, a more °Zmax — f ... (7) reasonable way of computation was obtained by considering ZB the infïnitely extending line distribution of load, in place of the where W is the weight of compaction equipment, and B is the uniformly distributed area load. contact width thereof. The stress analysis with the line load is much simpler and is Using the values of o-Zm3X observed in the field for several accurate enough for practical problems so long as the depth considered in the problem is moderate. Because the problem is considered as a two-dimensional one when the line load distribution is assumed, and since the actual width of a roller 0 \ ° \ is finite, this assumption is reasonable only when the above said v\ ° / c y restriction is satisfied. y Oo y y o é Loam o y s y s o / • •/ / • < •/ y /• / Fine sand / 0-4 06 1-2 Fig. 3 Relation between eo and Cc Relation entre eo et Cc types of roller, the values of v were calculated by équations 5 and 6. In général, values of v of 3 to 5 for loamy soil, and 5 to 6 for sandy soil were obtained. Seulement o f a fill due to the passages o f a roller—The seule ment Ah of a fill developed by the Mh passage of a roller is Fig. 2 Results of one-dimensional compression test Résultats des essais de compression à une dimension By Frôhlich’s formula, the vertical stress az due to the load p per unit of the length of a straight line of infinité extension is given by ctz =/-2CrP 0sl'+ 1 6 . . . . (4) in which the value v is called the concentration index, / is a function only of v represented by , 1 (v - 1)Q - 3)(v - 5) . . . 4-2 (when v is odd) J tt'(v — 2)(y — 4 )0 — 6) . . . 5-3 1 (V - 1)0 - 3)0 - 5 ) . . . 5-3 (when v is even) 2 \ v - 2)0 - 4)0 - 6) . . .4-2 Fig. 4 .... (5) expressed by the following empirical formula (Sasaki, J. 1952). and the other notations are illustrated in Fig. 4. The uz is maximum when 6 is zéro and this maximum is Mechanism in the compaction of the sand layer (2). Bulletin given by Nat. Inst. Agric. Sci., Japan, Sériés F, No. 5) N — f 1' .... (6) Ah = .... (8) °Zmax — / £ a + bN 135 in which a and b are coefficients. It will be shown later that The relationship between the thus obtained a and concentra these coefficients are connected with each other. tion indices v which was calculated in the preceding section is The ultimate value of Ah for an infinité number of passages shown in Fig. 7. is given by 1/6. It can be concluded from Figs. 5, 6 and 7, that the value a Equation 8 is accurate for any type of roller and for any depends on the characteristics of the stress concentration of thickness of a layer. soil, whereas fï is independent of soil properties. Estimation of Compaction with a Roller jj£ '12 * Method of estimation—The quantitative estimation of com - i=0-936b-0-150 / paction with a roller from laboratory data is made as follows : 10 W hen an earth fill is compacted with a roller, every part of soil « under the tread of the roller is compressed by the compressive - .y/ • stress azmax which is given by équation 6 or 7, and the volume OS • • is contracted in the région where aZmax is larger than the pre- • • • y: - • «• compression stress 07, determined by équation 3. If the one- 06 * • dimensional compression expressed by équation 2 can be - X* * assumed in calculating the volume change in each horizontal r/ # 0-4 • / J • slice of soil, the settlement at the depth Z due to a passage of a \y.- • • • - roller will be given by • 02 m z - j;%„z. - „ ) + c, i»g10s } e 1 1 / 1 . L _ . L . 1 1 .... (10) 0 0-2 04 06 01 10 1-2 H b 1/cm in which Z 0 is the depth from the surface to the place where Fig. 5 Relation between a and b Oaboratory test) - 0 Po • T by laboratory compression tests, and also et is known prior to 015 field compaction work. Therefore the settlement at the depth T oi Z , Ahz , can be estimated assuming that et is distributed - 1 W ê uniformly / 0-10 $ / - y / Ahz = j-j— [z0+MCc - z{(e, - e0) + Cc(logl0^ + m)}] ç y » s .... (11) 005 r i •r (when Z 0 â initial thickness, hh of the fill or layer), or 0/ Fj ,*p s . / R A h z = rri;H (e' “ eo) + Q(logloâ- + M)l 1 /1 /: / p. , ■Pi 1 0 0 02 006 010 0-14 013 — Z^(e,- — e0) + Cc{ \o g itj^ 2 ^ ) } ] ' ' ' ' b 1/cm Fig. 6 Relation between a and b (field test) (when Z 0 > A,-) in which M is a constant *|°gl° X = 0-4343, and Relation entre a et b (essai de chantier) On the other hand, plots in Fig. 6 were obtained from field Z 0 -/ixloV -’-/|« p (^ ) ....(13) compaction tests. Fig. 6 shows that a straight line can be fitted through each set of plots for each fill material, and these Taking Z to be zéro in équation 11 or 12, the total settlement lines intersect the ordinate at about — 0-150 l/cm. Therefore, of a fill, that is, the settlement of the surface, can easily be assuming /3 to be 0-150 l/cm, values of cc can be obtained from obtained. équation 9 and each plot on Fig. 6. The settlement AhN of a fill by the M h passage of a roller is 136 given by équations 8 and 9, if the settlement of a fill due to the The compaction control by measuring settlement is more first passage of a roller is designated as Ahu practical than that with measurement of density, because the (1 + «)N détermination of field density cannot be made without con àhN - (14) sidérable error. In this case, however, the excess settlement _*_(«* + N ) + _ 1) due to latéral displacement under the tread of a roller should be carefully separated. Examples of estimation o f settlement (a) Case of a model roller—A wooden flat-wheel roller (10 cm in diameter, 20 cm in width) was used for the model compaction test. Some of the measured settlements for sandy soils are shown in Fig. 8. The test conditions are shown in Table 1. Table 1 W in kg *% W: weight of the roller e^: initial void ratio iv : water content of soil h^: initial thickness of soil Iayer Results of one-dimensional compression tests for the same soils and calculated values of Z0 are shown in Table 2. The concentration index v for loose sandy soil was taken to be 6. Table 2 eo Ce Zo in cm a 1-35 0-600 25-6 ° Measured -Calculated b 111 0-495 36-4 Fig. 8 Settlement at the depth Z within a fill by the first passage of c 108 0-480 30-9 model roller d 1-44 0-635 36-6 Tassement à la profondeur Z en le remblayage par le premier passage du modèle rouleau In Fig. 8, the measured settlements due to the first passage The degree of compaction which has already been attained of a roller are plotted by circular marks and results of cal- by N passages can be estimated from the following équation culation with équation 12 are shown by real lines. AtlN - N - N (15) (b) Case of field compaction with four kinds of equipment— lim Ah - BAh Two examples obtained from field compaction tests are shown r + N ! + N N —>00 1 +j8Ah in Table 3. Contact pressures in the third column of Table 4 were calculated from the second column. Table 3 Measured Calculated Loam Sandy loam Sandy loam Initial thickness of about 50 cm about 50 cm roller) a layer Natural water con 123-3% 33-0% tent Liquid limit 150-2% 47-4% Plasticity index 21 -7 17-5 eo 4-53 1-45 Ce 2 11 1-105 V 3 3 Ahi (cm) Ahi (cm) (pneumatic - tyred' roller) Zo ______1______I_____ ei Zo et (cm) calcu mea (cm) calcu- mea- Fig. 9 Settlement of the surface of a fill developed by the Nth lated sured lated sured passage of roller Tassement de la surface du remblayage développé par N Pneumatic-tyred passages du rouleau roller 4-43 28-5 11-1 9-3 Tamping roller 4-70 14-8 5-5 2-7 1 -69 21 1 3-8 i 7-1 The estimation of the obtained density can be made from the Tandem road roller 4-70 23-0 8-5 8-7 1-55 24-5 4-6 ! 6-4 settlement data (équation 11 or 12) of every slice of soil, if Tractor 4-72 22-4 8-2 8-6 1-69 31 -2 5-1 ; 10-3 wanted. 137 Table 4 roller passage in Fig. 9. The values a and fi in équation 14 are obtained; that is, a = 2-56, /3 = 0-150cm-1, from Fig. 7, Weight o f equipment Contact pressure assuming v to be 3. in tons p in kg/cm Pneumatic-tyred roller 6 50 0 Tamping roller 2-31 19-3 Conclusion Tandem road roller 6 300* Estimation of settlement in the field compaction works can be Tractor 16 28-5f made by the proposed method with data obtained in the * Contact pressure at the rear wheel laboratory. It was established with some simplifying assump- t The weight of a tractor was assumed to be unifonnly distributed for five guiding tions and hypotheses. wheels It is hoped to carry out future research to remove such Calculated settlements are plotted against the répétitions of ambiguities. 138