Minimization of the energy consumption of soil deformation

Journal of Terramechanics, 1980, Vol. 17, No. 2, pp. 63 to 77 Pergamon Press Ltd. Printed in Great Britain © International Society for Terrain Vehicle Systems

MINIMIZATION OF

0022--4898/80/0601--0063 802. 00/0

OF THE ENERGY CONSUMPTION SOIL DEFORMATION M. SPEKTOR*

Summary--A study has been performed enabling the minimization of energy consumption during formation of residual strains in cohesive soils, with the aim, for example, of shaping holes. It is demonstrated that minimization of energy consumption is achieved within a definite regime of the soil-implement interaction. This regime is characterized by sequential repetition of the soil's loading and unloading. Within this regime, the controlling factor in ensuring a minimal energy consumption is the magnitude of implement displacement during the soil loading stage. As a result of analytic studies, based on corresponding experimental curves, expressions were obtained for determining the magnitude of displacement at which the minimum value of the soil-deformation energy consumption is reached. It is demonstrated that modern machines with cyclic action (vibration, vibro-impact etc.), intended for the shaping of horizontal and slanted holes for drain arrays and other communication channels, as well as those intended for pile driving, and the shaping of vertical holes for filling piles, operate at regimes characterized by relatively high energy consumption. The development and introduction into service of analogous novel machines based on the results of the present investigation may ensure considerable savings of energy, while simultaneously increasing the productivity of these machines. It is essential to note that the proposed work enables understanding the controversy arising from the opinions of various authors, on the subject of comparison of energy consumption of cyclic and quasi-static processes of soil-implement interaction, thus enabling the elimination of that controversy. INTRODUCTION THE ENERGYconsumed by the working processes o f machines intended for the shaping o f holes in cohesive soils, by the method o f inserting sharpened implements, depends, to a considerable extent, u p o n the soils' resistance forces. The resistance forces opposing the implement's penetration into the soil, as shown by numerous studies [1-6], are composed o f frontal resistance acting on the tool's fore shaft (or the tool's fore sharpened part), and external friction distributed along the tool's lateral cylindrical (prismatic) part. In the majority o f these processes, the external friction forces constitute an insignificant part o f the soil's resistance [2], and, in a series o f cases, they are either negligibly small or completely absent (depending upon the design of implement). The soil's frontal resistance forces, however, by exerting the predominant effect on the energy consumption o f the penetration process, do attract considerable interest and attention o f researchers. There are many works dedicated to the study *Faculty of Agricultural Engineering, Technion, Israel Institute of Technology, Haifa, Israel. 63

64

M. SPEKTOR

of frontal resistance forces' dependence upon the soil's properties, the implement's dimensions and shapes, their penetration velocity and loading regimes, as well as the implement's displacement, during the soil's loading and unloading stages [1, 4, 7-33]. Based on the analysis and generalization of studies on the soil's frontal resistance forces, we have developed a hypothesis as to the dependence of these forces upon the implement's displacement [5]. In the first approximation, this hypothesis makes it possible to find out the analytic solution to the problem of minimizing the energy consumption of the process of implement penetration in soil, for certain particular cases. In these cases, the minimization of energy consumption is achieved by realization of a special regime for cyclic tool-soil interaction. It is proposed to define that regime as an optimal one, and its parameters are defined on the basis of the stated analytic solution [6, 34, 35]. The present paper contains an attempt to solve the problem of minimizing energy consumption for the general case of implement penetration in the soil, and the finding of general analytic dependencies among the parameters for optimal regimes of soil-implement interaction in the hole-shaping process. CERTAIN PECULIARITIES OF THE SOIL LOADING AND UNLOADING PROCESS The analysis and generalization of a series of studies of the quasistatic and dynamic regimes of implement penetration in soil enable expressing, graphically, the dependence of the soil's frontal resistance force R upon the implement's displacement x, during the soil's loading and unloading stages [1-5, 7-14, 17]. This dependence has a very stable aspect within the alteration range of physical-mechanical properties of cohesive soils, load regimes, and parameters of implements conditioned by real working processes. Figure 1 is a generalized graph of the dependence of any random soil resistance upon the implement's displacement. The curve OABCD, termed 'Loading Curve', characterizes the process of continuous implement penetration into the soil, thus reflecting the peculiarities of the soil-loading process (or the soil-loading stage). Curves ANO, BB1, CC1, and DD 1 termed 'Unloading Curves', characterize the peculiarities of soil-unloading process (or soil-unloading stage). As is known, at unloading, some reverse deformation, or rebound, occurs, under the effect of the soil's elastic properties. Experimental investigations of continuous and cyclic implement penetration in soil have shown that the soil-loading stage can be divided into three parts, each of which is characterized by definite laws for the alteration of frontal resistance force and soil deformation. Curve OMA reflects the peculiarities of implement and soil interaction during the first part of the loading stage, in which, in the first approximation, only reversible soil deformations are originated. Thus, point A on the abscissa represents the tool's boundary displacement c in the process of generating fully reversible deformations. At the interruption of load action, the soil's deformations disappear corresponding to displacement c, i.e. there occurs a soil unloading the laws of which are characterized by curve ANO. Therefore, the closed OMANO curve may be assumed to constitute a hysteresis loop.

MINIMIZATION O F T H E E N E R G Y C O N S U M P T I O N

O F SOIL D E F O R M A T I O N

C A

65

D

B

E

tw

x $

i

i

b

]

i t tm

FIG. 1. Generalized graph of the dependence of the soil's frontal resistance force R upon the implement's displacement x.

Obviously, if the implement displacement is less than magnitude c, then, upon removing the load, soil deformations will disappear. Thus, the propagation of residual deformations is possible only in cases where the implement displacement exceeds magnitude c; at this, there takes place the second part of the loading stage, characterized by the simultaneous propagation of reversible and irreversible soil deformations, at continuous increase of the soil's frontal resistance, up to a given boundary value. The curve ABC represents the laws of implement-soil interaction during the second part of the loading stage. If the load is removed at a random point B of the loading stage's second part there occurs a soil unloading, characterized by curve BB1, in which the implement displacement, corresponding to the soil's reverse deformations, has, in the first approximation, a value of c. In this case, as seen from Fig. 1, the residual deformation corresponds to the difference S-c. The third part of the loading stage is characterized by the propagation of reversible and residual deformations at a boundary value of the soil's frontal resistance force Rm~x, at which the laws of implement-soil interaction are reflected by the straight line CD. If at a certain point D the load is removed, then soil unloading is characterized by curve DD1 for which the soil's residual deformation corresponds to the difference of the abscissas of points D and D1, and constitutes magnitude 1. Experiments show that the magnitude of reverse displacement for soil unloading in the second and third stages can be assumed equal to the boundary displacement for the first loading stage, i.e. to magnitude c [15-17]. It should be noted that, in all these cases, the unloading curves possess similar characteristics [15-17]. It must be stressed that precise determination of the coordinates of points A and C is very difficult; yet, for practical purposes, it is not difficult to determine experimentally approximate values of these coordinates.

66

M. SPEKTOR

It is also necessary to point out that, for the soils studied, abscissa b exceeds by several times abscissa c [15-17]. Experimental investigations of the cyclic loading and unloading process have shown that, after about ten cycles, the soil's modulus of elasticity practically remains constant [36]. The analysis of experimental data on the cyclic implement penetration in soil reveals that the dependence of the frontal resistance force upon the implement displacement is not altered, if considerable residual deformations are propagated (i.e. the second or third loading stage is entered) and if each subsequent loading stage occurs after a complete soil unloading [15-17]. Thus, for cyclic implement penetration in soil, hole formation can be realized at pre-boundary values of the soil's frontal resistance force. The experimental data lead to the conclusion that cohesive soils do not become more compact, nor do they become less compact as a result of repeated implement penetrations, and thus possess the properties of the so-called 'Cyclic Ideal Materials' [37].

ENERGY EXPENDITURE MINIMIZATION IN SOIL DEFORMATION Nowadays, no analytic expressions for soil loading and unloading are known. For the loading curve OMABCD, the dependence of soil frontal resistance force R upon implement displacement x, at a continuous penetration rate can be expressed in the following manner: r f ( x ) for 0 < x :: b

R = t Rma~ for x > b, where the function R = f ( x ) is given by a graphical method, and certain of its properties are determined from the analysis of experimental data. These data reveal that the function R = f ( x ) is continuous, single-valued, increasing and defined in a closed interval [0, b), for which f ( 0 ) > O,f(b) = R m a x and that it is also a smooth function, capable of possessing points of inflection in that same interval. It is obvious that, if the displacement per cycle is smaller than or equal to magnitude c, then the energy consumption of the hole shaping process tends to infinity. If, however, the displacement only slightly exceeds magnitude c and, consequently, the residual deformation per cycle is relatively low, then the process's energy consumption will be relatively very high. As displacement per cycle is further increased, a decrease of the energy consumption of the cyclic hole shaping process may be expected. Yet, the displacement increase per cycle leads to the increase of the soil resistance force upon which the energy consumption of the process is considerably dependent. Thus, there arises the possibility of the existence of a certain optimal value of the displacement magnitude per cycle, at which minimum energy consumption of the hole shaping process is achieved. In order to verify the existence of an optimal value, let us consider the case of cyclic hole shaping characterized by the segment of loading curve OMABC, corresponding to the second loading stage. Let us assume that the implement's weight and the soil's external friction are negligibly small. The energy expenditure necessary for an implement displacement of

MINIMIZATION OF THE ENERGY CONSUMPTION OF SOIL DEFORMATION

67

magnitude S in the soil loading process will be determined, as seen from Fig. 1, from the following expression: s

E, = I f ( x ) dx.

(1)

o

At unloading, the soil's regeneration forces can return to the working device an energy the magnitude of which is computed as follows:

E~ -= S qo (x) dx,

(2)

0

where tp (x) is a function characterizing the unloading curve and determining the dependence of the resultant of the soil's regeneration forces on the reverse implement displacement. The experimental data enable characterizing certain properties of this function. If, on Fig. 1, the coordinates origin is transferred to point 01, while considering the unloading curve CC1, it can be considered that function tp (x) has a convex curve directed downwards, and constitutes a continuous, increasing function, defined in the closed interval [-- c, 0] at which ~0(-- c) = 0. At the argument's approximation to nil (i.e. the implement's stopping point at the end of loading stage, and the start of unloading stage), function q~(x) sharply increases to the magnitude of the soil's frontal resisting force encountered at the end of the loading stage. In a series of working processes, energy E, cannot be returned to the working device. Yet, for the case under consideration, we shall assume that this energy is returned to the working device (is recuperated by the working device). We shall also consider the case when a return of energy is not possible. In connection with the case under consideration, the magnitude of energy expended in the course of one cycle of the cavity-shaping process is computed based on equations (1) and (2):

E1 -~ i f (x) dx -- icp (x) dx. 0

(3)

0

The number of cycles necessary for punching a hole of length 1, will amount to:

i

lm--C S--c

l S--c

(4)

Accordingly, for the shaping of a hole of the length stated, it is necessary, in conformity to equation (3) and (4), to expend energy of the following magnitude:

=

-

S--c

x) dx -

I ~(x)

o

dx

.

(5)

68

M. SPEKTOR

Under other conditions equal, the value of function (5) is altered dependent on the displacement alteration per cycle S. In connection therewith, let us perform the function (5) analysis to the extremum, by the variable S. The derivative with respect to S has the following form:

c~S

( SZ - - c~~ f ( S ) ( S -- c) --

If(x) dx + o q~(x) dx o

.

(6)

Equating the first derivative (6) to zero, and taking into account that mmC

(S-

c)"

>0,

let us determine the value of a displacement per cycle Se for a stationary point of function (5):

Se = c

+

~i

Se

1_~ f ( x ) d x -- Icp (x) d x f ( S e ) t-o o

]

(7)

.

In order to determine the stationary point's character, let us investigate the sign of derivative (6) in the vicinity of this point; for this, we shall give the following value to the displacement per cycle:

S . = nc + ~

f (xl d x -- ,,I q~ (x) d x

.

(8)

Thus, ifn < 1, then S, < Se; and, ifn > 1, then S,, > Se. Substituting the value of (8) in derivative (6), and performing the necessary transformation, we will obtain: t~E

c (n -

{c(n-- l)-+-f-~

1) (/,,, -

c)fS~)

f ( x ) dx--itP(x)o

}~

In this expression, the multiplicand co-factor is: c(l m -- c ) f ( S , , )

,

~(n - l) + f~ee)

(X) dx -- oi ~0 (x} dx

>0

]

)~

MINIMIZATION OF THE ENERGY CONSUMPTION OF SOIL DEFORMATION

69

and, consequently, the sign of derivative (9) depends upon the multiplicand in the numerator (n -- 1). Ifn < 1, then 8E/~S, < 0 (S, < S,); and, ifn > 1, then dElOS,, > o (s,, > s,). Thus, crossing the stationary point from left to right, the derivative changes sign from minus to plus, which means that, function (5) has a minimum at the stationary point. From the above it is deduced, for cyclic hole shaping with a displacement per cycle, Se in accordance with expression (7), the minimum energy expenditure is achieved; thus, the parameter Se can be termed the optimum displacement value per cycle. In the case where the return of energy to the working device is impossible, it is necessary to include, in equation (3), (5)-(9) an integral expression characterizing the action of the soil's regeneration forces, i.e. to assume that

i ~ (x) dx = 0. 0

Thus, it will result that the optimum value of displacement per cycle, at which the minimum energy consumption of the cyclic hole shaping process is achieved, is computed from the following expression: 1

=

+

S0e

I f(x)dx.

(10)

Introducing the value of displacement per cycle S,, in conformity to formula (7) in expression (5), we shall determine the minimum quantity of energy which must be spent for cyclic shaping of holes with length !, under the condition that energy Er is returned to the working device. Emin = f ( S e ) I.

(11)

If, on the other hand, it is considered that energy E, is not returned to the working device, then the minimum quantity of energy for cyclic punching of a hole with length 1, in accordance with expression (5) and (10) will amount to: Eomi. = f(So,,) I.

(12)

The magnitude of energy necessary for realizing a continuous penetration of a hole with length ! (i.e. at a quasi-static soil loading), as seen from Fig. 1, is determined in the following manner:

Ea~ = Rmx !

f (x) dx -- - - - 1 - + 1 .

(13)

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M. SPEKTOR

Insofar as parameter c has a magnitude of the order of several millimetres, and parameter b is of the order of several tens of millimetres [17], then, at a value of / of several metres, we will obtain the inequality:

l

b

I f ( x ) dx --

b--

:2/o

/

--

c

<0.01,

(13a)

which increases with an increase in the magnitude of 1. This enables considering, with a precision sufficient for practical purposes, that:

Eo,

=

Rm.~/.

(14)

Sincef(Se) < f(Soe) < Rma x, then comparing the values of expended energy, from expression (11), (12) and (14), we reach the conclusion that the energy consumption of cyclic hole shaping at optimal displacement values per cycle is lower than the energy consumption of continuous hole penetrating (i.e. at a quasi-static soil loading). Based on the above, it can be pointed out that the essence of minimizing energy expenditures on soil deformation, within the process of hole penetrating, consists of the realization of cyclic penetrating characterized by an optimal value of implement displacement per cycle. We shall continue the search for conditions ensuring minimal energy expenditures for cyclic hole penetrating, taking into account the weight of the working device and the soil's external friction force. Based on generally adopted assumptions on the dry friction force, originating between implement and soil, it is possible to determine the energy expended per cycle in overcoming the soil's external friction force:

E/= F(S+c),

(15)

where F is the external friction force. The energy per cycle required to overcome the effect of gravity forces is expressed as follows:

Eg = G(S + c) sin ~,

(16)

where G is the working device's weight, and ~ is the incidence angle between the horizontal and the direction of hole penetration. By means of equations (1), (2), (4), (15) and (16) we can determine the magnitude of energy spent for cyclic penetration of a hole with length h

Efg--S_

' c [i f ( x ) dx + (F + G sin ~t) (S -- c) -- o tp (x) dx ] .

(17)

MINIMIZATIONOF THE ENERGY CONSUMPTIONOF SOIL DEFORMATION

71

Performing the search for the extremum of function (17) with respect to variable S, we arrive at the conclusion that this function acquires a minimum value at a displacement per cycle which is given by the following equation:

I

S:, = c 1 + 2 F f(Sf,) + Gsin~

] + f-~-~r~)lL!:" f ( x ) d x - -

.J~~o(x) dx

].

08)

In the case where energy E, cannot be returned to the working device, then the minimum energy consumption of the process, taking into account the external friction force and the gravity force, is determined from the following expression:

So: = c [ l + 2 F + G sin o~ ] 1 s°zf f(So/f) + f(So/,---~) ! f ( x ) dx.

(19)

Since no limitations whatever are set on the sum F + G sin ~, then it is not excluded that, possibly, S/f or So:s, as computed by formulas (18) and (19) respectively would be greater than the magnitude of b, which constitutes the upper boundary of the area under the function f(x). Therefore, we must determine the value of the sum (F + G sin g)maxfor which we can unconditionally use formulas (18) and (19). In order to do so, we shall assume in equations (18) and (19), that Sir = b, and So:f =- b. Thus, these equations will acquire, correspondingly, that following form:

b=c[l+2(F+GsinoOmax] f (b)

1 [!

+ ~))

f (b)

+

c

f (x) dx -- o[" ~p(x) dx

]

,

f (x) dx.

Solving these equations relative to the sums of friction and gravity forces and taking into account that f (b) = Rmax, we will obtain: (F + G sin ~)max ----- ~c1 [Rm=(b

--

c)

--

b f(x) dx + i cp (x) dx ] ,

J' 0

1 (F + G sin ~)omax--=~c

[ Rm~(b -- c) -- Ib0 f ( x ) dx ] .

(20)

0

(21)

Thus, if the sum of friction and gravity forces does not exceed values in agreement with formulas (20) and (21), then the minimization of the energy consumption of the

72

M. SPEKTOR

hole penetrating process is achieved at optimal values of displacement per cycle, computable in accordance with formulas (18) and (19). QUANTITATIVE EVALUATION OF MINIMIZATION OF THE ENERGY CAPACITY FOR THE HORIZONTAL HOLES SHAPING PROCESS The comparison of energy output of existing machines for shaping holes with minimum energy consumption, achieved by ensuring optimal implement displacements per cycle, presents considerable interest. The hole penetrating may be realized by hydraulic jacks, quasi-statically loading working devices (implements), as well as by machines with a cyclic (vibrational, vibro-impact) action. The energy consumption of the working processes of such machines can be determined from corresponding information about the dependence of the soils' frontal resistance force upon the implement's displacement. Let us use the soil loading and unloading curves in Fig. 2, which were obtained by experimental investigations, the content of which is stated in reference [17]. Curve OAB in Fig. 2 characterizes the soil's dynamic loading stage by a conical implement with a diameter of 100 mm, and curve B C is the unloading stage. Using the least squares method, it is possible to express the 0A part of the loading curve by the following power function: (22)

f (x) = K x v,

where K : 960, 3' : 0.4, at which the value o f x is set in mm, and the result is obtained in kg.* Substituting expression (22) in expression (10), we will obtain: So, = c(l ÷ 7__________) 7

(23)

For the considered curve, c = 4 mm; accordingly, the optimum value of displacement per cycle amounts to S0e = 14 mm. Substituting the value of S0, in equation (22), we obtain :f(S0,) -----2759 kgf (25.3 kN). Using the valuef(S0,) in equation (12), we find Eomin -----2759 l. Taking into account that, for the loading curve 0A (Fig. 2), b -----22 mm, we determine, by means of expression (22), the boundary value of the frontal resistance force to be R m a x : 3305 kgf (32.4 kN). Let us determine the magnitude of the left part of inequality (13a), for the case of shaping a hole with a length o f / = 1000 mm:

I

b

J" f ( x ) dv RmaxI o

b--

c

/

--

0.00226.

This result confirms the validity of equation (14), serving as basis for determining energy expenditures at a quasi-static regime of implement penetration in soil which, *If K = 9.41, the result is obtained in k N

MINIMIZATION OF THE ENERGY CONSUMPTION OF SOIL DEFORMATION

73

b = 22ram

3 x 103

/ d " I00 mm

2 5 x 103 2xtO a

o:"

/

1.5 x 10 3 I x I0 3

0 5 x 103

k 9f

• R max • 3305 [

I

L

I

I

I0

15

20

25

30

35

]

I

40

45

C

I

TriO

55

×' FIG. 2.

Experimental graph of the dependence of the soil's frontal resistance force upon the implement's displacement for a dynamic loading regime.

in the case under consideration, will amount to Eas = 3305 1. The ratio of that energy to the value of E0mln equals Eq~ _ 1.198.

Eomin Thus, with cyclic penetration, characterized by a minimum energy consumption, it is possible to achieve a considerable saving of energy, in comparison to continuous quasi-static penetration. The energy-capacity evaluation of machines intended for the propagating of holes can be performed with the aid of the graph represented in Fig. 3. This graph is constructed based on expressions (5) and (22), taking into account the assumption that the energy of reverse soil deformations is not returned to the machine. Thus, on the ordinate axis of the graph is set the value of the ratio of the spent energy to the shaped hole length: e = Eft. From Fig. 3, it is seen that, at a displacement per cycle approximating the magnitude c = 4 mm, the process's energy consumption tends to infinity. With an increase of S there is a sharp decrease of the process's energy consumption, reaching the minimal value emin at an optimal displacement per cycle of Soe = 14 mm. At a further increase of S, there is an extremely slow increase of the process's energy consumption. In Fig. 3, ordinate eq, corresponds to the energy consumption of hole formation by quasi-static implement loading. It is extremely important to stress that, in existing machines with cyclic action, (pneumo-shock punchers, etc.) intended for shaping horizontal holes with a diameter in the order of 100 mm under soil conditions described in reference [17], the displacement per cycle fluctuates within the range of 4.5-6.0 mm. Consequently, the energy con-

74

M. SPEKTOR

c = 4mm b= 2 2 m m

8 x I0 3 -

Soe = 14 m m e=,o= 2 . 7 5 9

7 x 103 -

e~s =

xlO s kgf.m/m

3.305x10 ~

kgf'm/m

Gx I0 ~ -

E b

E

5 x lOCi_ 4 x I0 ~

____

3x IOS~ C 2

x

IO~ -

I x I0 ~ -

i

eq.,

!

emln

l

o 2 4

I I~1

!

6

12 14 16 18 2 0 2 2

8

I0

S, FIG. 3.

[

]

~

I

mm

Graph of the process's energy consumption dependence upon displacement per cycle.

sumption exceeds by 1.4 4 times the corresponding minimum energy consumption which can be achieved at optimal displacement per cycle. The development of novel machines with cyclic action realizing optimal values of displacement per cycle will ensure not only a considerable attenuation of the process's energy consumption, but will also lead to an increase of the average penetrating velocity, i.e. to the machines' productivity rise. It is interesting to point out that various authors, as a result of their experimental investigations of methods for implement-soil interaction, reach contradictory conclusions about the comparison of energy consumptions of cyclic (vibrational, vibroimpact) and continuous (quasi-static) processes of implement penetration. Thus, certain researchers consider that for a cyclic process, the energy consumption is higher than for a continuous one; others are of the contrary opinion, while a third group believes that the compared energy consumptions are identical [18, 83, 39]. Based on the graph in Fig. 3, it can be demonstrated that all these contradictions can easily be eliminated by assuming that authors of different opinions found in their experiments values of displacement per cycle S different from the optimal value So, at which the minimum process energy consumption is reached. Thus, it may be assumed that authors of the opinion that energy consumption in cyclic penetration is higher than for continuous penetration, have realized a value of S equalling, for example, 6mm. In this case, e = 4212 kgf.m/m, which exceeds the value eq, = 3305 kgf.m/m. Those authors who consider that energy consumption for cyclic loading is lower than for the quasi-static case could realize, for example, S = l0 ram.

MINIMIZATION OF THE ENERGY GONSUMPTIONOF SOIL DEFORMATION

75

For this, e ---- 2870 kgLm/m, which is obviously lower than the value of eq,. And, finally, the values S = 7.45 ram, and e = 3305 kgf.m/m, which coincides with the value of eg, correspond to the opinion of authors who claim that, for cyclic and continuous processes, the energy consumption is identical. Thus, the present paper resolves apparent contradictions in the evaluation of cyclic processes of working devices' (implements') interaction with soil, and establishes the basis for improving a series of machines. Based on experimental data used in the previous examples, equation (22) gives the maximum value of the sum of the soil's external friction force and the implement's weight, for which, up to that maximum, it is admissible to use formula (19) for computing the optimal displacement per cycle Sofg, (F + G sin ~t)om~ = 943 kgf (9.25 kN). Thus, the weight of a pneumo-shock puncher for the shaping of horizontal and sloped holes with a 90 mm diameter amounts to approximately 30 kgf (2.94 N) and the external friction force for soil conditions, described in reference [17], reaches 150 kgf (1.47 kN). Consequently, F + G = 150 + 30 = 180 kgf (1.77 kN), which is considerably lower than the maximum sum of forces admissible for the case under consideration amounting, as shown above, to 943 kgf (9.25 kN). Thus, using formula (19) for computing Soi~ in the case of developing of an adequate machine for hole punching, it is possible to exclude the risks that the sum of the soil's external friction force and the implement's weight would exceed the value determinable by formula (21). All this enables recommending the result of the present investigation for practical realization. It is necessary to mention that the present work yields a certain basis for assuming that the revealed laws are valid not only for the implement's penetration in soils, but also in processes of cutting, crushing, shovelling of soil, as well as in other similar processes of implement-soil interaction. CONCLUSIONS AND PROPOSALS For the propagation of residual deformations in cohesive soils, with the aim, for example, of shaping holes by means of consecutive repetition of adequate soil loading and unloading stages, the implement displacement required is determinable by formulas, presented here, for the so-called 'Optimal Displacement per Cycle'. The energy output capacity of existing machines with cyclic action, intended for shaping horizontal holes in soil, considerably exceeds the possible (admissible) minimum energy consumption, determinable by a computation method based on the present paper. The development of novel machines with cyclic action, ensuring optimal values of displacement per cycle, will make it possible to attenuate considerably energy expenditures of working processes, while simultaneously increasing machine productivity. The work performed reveals the causes of principal differences and eliminates those controversies arising from the results of experimental investigations made by

76

M. SPEKTOR

various authors, c o m p a r i n g the energy c o n s u m p t i o n of cyclic (vibrational, vibroimpact) processes o f i m p l e m e n t - s o i l interaction to the energy c o n s u m p t i o n o f a c o n t i n u o u s (quasi-static) i m p l e m e n t p e n e t r a t i o n in soil.

REFERENCES [1] F. E. RICHART, JR, Some effects of dynamic soil properties on soil-structure interaction, J. Geotechn. Eng. Div., .4SCE 101 (GT 12), Proc. Paper 11764, 1193-1240 (1975). [2] D. D. BARKAN, Vibromethod in Construction. Gosstroyizdat (Government Construction Technology Publishing House), Moscow (1958) (in Russian). [3] O. A. SAVINOVand A. YA. LUSKIN,Vibrational method of pile driving, and its application in construction. Gosstroyizdat, Moscow-Leningrad (1960) (in Russian). [4] G. W. TURNAGE,Influence of viscous-type and inertial forces on the penetration resistance of saturated, fine-grained soils. J. Terramechanics 1 (2), 63-76 (1973). [5] M. B. SPEKTOR,On the soil's frontal resistance force of a soil subjected to the action of dynamic loads, Mining, Construction, and Road-Laying Machines, No. 16, Tekhnika Publishing House, Kiev (1973) (in Russian) [6] M B. SPEKTOR,Theoretical justification of the shaping of horizontal holes in soil, by shock action machines, Mining, Construction, and Road-Laying Machines, No. 17. Publishing House, Kiev (1974) (in Russian). [7] DE BEERet al., Scale effects in results of penetration tests performed in stiff clays, Proc. European Syrup. on Penetration Testing ESOPT. Stockholm, 5-7 June 1974, Volume 2: 2, pp. 105-118. National Swedish Building Research (1975). [8] A. S. VESIC, et al., An experimental study of dynamic bearing capacity of footings on sand. Proc. Sixth Int. Conf. on Soil Mechanics and Foundation Engng, Vol. II, Divisions 3-6, pp. 209-213, Montreal, 8-15 September 1965, University of Toronto Press (1965). [9] J. G. HE,RICK and W. R. GILL, Soil reaction to high speed cutting. Trans. ASAE 16 (3), 401-403 (1973). [10] G. E. COLEMANIII and J. V. PERUMPRAL,The finite elements analysis of soil compaction. Trans. AS,4E 856-860 (1974). [11] A. K. SRXVAS'rAVAand G. E. REHKUGLER,Strain rate effects in similitude modelling of plastic deformations of structures subject to impact loading. Trans. ASAE 19 (4), 617-621 (1976). [12] M. BALIGHand R. F. SCOTT,Quasi-static deep penetrations in clays, J. Geotechn. Engng Div., ASCE 101 (GT 11), Proc. Paper 11706, I I 19-1133 0975). [13] I. M. ARTOBOLEVSKIY,A. P. BESSONOVand N. L. RAEVSKIY,Dynamic pressure diagrams of vibrationally-drivenpile, lzvestiya AN SSSR, OTN No. 7 (1954) (in Russian). [14] Yu. E. IVASHOV,T. T. PAVLOVAand A. V. SHLYAKTIN,Transducer for determining frontal resistance forces in vibratory pile driving, .4N SSSP ITEI Series 31, No. T-56-166/4, Moscow (1956) (in Russian). [15] M. B. SPEKTOR,Analysis of frontal resistance of soil to penetration with conical tools, Stroitel'stvo Truboprovodoc (Pipeline Construction) No. I 1. Moscow (1970 (in Russian). [16] M. B. SPEKTOR,Soil penetration by tools under dynamic loading. Stroitel'stvo Truboprovodov (Pipeline Construction) No. 5, Moscow (1972) (in Russian). [17] M. B. SPEKTOR,Experimental study of soil resistance under dynamic loading. Izvestiya Vyssh. Ucheh. Zaved., Stroitel'stvo i Arkhitektura. Novosibirsk No. 4 (1973) (in Russian). [18] V. L. BALADINSKY,Dynamical destruction of soils. Kiev University Publishing House (1971) (in Russian). [19l A. R. DEXTERand D. W. TANNER,Soil deformations induced by a moving cutting blade, and expanding tube, and a penetrating sphere, J. Agric. Engng Res. 17, 371-375 (1972). [20] J. G. HENDRICKand W. R. GILL,A critical soil deformation velocity? Conf. Proe. RapidPenetration of Terrestrial Materials, pp. 243-250. Texas A and M University (1972). [21] J. D. MURFFand H. M. COVLE, A laboratory investigation of low-velocity penetration, Conf. Proc. Rapid Penetration of Terrestrial Materials, pp. 319-360. Texas A and M University (1972). [22] J. B. TOMPSONand J. K. MITCHELL,Soil property determination by impact penetration, Conf. Proc. Rapid Penetration of Terrestrial Materials, pp. 361-388. Texas A and M University (1972). [23] S. J. KNIGHTet al., Low-velocity dynamic penetration of small footings in clay, Conf. Proc. Rapid Penetration of Terrestrial Materials, pp. 415--430. Texas A and M University (1972). [24] W. A. DUNLAP,Influence of soil properties on penetration resistance, Conf. Proc. RapidPenetration of Terrestrial Materials, pp. 515-526. Texas A and M University (1972).

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[25] T. L. ADAMSand F. C. STEPANICH,Experiments in expandable tip filling, J. Soil Mechanics Foundations Div., ASCE99, (SM 11), Proc. Paper 10161, 957-977 (1973). [26] J. D. MURVFand H. M. COYLE, Low-velocity penetration of kaolin clay, J Soil Mechanics Foundations Div., ASCE 99 (SM 5), Proc. Paper 9737, 375-389 (1973). [27] J. BINQUET and K. L. LEE, Bearing capacity tests on reinforced earth slabs. J. Geotechnical Engng Div., ASCE 101 (GT 12), Proc. Paper 11892, 1241-1255 (1975). [28] D. SCHURXNG,A contribution to soil dynamics, J. Terramechanics 5 (1), 31-37 (1968). [29] T. MUROMXCHI,Experimental study on application of static cone penetrometer to subsurface investigation of week cohesive soils, Proc. European Symp. on Penetration Testing ESOPT, Stockholm, 5-7 June, 1974, Volume 2: 2, pp. 285-291. National Swedish Building Research (1975). [30] H. T. DURGUNOGLUand J. K. MITCHELL,Influence of penetrometric characteristics on static penetration resistance, Proc. of the European Symp. on Penetration Testing ESOPT, Stockholm, 5-7 June 1974, Volume 2: 2, pp. 133-139. Swedish National Building Research (1975). [31] A. O. URIELet al., Test results concerning the influence of the cone angle in the dynamic penetration resistance, Proc. European Symp. on Penetration Testing ESOPT, Stockholm, 5-7 June, 1974, Volume 2: 2, pp. 401-405. Swedish National Building Research (1975). [32] D. J. CAMPnELL,A laboratory penetrometer for the measurement of the strength of soil clods. J. Agric. Engng Res. 22, 85-91 (1977). [33] J. M. E. AUDIEBERTand K. J. NYMAN, Soil restraint against horizontal motion of pipes. J. Geotechn. Eng Div., ASCE, 103, No. GT 10, Proc. Paper 13303, pp. 1119-1142 (1977). [34] M. B. SPEKTOR,Energy capacity of soil deformation at vibro-impact hole penetrating. Science and Technique in Urban Economy. Stroitel (Constructor). Publishing House, Kiev, XXIth Edition (in Ukrainian). [35] M. B. SPEKTOR, Problems of the theory on deformer motion in soil under impulse loadings, Science and Technique in Urban Economy, XXIII edition. Stroitel (Constructor) Publishing House, Kiev (1973) (in Ukrainian). [36] M.L. S[LWR and H. B. SEED, Deformation characteristics of sands under cyclic loading, J. Soil Mechanics Foundations Div., ASCE97 (SM 8), Proc. Paper 8334, 1081-1098 (1971). [37] V. V. MOSKVmN, Plasticity under alternating loading, Moscow University Publishing House (1965) (in Russian). [38] A. EGOENMULL~R,Experiments with groups of hoes oscillating in opposite phase, Grundlagen der Landtechnik 10, 70-88 (1958). [39] B. P. VERMA,Oscillating Soil Tools--A Review, Trans. ASAE, 14 (6), 1107-1115, 1121, (1971).