Abstract:
Method and apparatus for compacting soil and for determining a mechanical characteristic of soil, including a method and apparatus for periodically compacting soil with a soil compacting device so as to make the soil and the soil compacting device vibrate together as a single oscillatory system, analyzing the vibration of the soil and soil compacting device, and adjusting an oscillatory driving force so as to drive the single oscillatory system towards a characteristic resonance frequency Ω.

Description:
This application is the national phase under 35 U.S.C. §371 of PCT International Application No. PCT/CH97/00396 which has an International filing date of Oct. 21, 1997 which designated the United States of America. 
     FIELD OF THE INVENTION 
     The invention relates to a method for measuring the mechanical data of a graded and tampered soil, or a soil that is to be graded and tampered, to a grading and tampering method in order to achieve optimal, in particular, homogeneous grading and tampering of a soil, to an apparatus for measuring the mechanical data of a graded and tampered soil, or of a soil that is to be graded and tampered, and to an apparatus for grading and tampering a soil in order to achieve optimal, homogeneous compacting of that soil. 
     DESCRIPTION OF RELATED ART 
     A method for soil grading and tampering is known in the art from WO 95/10664. With this known method, the frequency of a rotating unbalance is adjusted in such a way that the grader and tamper unit, which has contact with the ground that is to be graded and tampered, will not exceed a preset harmonic oscillation value - here twice the value of the fundamental oscillation. Staying below this preset value is defined as a stability criterion. Using two acceleration recorders, arranged vertically to each other on the grader and tamper unit, their accelerations are measured. One acceleration recorder measures the horizontal, the other measures the vertical acceleration component. Determined are the oscillation amplitude of the grader and tamper device, and the direction of the maximum compacting amplitude. The frequency of the eccentric, as well as its weight and the rolling speed are adjustable with the aid of a computer. However, these values are adjusted in such a way so as to avoid machine and chassis resonance. Adjustment of the eccentric&#39;s frequency and weight is carried out without accounting for the qualities of the soil that is to be graded and tampered. Based on the measured acceleration values, the modulus of elasticity in shear of the compacted soil and its plastic parameter are determined. 
     Another method for soil grading and tampering is known in the art from EP-A 0 459 062. With this known grading and tampering method, emphasis is placed on adjusting the machine parameters in such a manner that preset forces acting upon the the soil, which is to be graded and tampered, are achieved. 
     SUMMARY OF THE INVENTION 
     The object of the invention is to describe a method for measuring and/or grading and tampering a soil, and to create an apparatus for measuring and/or grading and tampering a soil which allows homogeneous soil compacting by using a grading and tampering method that requires as few equipment runs as possible; in particular, with a preset, desired soil rigidity and/or, in particular, a desired modulus of elasticity, and which allows the determination of mechanical data for the soil to be graded and tampered, or the graded and tampered soil. 
     The object of the invention is realized in that, in contrast to patent WO 95/10664, reliance is not placed on the local phase position of a maximum oscillation amplitude of a grading and tampering or measuring device, but instead reliance is placed on the temporal phase of the exciting oscillation of the eccentric(s) in relation to the phase of the excited oscillation of the soil grading and tampering and/or measuring systems, which is identical to the oscillation of the grading and tampering and/or the measuring devices. Also contrary to WO 95/10664, work is performed in the resonant range of an oscillation system, which consists of the grader and tamper or measuring device, acting upon the soil that is to be compacted (or has been compacted), and the soil. Although the soil grader and tamper apparatus described in EP-A 0 459 062 operates in the resonant range of its grader and tamper device, it is unable, however, to determine the soil rigidity C B , which is reached with the compacting process, and is therefore not able to optimize the compacting process on the basis of these established values. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     To illustrate the invention, the following figures will describe a soil grader and tamper apparatus according to the invention. The soil grader and tamper apparatus includes a measuring device according to the invention for the purpose of determining the mechanical data that are essential for the compacting process. They show: 
     FIG. 1 a schematic depiction of a double tandem vibrating roller with center pivot steering, which allows soil grading and tampering according to the invention, 
     FIG. 2 a mechanical equivalent circuit diagram, in terms of oscillation, of the soil grader and tamper apparatus described in FIG. 1, 
     FIG. 3 a signal block wiring diagram for implementing the soil grading and tampering according to the invention, 
     FIG. 4 a standardized oscillation amplitude of the soil grader and tamper device (ordinate) in accordance with FIG. 2 that is interdependent on a standardized oscillation frequency of the unbalance (abscissa), which excites the oscillation. 
     FIG. 5 the position of a soil element to be compacted in the ground, 
     FIG. 6 a compacting force that acts upon the soil element shown in FIG. 5, 
     FIG. 7 a start-up procedure of a soil grader and tamper device in order to achieve an optimal point of operation shown in a depiction analogous to that in FIG. 4, and 
     FIG. 8 a schematic depiction of a gearing unit for driving two unbalances of the soil grader and tamper device with adjustable moment of inertia. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The double tandem vibrating roller  1  with center pivot steering, shown in FIG. 1, features a front surface and a back surface  3   a  and  3   b  that serve as the ground compacting devices. In the following descriptions only the one or the other of the two surfaces  3   a  and  3   b  will be considered, and both are designated with the reference number  3 , if there is no difference between front and back surface  3   a  and  3   b . A coupling between the two surfaces  3   a  and  3   b  in the context of the double tandem vibrating roller  1  described here, for example, is not relevant for the operating performance. 
     The surface  3 , as shown schematically in the FIGS. 2 and 3, features a rotating unbalance with adjustable static unbalance moment m u ·r u . The unbalance moment is adjusted by modifying the radial unbalance distance r u  of the unbalance  5 . Adjusting the moment of inertia and of the frequency f is described below. To simplify the following remarks, let us assume the mass m u  of the unbalance is arranged punctiformally, rotating at a distance of r u  from the axis of revolution  7  of the surface  3 . The static unbalance moment is therefore m u ·r u [kg·m]. An acceleration recorder is positioned vertically above the axis of revolution  7 , on the side of a support bracket  9  of the surface holding fork  10 . The acceleration recorder  11  is able to measure the acceleration values of surface  3  in a vertical direction. The acceleration recorder  11  is connected with an arithmetic unit  12  in terms of signals, which determines the oscillation amplitude a of the surface  3  by performing double integration. The surface holding fork  10  is connected with the machine chassis  15  by way of spring and damping elements  13  and  14 . The spring and damping elements  13  and  14  are designed in such a way that the dynamic forces inside the damping element  14  are considerably smaller than the static forces. 
     With the method according to the invention for the purpose of achieving optimal, in particular, homogeneous ground compacting, the movement and/or the acceleration of the surface  3  is measured with the acceleration recorder  11 , as indicated above. The vibration of the surface  3 , excited by the unbalance  5 , can be expressed mathematically with the following equation [1]: 
     
       
         X d (t)= a   ½  cos [(Ω/2)t+δ ½   ]+a   1  cos [Ωt+δ 1   ]+a   {fraction (3/2)}  cos [(3 Ω/2)t+δ {fraction (3/2)}   
       
     
     
       
         ]+ a   2  cos [2 Ωt+δ 2   ]+a   {fraction (5/2)}  cos [(5 Ω/2)t+δ {fraction (5/2)}   ]+a   3  cos [3 Ωt+δ 3 ] 
       
     
     In this formula the index  1  indicates an allocation to values, which have the same radian frequency Ω (Ω=2 πf, which f being the frequency of the unbalance  5 ), as the exciting vibration of the unbalance 5. ½ refers to half the radian frequency Ω, {fraction (3/2)} refers to one and one half of the radian frequency, and {fraction (5/2)} refers to two and one half of the radian frequency Ω. a is the maximum amplitude value of the relevant partial oscillation. δ refers to the allocation of partial oscillations to each other in terms of phases. 
     With the Fourier analysis, and in accordance with the above equation, the partial frequencies can be determined by the arithmetic unit  12  on the basis of the acceleration signal. Depending on the required compacting procedure, the static unbalance moment of the unbalance  5  and its frequency f is now adjusted differently: 
     a) If the surface  3  always maintains contract with the ground, essentially, only the rotational frequency 1·f of the surface is determined with the Fourier analysis. This compacting procedure is called load operation. 
     b) If the surface  3  periodically lifts off the ground, which in comparison to a) results in more effective compacting, the Fourier analysis is used to determine harmonic oscillations, i.e. radian frequencies of 2Ω, 3Ω, . . . with drastically decreasing maximum amplitudes. The lift-off of the surface  3  from the soil is characteristic of the optimal mode of operation because in this case the forces transferred upon the soil are more effective than in case a), which results in more effective compacting. 
     c) If the machine, i.e. the entire roller  1 , shows signs of jumping, which means the machine chassis  15  is beginning to exhibit vibrations around its steady position, the upper harmonic waves are joined by oscillations with half the exciting radian frequency Ω of the unbalance  5 , i.e. plus (½) Ω, ({fraction (3/2)}) Ω, ({fraction (5/2)}) Ω, . . . This condition is not stable, and may potentially loosen the graded and tampered soil. Moreover, the machine chassis  15  may begin to vibrate around its longitudinal axis. 
     In accordance with the equivalent circuit diagram in FIG. 2, the soil  20 , which is to be graded and tampered, is depicted as a spring  17  and a damping element  19 . This means a soil grading and tampering system which consists of a surface  3  with oscillation exciting unbalance  5 , the spring element  17 , and the damping element  19  of the soil  20 , that is to be compacted, and the spring element  13  and the damping element  14  between surface  3  and machine chassis  15 , shows signs of self-oscillation. This is confirmed by the measurement curves shown in FIG.  4 . The abscissa represents the oscillation radian frequency Ω of the surface  3 , and the ordinate represents the measured maximum oscillation amplitude. However, the oscillation radian frequency Ω is standardized to the resonant frequency w 0  of the soil grading and tampering system, and the value a is standardized to a value a 0 . The static unbalance moment is the curve parameter [the product of a punctiformally arranged, imagined unbalance mass m u  and the radian distance r u  to the axis  7 ]. The unbalance moment of the curve  21   a  is smaller than the unbalance moment of the curve  21   b , etc. Above curve  23  the roller  1  begins to jump [case scenario c]. Therefore, during compacting operation the curve  23  must not be exceeded. The group of the resonance curves  21   a  through  21   d  represents an essential identification value with respect to the behavior of the soil grading and tampering system during operation. As shown below, the various influences of the machine parameters and the basic step-by-step process of the compacting operation can be derived from the curves. Compacting is optimal when the soil grading and tampering system, consisting of the compacting device that is to act upon the soil to be compacted  20 , and the actual soil to be compacted  20 , resonates. Optimal operation is reached when the process can be carried out with the greatest speed and the least energy. 
     The resonant frequency w 0  of the soil grading and tampering system is the square root of the quotient of the soil rigidity C B  [MN/m] and the weight m d  [kg] of surface  5 : 
     
       
         W 0 =(c B /m d ) ½   
       
     
     In the above equation a share of the respective wheel support as well as mathematical “shares for the soil” must be added to the weight of the surface  5 . However, at a maximum these additional shares are only 10% of the surface&#39;s net weight. Preferably, these shares are determined by trial and error and may be neglected for the purpose of a general approximation. Normally, the soil rigidity C B  is between 20 MN/m and 130 MN/m. The soil rigidity is established according to the invention, as described below. The easiest way to measure the resonant frequency w 0  is by running the device across the soil  20  with a small static unbalance moment in accordance with curve  21   a . The frequency of the unbalance  5  at the maximum curve value of 25 of a/a 0  indicates the resonant frequency w 0 . The standardized amplitude value of a /a 0 =1 is at that point where the curve  27 , which connects the maximum values of the curves  21   a  through  21   d ,starts going off to the left. The amplitude value of a 0  can be approximated based on the following formula 
     
       
           a   0 =( m   f   +m   d ) g/c   B   [2] 
       
     
     provided the surface  3  does not lift off (case scenario b). However, this is not the case here. m f  is the load of the machine chassis  15  per surface  3 . g is the Earth&#39;s acceleration due to gravity with g≈10. 
     A position sensor  29  is arranged, fixed in relation to the support bracket  9 , next to the acceleration recorder  11 , and it determines the time the rotating unbalance  5  passes through its minimum point (=direction of compacting). Passing this point is identical with the point in time the maximum unbalance force is directed against the soil  20 . The maximum force acting upon the soil  20 , is transferred by the surface  3  into the soil  20 ; this process takes place accompanied by a phase displacement at an angle of ø. This means, in effect, that the phase displacement ø reflects the position of the exciting oscillation from the unbalance  5  in relation to the oscillation of the soil grading and tampering system. 
     Maximum compacting force in the soil  20  is achieved if the soil grading and tampering system resonates. Resonance of the grading and tampering system always occurs at the maximum values of the curves  21   a  through  21   d ,which are located on curve  27 . If resonance occurs, there is also a phase displacement of the exciting oscillation system by the unbalance  5  in relation to the soil grading and tampering system, with ø=90°. This means optimal compacting is achieved with roller parameters [static unbalance moment m u ·r u  and unbalance rotation radian frequency Ω] that allow operation on the curve  27 . The resonance curves  21   a  through  21   d  in FIG. 4 are recorded with constant soil characteristics. The soil characteristics, alternatively represented by spring element  17  and damping element  19  in FIG. 2, are changeable which is why the position of the resonance curves  21   a  through  21   d  may also change. As depicted in FIG. 4, the oscillation amplitude, responsible for compacting the soil  20 , changes considerably in the below-resonance range [oscillation radian frequency Ω is smaller than the resonance frequency, phase angle ø is smaller than 90°]; however, in the above-resonance range [oscillation radian frequency Ω is larger than the resonance frequency, phase angle ø is larger than 90°] it changes relatively little. Consequently, for stable grading and tampering operation the above-resonance range should be chosen, and the phase angle ø should be adjusted to a value of between 95° and 110°, preferably 100°. 
     The adjustment of the phase angle ø is accomplished, with preset static unbalance moment m u ·r u ,by reducing the rotation radian frequency Ω of unbalance  5 . For example, on the resonance curve  21   d  movement occurs in the direction of the arrow  35 . Naturally, the range in which the roller lifts off, characterized by the area above curve  23 , must be avoided. Penetration into that range will be felt by the roller operator because the vibration behavior of the roller  1  will change. In terms of measuring technique, as indicated above, oscillations with half the frequency [and odd multiples] of the rotation radian frequency Ω of the unbalance  5  will occur at that point. This unstable [lift-off] operation may also be ascertained based on the fact that sequential oscillation amplitudes of the surface  3  exhibit different heights. 
     To achieve maximum grading and tampering results, the compacting amplitude of the surface  3  must be chosen as large as possible. For achieving a preset soil modulus of elasticity E or a preset soil rigidity C B , the arithmetic unit  12  and adjusting unit  36  automatically set the necessary amplitude, as described further below. 
     The travel speed v of the roller  1  is also adjusted for a regular compacting operation per unit distance traveled, despite a variable rotation radian frequency Ω of the unbalance  5 . The speed variable depends on the type of layer that is to be compacted. Due to a low rotation radian frequency Ω, a non-consolidated layer requires a slower travel speed v than a consolidated layer. For example, for a non-consolidated layer the travel speed is v u =3 km/h with a rotation frequency of f u =30 Hz, and for a consolidated layer the travel speed is v g =4.5 km/h with a rotation frequency of f g =45 Hz. 
     A soil element  37 , as depicted in FIG. 5, depth of z 0 , “sees” a two-surface roller  1  with a speed of v pass by during the compacting process. Depending on the location of the two surfaces  3   a  and  3   b  that roll across the soil element  37 , the latter experiences, in accordance with FIG. 6, a different load peak  39 . The two load processes for the two surfaces  3   a  and  3   b , with a pulse draw  40   a  originating at the surface  3   a  and a pulse draw  40   b  originating at the surface  3   b , can be linearly superimposed. Their effect is cumulative. Depending on the oscillation amplitude a of the soil grading and tampering system, the axis distance d of the two surfaces  3   a  and  3   b , and the depth z 0  of the soil element  37  in question, a zone of overlap  41  may result, through which the ground element  37  receives parts of the loads from the surfaces  3   a  and  3   b . During operation, the time distance t s  of the partial loads acting upon the soil element  37  should be constant in order to always achieve consistent compacting quality. As described below, when the soil rigidity C B  increases the roller  1 , which is controlled according to the invention, will operate with a higher rotation radian frequency Ω which, consequently, results in an increase of the speed travel v. This means the compacting process is carried out with increasing speed. 
     In contrast to rollers and compacting procedures known in the art (e.g. WO 95/10664), grading and tampering is no longer carried out only in relation to a constant modulus of elasticity in shear but with a preset, preferably constant soil rigidity C B , and, if necessary, with a preset constant modulus of elasticity E. With rollers and compacting machinery in the past it was always assumed that at least minimum compacting, as defined by the soil rigidity C B  or the ground modulus of elasticity E could be achieved. The tremendous differences between minimum and maximum grading and tampering, resulting from the method known in the art, lead to the commonly known, however undesired, irregular sinking and development of unevenness of, for example, road surfaces. With the invention these differences will be avoided. 
     In contrast, the method according to the invention envisions compacting, for example, with a constant modulus of elasticity E. In contrast to the soils known in the art, which are compacted for minimum soil rigidity, a constant soil modulus of elasticity E results in considerably better long-term stability. It should be reiterated here that compacting is carried out on the basis of both, the preset soil rigidity C B  and the preset soil modulus of elasticity E. For example, a soil  20  of a road construction, compacted with a constant modulus of elasticity, will sink evenly while it ages due to the traffic volume, and will therefore have a level surface for much longer than a road compacted in accordance with the state of the art. Roadways that were graded and tampered in accordance with the method known in the art become uneven over time due to non-homogeneous compacting; they show superficial tears and, thus, become vulnerable to destruction due to traffic and weather influences. 
     According to the invention, the soil modulus of elasticity E is constantly determined by roller  1 , and the machine parameters are constantly adjusted; however, caution should be exercised that no dips are left behind, i.e. the soil&#39;s surface  42  is already well compacted at that point. In practical application, the exact soil modulus of elasticity E is not important until the grading and tampering process is concluded. At that time, however, the soil surface ( 42 ) has already been sufficiently compacted. The soil modulus of elasticity formula E can be derived from the following formula [3]:              E   =         C   B     ·       2        (     1   -     μ   2       )         L   ·   π              (     1.89   +       1   2          ln        [       π   ·     L   3     ·   E       16        (     1   -     μ   2       )            (       m   f     +     m   d       )     ·   g   ·   R         ]           )               [   3   ]                                
     The above equation results from a postulated continuum mechanical perspective of a curved body which is in contact with an elastic, semi-infinite area. 
     Since the value of interest with respect to the soil modulus of elasticity E appears on both sides of the above equation, its value must be determined with a simple iteration. To begin the calculation, on the right side of the equation, for E is put in 
     
       
         E[MN/m 2 ]=2.3 [1/m]·C B [MN/m]  [4] 
       
     
     The soil rigidity C B  is determined by the arithmetic unit  12  with the assistance of the formulas a below, because that unit knows all values, or said values were set by it. 
     During load operation [case scenario a)], i.e. there is no lift-off by the surface  3  (this operational status applies for the amplitudes up to a/a 0 =1), the ground rigidity C B  is determined with the formula                C   B     =       Ω   2     ·     [       m   d     +         m   u     ·     r   u     ·     cos        (   φ   )         a       ]               [   5   ]                                
     If the surface  3  lifts off, which is registered by the arithmetic unit  12  based on the occurrence of radian frequencies with 2 Ω, 3 Ω, . . . the arithmetic unit calculates the soil rigidity C B  with the formula                C   B     =       F        (       at                 å     =   0     )           [     1   -     cos        (         π   2     /   2        K     )         ]     ·   a               [   6   ]                                
     while 
     
       
         F=−m d ·ä+m u ·r u ·Ω 2 ·cos ø+(m f +m d )·g  [7] 
       
     
     and              K   =       F     m                 a                 x           (       m   f     +     m   d       )     ·   g               [   8   ]                                
     {dot over (a)} is calculated by integration of the value measured with the acceleration recorder  11 . {dot over (a)} is the vertical speed of the surface  5 . This is the surface speed that changes according to time, and should not be confused with the travel speed v. {dot over (a)}=0, i.e. a speed zero of the surface  5  is always reached in both the upper and lower oscillation cuspidal points. a is the value established by the acceleration recorder  11 . The static imbalance moment m u ·r u [kg m] in the above formula can be determined on the basis of the unbalance  5  data. How to establish the phase angle ø has been described above. m d  [kg] is known as the weight of the respective surface  3 . Ω is adjusted as rotation radian frequency of the surface  3 , and is therefore known. The maximum oscillation excursion a of the surface  3  can also be determined. 
     In formula [3] the transversal contraction number of the sub-soil is set at μ=0.25 (it is between 0.20 and 0.30). L [m] is the width of the surface  3 , (m f +m d ) the load each surface  3   a  and/or  3   b  is carrying, plus the respective weights of surfaces  3   a  and/or  3   b , R [m] is the radius of the surface  3 , g [=10 m/s 2 ] the Earth&#39;s acceleration due to gravity, and in the natural logarithm. Thus, all values for automatic determination of the soil rigidity C B  are known, or can be determined with the arithmetic unit  12 , which means that the modulus of elasticity E can also be established with the assistance of the arithmetic unit  12 . 
     To arrive at the above formula [3] we assume that two elastic rolls are touching. The first roll has a modulus of elasticity E 1 , a radius R 1  and a transversal contraction number μ 1 . The second roll has a modulus of elasticity E 2 , a radius R 2 , and a transversal contraction number μ 2 . Both rolls have a length L. For the surface pressure p [N/m 2 ] between the two rolls, therefore, results 
     
       
         
           
             
               
                 
                   p 
                   = 
                   
                     
                       
                         4 
                         · 
                         P 
                       
                       
                         π 
                         · 
                         L 
                         · 
                         b 
                       
                     
                     · 
                     
                       
                         ( 
                         
                           [ 
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   4 
                                   · 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                               / 
                               
                                 b 
                                 2 
                               
                             
                           
                           ] 
                         
                         ) 
                       
                       
                         1 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   10 
                   ] 
                 
               
             
           
         
                 
         
             
         
      
     
     P is the force acting on the first roll, b is the width of the contact surface ( L·b), in relation to which the two rolls are touching due to elastic deformation, and y is the running coordinate vertical to the axis of the roll, and with the origin of coordinates on the axis of the roll. 
     As transition for a roll compacting the soil (surface) we assume that the soil is the second roll described above. The radius R 2 =∞ is set. In addition, the modulus of elasticity E 1  of the first roll is considerably larger than the E 2  of the soil. Therefore, it is valid 
     
       
         E  1 &gt;&gt;E 2 . 
       
     
     Thus, in relation to E 2 , it can be set E 1 →∞ 
     The force P which acts upon the first roll is, in the context of a soil grading and tampering apparatus, a function of time. It is not temporally constant. The force P is identical with the soil reaction force F in the equations [6], [7], and [8]. Establishing the temporal mean with regard to the force P during one rotation of the surface  3  leads to                1   T     =         ∫   0   T          P   ·                   t         =       (       m   f     +     m   d       )     ·   g               [   11   ]                                
     Thus, in equation [10] it is set P=(m f +m d )·g. Solving the equation [10] with respect to b results therefore in                b        [   m   ]       =       (     [       (     16   /   π     )     ·       (     1   -     μ   2   2       )       E   2       ·           R   1          (       m   f     +     m   d       )       ·   g     L       ]     )       1   2               [   12   ]                                
     μ 2  and E 2  are the transversal contraction and the modulus of elasticity of the soil. 
     Due to the elasticity of the soil E 2 , when applying the force P, the mid point of the first roll approaches the soil&#39;s surface. This approximation δresults with regard to                δ        [   m   ]       =       P   L     ·       1   -     μ   2   2         E   2       ·     E        (     b   /   L     )                 [   13   ]                                
     Since the width of the contact surface (L·b) is considerably smaller than its length L (b&lt;&lt;L) it is valid that          ⊖     (     b   /   L     )       ≈       2   π     ·     [     1.89   +     ln        (     L   /   b     )         ]                              
     Also valid is (spring equation) 
     
       
         F=C B ·δ 
       
     
     and therefore                C   B     =         F   δ     ≡     P   δ       =       L   ·     E   2           (     1   -     μ   2   2       )     ·     ⊖     (     b   /   L     )                     [   14   ]                                
     therefore it follows                E   2     =         (     1   -     μ   2   2       )     L     ⊖       (     b   /   L     )     ·     C   B                 [   15   ]                                
     Now b is replaced with the above value          ⊖     (     b   /   L     )       =       2   π     ·     [     1.89   +       1   2          ln        [       π   ·     E   2     ·     L   3         16          (     1   -     μ   2   2       )     ·     R   1     ·     (       m   f     +     m   d       )     ·   g         ]                                      
     If equation [16] is put into equation [15], the above equation [3] results, with R 1 =R. 
     For optimum grading and tampering of the soil areas to be compacted, the roller  1  must run across them several times. Due to the fact that, normally, the soil in question is not pre-compacted, the first and/or following grading and tampering runs will result in maximum compacting. 
     Adjusting the optimal unbalance radian frequency Ω as well as of the optimal static unbalance moment is described in FIG. 7, while, analogous to FIG. 4, the standardized unbalance radian frequency Ω [Ω/w 0 ] is represented as abscissa value, and the standardized maximum amplitude a [a/a 0 ] of the unbalance  5  is represented as ordinate value. At the beginning of a soil grading and tampering process the unbalance  5  shows a minimum distance r u0 to the rotation axis  7  [static unbalance moment m u ·r u0 ]. The rotation radian frequency Ω of the unbalance  5  is increased, starting from standstill, to the value Ω 0  located above the resonance of the soil grading and tampering system referred to above. The respective travel speed v of roller  1  is adjusted, in accordance with the above comments, to the rotation frequency f of the unbalance  5 . The amplitude a of the surface  3  is interdependent on the rotation radian frequency Ω in correspondence with the curve  43   a . The resonance of the soil grading and tampering system is located in point  45 . This resonance point is exceeded, based on the tolerance reasons explained above, until the phase angle ø between surface oscillation and unbalance oscillation is approximately 100° [point  47 ]. In a next step the static unbalance moment is increased, by increasing the radial distance of r u0  to r ul [m u ·r ul ]. Due to the fact that the static unbalance moment is increased while the unbalance rotation frequency f remains unchanged, the phase angle ø increases to a value of above 100°, as seen by the distance of the new adjustment point  50  from the resonance curve  49  (analogous to curve  27  in FIG.  4 ). In a next step the rotation radian frequency of the unbalance  5  is lowered from Ω 0  to Ω 1 , while the static unbalance moment remains constant [m u ·ru i ], until the phase angle ø returns to 100°. The radial distance r u  and the rotation radian frequency Ω are now changed alternately until the roller  1  starts to lift off. This “lift-off” is, in accordance with the comments above, noticeable at the point when odd multiples of one half of the unbalance rotation frequency occur [when curve  52  is exceeded]. The static unbalance moment m u ·r u  is reduced in order to reach the stable curve point  51 . It is also possible to lower the unbalance radian frequency Ω, however, this type of adjustment is difficult to carry out because with this alternative two values change, i.e. the radian frequency Ω and the moment of inertia. The machine parameters allocated to curve point  51  define the conditions under which maximum grading and tampering operation is realized. The curve  53  in FIG. 7 represents the optimal adjustment curve which always ensures a phase angle ø of 100°. 
     After the first runs, for as long as the soil maintains its plastic properties, maximum compacting performance is reached. The plastic properties are derived from the measured values. In the “plastic range” the soil rigidity C B  can only be approximated. Aware of the fact that the determination of the soil modulus of elasticity is flawed as long the sub-soil still exhibits plastic properties, it is calculated following the above explanations. When approximately 90% of the required soil elasticity value is reached, the plastic range is exceeded and the control adjusts, using the above calculation procedure, the static unbalance moment m u ·r u  and the unbalance rotation frequency f (unbalance rotation radian frequency Ω) in such a way that a preset soil modulus of elasticity E is reached. Using the formulas [3] and [5] the arithmetic unit  12  is able to determine during compacting the respective soil modulus of elasticity E that has already been achieved, and based on these values, for further compacting, the relevant machine parameters can be adjusted, such as static unbalance moment m u ·r u  unbalance frequency f and travel speed v. The adjustments are effected during the process. Adjusting the travel speed v is accomplished easily and rapidly. However, in order to adjust the static unbalance moment m u ·r u  in the fractional second range to a preset, determined value e.g. the process described below is used. 
     Instead of changing, as indicated above, the radial distance r u  of the unbalance mass, two unbalances  56  and  64  running in the same direction can be used, and their mutual radial distance is adjusted by means of a planetary gearing. If the radial distance is 180°, the effective, total unbalance value is zero. At 0° the unbalance value is at its maximum. Using angle values of between 0° and 180° all intermediate values between zero and maximum unbalance mass can be adjusted. 
     The planetary gear  53 , depicted schematically in FIG. 8, serves as a drive mechanism for the two unbalances  56  and  64 , which run in the same direction, and the mutual locations of which can be modified in order to adjust the static unbalance moment m u ·r u . In contrast to the above remarks, it is no longer the radial distance r u  of an punctiformally imagined eccentric mass that is adjusted, but, with an unchanged radial distance r u , the effective unbalance mass m u  is now adjusted. The adjustments according to FIG. 7 are carried out on the basis of [Ω 0 , m u0 ·r u0 ] at the curve point  47  for the following curve points with [Ω 1 , m u1 ·r u0 ] instead of [Ω 0 , m u ·r u1 ] at the adjustment point  50 , with [Ω 1 , m u1 ·r u0 ] instead of [Ω 1 , m u ·r u1 ], [Ω 1 , m u2 ·r u0 ] instead of [Ω 1 , m u ·r u2 ]etc. With the planetary gearing  53 , depicted in FIG. 8, unbalance mass adjustments are possible in fractions of a second. 
     The planetary gearing shown in FIG. 8 is driven by a drive  54  via a spindle  55 , which acts directly on the unbalance  56  and without any intermediate gears. On the spindle  55  a tooth lock washer  57  is arranged which acts via a toothed belt  59  on a tooth lock washer  60 . The tooth lock washer  60 , on the other hand, acts in conjunction with a gearing part  61 . The gearing part  61  features three meshing gears  63   a ,  63   b  and  63   c ; the gear  63   a  and the tooth lock washer  60  are connected with torsional strength. The axis of the gear  63   b  can be turned radially in relation to the rotation axis of the gear  63   a . The twisting angle is a measure for the radial torsion of the two unbalances  56  and  64 , and thereby a measure for the effective total unbalance mass, or the effective static unbalance moment m u0 ·r u  to m u3 ·r u . On the axis  65  of the gear  63 c is located a gear  66  which meshes with a gear  69  located on a hollow shaft. The hollow shaft  67  acts in conjunction with the second unbalance  64 . 
     Since one of the two unbalances  56  and  66  is driven directly, and only the unbalance  64  is driven by the planetary gearing  53 , the latter only has to transfer half of the torque. Reference point for determining the phase angle ø is the bisecting line between the centers of gravity of the unbalances  56  and  64 . 
     It is not necessary to let the two unbalances run in the same direction with identical rotation frequencies Ω. With a corresponding selection of tooth lock washers  57  and  60  and/or the gears  66  and  69 , it is possible to let one of the two unbalances run with double the rotation frequency. 
     The gearing described above, and as shown in FIG. 8, can also be replaced with superimposed gearing that acts identical but is constructed differently. For example, good results were achieved with the so-called “harmonic drive gearing” which reaches high one-step speed increasing ratios with only three components [wave generator, circular spline, and flex spline]. With this gearing, the circular spline is a rigid steel ring with internal toothing, which meshes into the external toothing of the flex spine in the area of the large elliptical axis of the wave generator. The flex spline is an elastically distortionable, thin-walled steel bushing with external toothing featuring a smaller partial circle diameter than the circular spline. It has therefore e.g. two fewer teeth with regard to its overall circumference. The wave generator is an elliptical disc with an open thin ring ball bearing which is inserted into the flex spine and deforms it elliptically. During the turns of the wave generator the toothing meshes with the large elliptical axis. After the wave generator has completed a 180° turn, a relative movement by one tooth occurs between the flex spline and the circular spline. After each turn that the wave generator completes, the flex spline, as drive element, turns by two teeth in the opposite direction of the drive. When this gearing is used the mechanical assembly is extremely compact. 
     If fill-in material is to be compacted at a construction site, it is recommended that before the material to be compacted is deposited, to establish or to test the rigidity C B  of the sub-soil by one machine run across the soil. Of course, the soil modulus of elasticity E can also be determined. If the sub-soil already contains weak points, the fill-in material cannot be compacted to the extent that is necessary. 
     Instead of using rotating unbalances, the use of vertically oscillating unbalances, designed as piston-cylinder units, is also possible. To grade and tamper, the surfaces can be rolled across the soil  20 , but it is also possible to move a vibrating plate across the soil  20 . 
     The measuring apparatus according to the invention differs from the soil grading and tampering apparatus only insofar as the apparatus that acts upon the soil and forms an oscillation system with the latter does not essentially effect the compacting of the soil, which is in contrast to the grading and tampering device of the soil grading and tampering apparatus. This means that during the measurement procedure the force that acts upon the soil is reduced. Also, while measuring a smaller mass of the oscillating force is usually selected. The measuring apparatus according to the invention can be combined with grading and tampering devices known in the art in order to improve soil compacting operation also in conjunction with that machinery.