Abstract:
A soil compaction device has a vibrated contact element that makes contact with the soil during a contact phase and that is exposed to a contact force exerted by the soil and travels over a contact distance. A dynamic stiffness of the soil is formed from the gradient of the contact force and from the contact distance. Furthermore, a contact surface parameter to take account of the actual contact surface of the contact element with the soil is determined. The dynamic deformation modulus is then the product of the contact surface parameter and the dynamic stiffness. The method allows the determination of the dynamic deformation modulus, and hence of the soil stiffness, during the compaction operation.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method for determining a soil parameter using a soil compaction device that has a contact element that is charged with vibration for soil compaction. 
     2. Description of the Related Art 
     Vibrating plates and vibrating tampers, as well as vibrating rollers, are known for use as soil compaction devices. Each of these has at least one soil contact element that is charged with vibration by a vibration exciter and that introduces the vibration into the soil in order to achieve a compaction effect. 
     In order to monitor the quality of compaction work, it is helpful to determine particular soil parameters, such as for example soil rigidity, deformability, load capacity, etc. 
     In order to determine soil parameters, methods and devices are known that operate separately from soil compaction devices. Thus, there is a standardized plate load method (DIN 18134) in which a modulus of deformation E v  is determined in the context of a static load plate pressure test. Likewise, a dynamic load plate pressure test is known Technical test specifications for soil and rock in roadway construction, TP BF-StB, Part B, 8.3 (1997)). 
     Conventional measurement methods and devices separate from the compaction devices require a significant additional expense, because in addition to the compaction device measurement devices must also be made available, which generally require a correspondingly trained operator. Moreover, the number of measurements on a given surface is limited by time constraints; i.e., only some spot samples can be measured. 
     On the other hand, methods are also known in which special soil compaction devices are themselves used to measure, in particular, soil rigidity and/or moduli of deformation of the soil, these parameters being the central criteria for successful compaction. Such devices and methods are known for example from DE 27 10 811 C2, WO 98/17865, DE 29 42 334 C2, and EP 1 164 223 A1. Each of these publications indicates vibrating rollers that are moved over the soil that is to be compacted, and that draw conclusions concerning the soil rigidity on the basis of the vibration characteristics of the roller drum (roller tire). 
     As a rule, vibrating rollers are operated in such a way that the roller tires that act as the soil contact element do not lift off from the soil even when charged with vibration. As a whole, the roller tires move periodically, resulting in a relatively uniform amplitude movement of the roller tires. In contrast, the known measurement methods and devices are not suitable for other soil compaction devices, in particular vibrating plates or tampers. Vibrating plates and vibrating tampers standardly do not make contact with the soil during a significant part of a vibration-load cycle. Here, contact times have been determined that make up only about 10% of the overall vibration period. The measurement methods described above, used with vibrating rollers, are geared towards measuring signals that result from a largely constant state. Even if the roller tires jump off the soil, these airborne phases are relatively short, so that the influence of the error is low. 
     In contrast, in the case of tampers and vibrating plates long airborne phases and short contact times must be assumed, so that the measurement methods known from the prior art, which are geared toward a periodic movement characteristic, are not suitable. In addition, the soil contact elements of vibrating plates and tampers are subject to a rather chaotic movement characteristic, because they constantly have to absorb soil forces at different places due to the jumping or airborne phases. 
     OBJECT OF THE INVENTION 
     The object of the present invention is to indicate a method for determining soil parameters that is also suitable for soil compaction devices whose soil contact element repeatedly lifts off from the soil, in particular even for those devices in which the airborne phase is fairly long relative to a vibration cycle. The method should permit a determination of the soil parameters whenever, independent of its particular movement characteristic and/or contact behavior, the soil compaction device makes contact with the soil during an excitation cycle. Preferred applications are soil compaction devices having fairly chaotic movement patterns, such as in particular vibrating plates and tampers. 
     According to the present invention, this object is achieved by a method according to patent claim  1 . A soil compaction device that uses the method is defined in Claim  29 . Advantageous further developments of the present invention are indicated in the dependent claims. 
     A method according to the present invention is used to determine a soil parameter by means of a soil compaction device that has a contact element that is charged with vibration for soil compaction. During a contact phase, the contact element is in contact with the soil, and is thus exposed to a contact force F contact  exerted by the soil, and travels a contact path s contact . In the following, contact force F contact  is also referred to simply as contact force F, and contact path s contact  is referred to simply as contact path s. 
     The soil compaction device can be a vibrating plate or a vibrating tamper. It has a lower mass that comprises the contact element and an upper mass that standardly comprises a drive. The lower mass is coupled to the upper mass via a spring device. A vibration exciter that charges the contact element can also be a component of the lower mass, for example in a vibrating plate. In a vibration tamper, the vibration exciter operates by means of a path excitation, e.g. a crank mechanism situated between the upper mass and the lower mass. 
     The soil parameter that can be determined by the method according to the present invention is designated as dynamic modulus of deformation E v,dyncompaction , and is determined using the equation: 
     
       
         
           
             
               
                 
                   
                     E 
                     v 
                   
                   ⁢ 
                   
                     , 
                     dyncompaction 
                   
                   ⁢ 
                   
                     = 
                     
                       α 
                       - 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             F 
                             contact 
                           
                         
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               s 
                               contact 
                             
                           
                           
                             ︸ 
                             
                               k 
                               dyn 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Here, ΔF contact /Δs contact  represents an approximation (averaging) of the actual gradient of the contact force dF contact /ds contact . α is a contact surface parameter that takes into account the geometry and shape of the actual contact surface of the contact element with the soil during a particular time segment used for the determination of the actual contact surface. 
     On the basis of the dynamic modulus of deformation E v,dyncompaction , a dynamic shear modulus G v,dyncompaction  can be calculated, taking into account soil-dependent parameters (transverse contraction index υ) if warranted. 
     Soil contact parameter α, which expresses the influence of the actual contact surface as a geometric factor, is discussed in more detail below. Because the contact surface active during a load cycle, and also the contact force and the relevant contact path, can change from cycle to cycle both in their direction and in their magnitude, contact surface parameter α, as well as the contact force and the contact path, are determined during each load phase, i.e. during each load cycle. 
     The factor k dyn  represents the dynamic rigidity of the soil, and is formed as a gradient of contact force F and contact path s. The dynamic rigidity k dyn , which can also change within the load phase, is determined during each load phase in order to enable precise monitoring of the rigidity of the soil during the compaction process. 
     In order to determine the dynamic rigidity k dyn , first the contact force and the contact path traveled by the contact element during the contact phase must be determined. 
     Preferably, the components of the contact force F in the three spatial directions are determined from the center of mass principle, relative to a coordinate system fixed in the center of gravity of the contact element. Alternatively, the components can also be determined for a stationary coordinate system, e.g. relative to the soil. 
     In the case of a moving coordinate system, the resultant acceleration components result from the sum of the externally acting forces in the z direction, in accordance with:
 
 m   U ( {umlaut over (x)}   S   −{dot over (y)}   S   ·{dot over (N)}+ż   S ·{dot over (Φ)})=Σ F   X  
 
 m   U ( ÿ   S   −ż   S   ·{dot over (X)}+{dot over (x)}   S   ·{dot over (N)} )=Σ F   Y  
 
 m   U ( {umlaut over (z)}   S   −{dot over (x)}   S   ·{dot over (Φ)}+{dot over (y)}   S   ·{dot over (X)} )=Σ F   Z   (2)
 
where {dot over (Φ)}, {dot over (X)}, {dot over (N)} represent the corresponding rotational speeds in the pitch direction (about the y axis), the roll direction (about the x axis), and the yaw direction (about the z axis), and m u  represents the mass of the contact element. {dot over (x)} S , {dot over (y)} S , ż S  represent the respective translational speeds in the center of gravity of the contact element, while {umlaut over (x)} S , ÿ S ,{umlaut over (z)} S  represent the corresponding accelerations.
 
     The forces acting on the lower mass are composed (with i=x,y,z) from the respective force components on the basis of an imbalance excitation F ECC,i , from the resultant contact force to the soil F C,i , from the internal forces to the rest of the machine (e.g., the upper mass of the soil compaction device) F U,i , and from the components of the weight of the contact element. The sum of the acting forces can therefore be indicated as follows for the individual spatial directions:
 
Σ F   X   =F   C,X   +F   ECC,X   +F   U,X   −m   U   ·g ·sin(Φ)·cos( X )
 
Σ F   Y   =F   C,Y   +F   ECC,Y   +F   U,Y   +m   U   ·g ·cos(Φ)·sin( X )
 
Σ F   Z   =F   C,Z   +F   ECC,Z   +F   U,Z   −m   U   ·g ·cos(Φ)·cos( X )  (3)
 
where F C,i  is a contact force of contact element (1) to the soil, F U,i  is an internal force between contact element (1) and the rest of the machine (upper mass), m u  is the mass of the contact element, F ECC,i  is the exciting force of a vibration exciter that excites the contact element, and Φ and X represent the corresponding pitch or roll angle.
 
     If the two equation systems (2) and (3) above are set equal to each other, and solved for the respective contact force components, the following results:
 
 F   C,x   =m   U ( {umlaut over (x)}   S   −{dot over (y)}   S   ·{dot over (N)}+ż   S ·{dot over (Φ)})− F   ECC,x   −F   U,x   +m   U   ·g ·sin(Φ)·cos( X )
 
 F   C,y   =m   U ( ÿ   S   −ż   S   ·{dot over (X)}+{dot over (x)}   S   ·{dot over (N)} )− F   ECC,y   −F   U,y   −m   U   ·g ·cos(Φ)·sin( X )
 
 F   C,z   =m   U ( {umlaut over (z)}   S   −{dot over (x)}   S   ·{dot over (Φ)}+{dot over (y)}   S   ·{dot over (X)} )− F   ECC,z   −F   U,z   +m   U   ·g ·cos(Φ)·cos ( X )  (4)
 
     The overall resultant contact force can then be calculated from the individual components F C,i  by corresponding vectorial determination of the amplitude and direction of the overall acting contact force from the partial components. 
     The method according to the present invention can be used for example in a vibrating plate or a vibrating tamper. Because in such devices the contact force acts predominantly normal to the contact surface, the contact force portion in the contact normal direction, i.e. in the direction of the z axis, is preferably determined by evaluating the impulse balance in this direction. 
     The contact force can then for example be determined, as a simplification, as
 
 F   C,Z   =m   U   ·{umlaut over (z)}   S   −F   ECC,Z   (5)
 
where m u  is the mass of the contact element, {umlaut over (z)} S  is the acceleration of the contact element in the direction of the contact normal (z axis), and F ECC,Z  is the exciting force of a vibration exciter that charges the contact element.
 
     In order to determine the translational accelerations and the rotational accelerations: The translational acceleration {umlaut over (x)} S , ÿ S , {umlaut over (z)} S  of the contact element in the center of gravity can be measured for example by an acceleration sensor provided on the contact element itself. As an acceleration sensor, for example a triax sensor attached at the center of gravity, for measuring all three spatial directions simultaneously, is suitable. The translational speed components {dot over (x)} S , {dot over (y)} S , ż S  in the three spatial directions can then be determined for example by simple integration of the acceleration signals. 
     Alternatively, if for example as a result of the design a sensor cannot be attached at the center of gravity, the translational acceleration of the center of gravity in the three spatial directions (x, y, z), as well as the rotational acceleration about the three axes x, y, z, can also be determined using at least six acceleration sensors. These are preferably distributed around the center of gravity of the contact element in such a way that with regard to their measurement direction, each of three acceleration sensors is attached to the contact surface in the direction of a normal (z direction), but as far as possible these three sensors are not situated on a single line. Three additional acceleration sensors are situated such that they also are not situated on a single line, but are attached in the direction of a tangent to the contact surface, with respect to their direction of measurement. 
     Both the desired translational accelerations and the rotational accelerations can now be determined from the kinematic relation between acceleration at the center of gravity and the acceleration measured at an arbitrary point of the body, given existing, i.e. measured, rotational accelerations {umlaut over (Φ)}, {umlaut over (X)}, {umlaut over (N)}. The required angles of rotation Φ and X can then be determined by double integration of the rotational accelerations {umlaut over (Φ)}, {umlaut over (X)}. 
     In some cases of application, it can be sufficient to reduce the number of required sensors because some degrees of freedom are not present due to the design. Thus, the contact element of a vibrating tamper, i.e. its soil contact plate, executes a movement mainly in a translational direction, namely the direction of the normal to the contact (z axis), due for example to the parallel guiding of the tamper foot. Accordingly, for this application in some circumstances the use of a single acceleration sensor on the contact element is sufficient. If warranted, additional movement components can be determined using measurement sensors on the upper mass. 
     Another alternative is to determine the acceleration components in the direction of the contact normals in contactless fashion, e.g. using optical laser sensors. The sensors are then preferably provided not on the contact element, but rather on an upper mass that is connected to the contact element via a spring device. The upper mass can for example also comprise a drive motor for the soil compaction device, in a known manner. With the aid of the sensors, for example a change of distance between the upper mass and the contact element can be measured, so that, given knowledge of the position and orientation of the upper mass, the accelerations of the contact element in the contact normal direction at the corresponding measurement points can be determined by double differentiation. 
     Finally, radar sensors can also be used to determine the speed of the contact element relative to the upper mass, e.g. on the basis of the Doppler effect, or else on the basis of the distance, for example using interference radar, which also makes possible a calculation of the accelerations as described above. 
     In order to determine the exciting force F ECC : 
     In a specific embodiment of the present invention, the exciting force F ECC  coming from the vibration exciter can be measured by a force measurement device provided between the vibration exciter and the contact element. A suitable force measurement device is for example a force measurement cell attached below the vibration exciter. 
     Alternatively, the exciting force F ECC  can also be calculated from the momentary position of the exciter imbalance masses. For the case in which the vibration exciter has two shafts rotating in opposite directions, each having equally large imbalance masses, and whose axes of rotation have the same orientation as the y axis of the contact element and whose phase position to one another is adjustable, the components of the exciting force F ECC  relative to the stationary coordinate system on the contact element are calculated in simplified fashion, as a function of time t, using the following equations:
 
 F   ECC,X ( t )= EM·Ω   2  sin(φ Phase /2)·cos(Ω· t )
 
 F   ECC,Y ( t )=0
 
 F   ECC,Z ( t )= EM·Ω   2  cos(φ Phase /2)·cos(Ω· t )  (6)
 
where EM is the resultant mass of a rotating imbalance mass, Ω is the exciting frequency of the vibration exciter, and φ Phase  represents the phase angle between the two imbalance masses.
 
     Thus, the direction and magnitude of the momentarily acting imbalance force can be determined from the momentary position of the imbalance masses, as well as the knowledge of the angular speed of the exciter shafts and the size of the imbalance mass. 
     The exciting force F ECC  can of course also be calculated in vibration exciters having a different design. As a rule, it is represented as a function of time t, but can also be made a function of the phase position or angular position of the relevant imbalance masses. 
     For the case of the above-mentioned vibrating plate or vibrating tamper, in order to determine the exciting force F ECC  it is possible for example to make the calculation exclusively using the component F ECC,Z  acting in the direction of the contact normal, because for this purpose only the excitation in the direction of the z-axis, i.e. the direction of the normal to the contact surface, is significant. 
     The phase angle φ Phase , i.e. the relative phase position of the two imbalance masses to each other, is variable as a function of the user setting. The position of the imbalance masses can for example be determined using proximity sensors (inductive sensors or Hall sensors). The angular speeds of the imbalance shafts can then also be determined from the positions of the imbalance masses. 
     The internal forces F U,i  between the contact element and the rest of the machine can be determined for example by force measurement cells situated between the contact element and, for example, the upper mass of the soil compaction device. 
     In order to determine the contact path s: 
     The contact path s required for the determination of the dynamic rigidity k dyn  is determined at the times at which the contact element transmits soil contact forces, preferably in the vicinity of or at the resultant force application point, because the path of the force application point is the most closely connected to the change of the acting contact force. The determination of the position of the force application point is described in more detail below. 
     In order to determine the contact path, first the accelerations of the force application point are determined. Through double integration of the accelerations at the force application point, the amplitude and direction of the path at the force application point (contact path) can then be determined. 
     Accordingly, it is first necessary to determine the position of force application point P, which is explained in more detail below in connection with the calculation of contact surface parameter α. Given the position, determined in this way, of the force application point {right arrow over (SP)}=[SP x , SP y ,SP z ] T  (relative to a coordinate system in center of gravity S), the acceleration at force application point {right arrow over (a)} p  can be determined from the kinematic equations, according to:
 
 {right arrow over (a)}   P   ={right arrow over (a)}   S +{dot over ({right arrow over (ω)}× {right arrow over (SP)}+ {right arrow over (ω)}×({right arrow over (ω)}× {right arrow over (SP)} )  (7)
 
     As described above, the vector {right arrow over (ω)}=[{dot over (Φ)}, {dot over (X)}, {dot over (N)}] T  of the rotational speeds and of the rotational accelerations {dot over ({right arrow over (ω)}=[{umlaut over (Φ)}, {umlaut over (X)}, {umlaut over (N)}] T , as well as the translational acceleration at the center of gravity {right arrow over (a)} S =[{umlaut over (X)} S , Ÿ S ,{umlaut over (Z)} S ], can be determined using suitable sensors, which can for example be situated on the contact element. Preferably, however, only the contact path in the direction of the resultant contact force is taken into account for the evaluation. 
     If, for example, the contact force in a vibration plate acts predominantly normal to the contact surface, the contact path at the location of the force application point in the contact normal direction is preferably determined by evaluating the translational and rotational movement components. The evaluation of equation (7) for the component of acceleration at point P (force application point) in the z direction yields (ignoring the yaw movement; i.e. {umlaut over (N)}={dot over (N)}=0):
 
 a   P,z   ={umlaut over (z)}   S   +{umlaut over (X)}·SP   Y   −{umlaut over (φ)}·SP   X −({dot over (φ)} 2   +{dot over (X)}   2 ) SP   Z   (8)
 
     Double integration of a P,z  then yields the desired contact path s in the contact normal direction. 
     For the determination of the translational or rotational movement components, as already described above, for example three acceleration sensors are situated on the contact element in such a way that they do not lie on one line, but are attached so that their measurement direction lies in the direction of a normal to the contact surface. 
     In this way, for various measurement times a plurality of measurement point pairs can be formed from contact force F and associated contact path s. 
     In this way, for various points in time information is provided in a particularly advantageous manner about contact force F and the associated contact path s, so that for each point in time a measurement point pair can be formed of contact force F and contact path s. 
     Preferably, those measurement point pairs are determined that occur during a load phase, during which the contact element is increasingly pressed against the soil. In this context, measurement point pairs that occur during a relief phase, in which the load on the contact element is lessening, or an airborne phase, in which the contact element is in the air without touching the soil, are excluded from further evaluation. 
     For each of the measurement point pairs of the load phase, a gradient dF contact /ds contact  is formed that corresponds to the dynamic rigidity k dyn  at that point in time. The gradient dF/ds can also be formed as a ratio of two temporal changes (of the force and of the path). 
     Preferably, however, the gradients used for the respective measurement point pairs are averaged using a statistical method, so that the resulting average value can be determined as the decisive dynamic rigidity k dyn . 
     Alternatively, or in addition, a phase diagram can be created by computer for contact force F and contact path s, as a function of time t. For the part of the phase diagram representing a load phase, in which the pressure of the contact element against the soil is increasing, an average gradient dF/ds is formed that represents the dynamic rigidity k dyn . 
     For the determination of contact surface parameter α: 
     As already stated above, in order to determine the dynamic modulus of deformation E v,dyncompaction  a contact surface parameter α is also required in order to take into account the actual contact surface of the contact element with the soil. Advantageously, contact surface parameter α is determined on the basis of a calculated position of a force application point of contact force F. 
     The contact element, in particular a soil contact plate in a vibrating plate or vibrating tamper, has a base surface that is in contact with the soil when the soil compaction device is at a standstill. However, during operation, during which the method according to the present invention is intended to be applied, as a rule it is no longer the case that the entire base surface of the contact element is involved in the transmission of the contact force; rather, only a partial surface thereof, namely the actual contact surface, participates in this transmission. 
     Due to the forward movement, characterized by cyclical airborne phases of the contact element, and the concomitant oblique position of the soil contact element relative to the surface of the soil being compacted, but also due to an oblique position of the surface itself, only a part of the underside of the contact element is in contact with the soil, while the rest of the underside of the contact element extends into the air. In practice, this can mean that, in a soil compaction device having a contact element that has a rectangular base surface that, during standstill, completely contacts the soil, during operation the actual contact surface is less than one-third of the base surface. The actual contact surface can then also be rectangular, triangular, or can have some other geometry, but can be significantly smaller than the base surface. The contact surface also need not be flat, as in standardized plate load methods, but rather can be concave or convex in the various directions (axes). In addition, within the momentary actual contact surface there may be regions in which, due to the momentary speed distribution on the contact element, a small transmission, or no transmission at all, of contact forces takes place. These regions must be taken into account in the determination of the relevant contact surface. 
     Because the size of the momentary actual contact surface has a decisive influence on the magnitude of the transmissible contact forces (given a larger contact surface, a larger contact force can be transmitted, assuming otherwise equal, isotropic soil characteristics), this size must be taken into account in the determination of the moduli of deformation. 
     Because the actual contact surface during a time interval under consideration in an exciter vibration cycle does not have to be situated symmetrically relative to the base surface of the contact element, but rather can be for example situated in a rear area (relative to the main direction of travel of the soil compaction device) of the contact element, the contact force F resulting from the soil contact tension acts not at the center of gravity of the base surface of the contact element, but rather at some other location, in particular at or in the vicinity of a center of gravity of the actual contact surface. Due to this deviation of the two centers of gravity, or deviation of the force application point from the center of gravity of the contact element, additional forces and moments act on the contact element that must be taken into account in the determination of the soil parameters. 
     The size and geometry of the contact surface change during the contact. If, for example, a rectangular contact element contacts the soil with a corner (forming a triangular contact surface) at the beginning of a contact phase, this triangular surface will at first become larger due to penetration. The inclination of the contact element will subsequently change in such a way that its contact center of gravity (contact surface and force) will be displaced during the penetration. At first it will move toward the center of gravity of the contact element. However, under some conditions the contact center of gravity can also migrate past the center of gravity of the contact element. In the extreme case, the contact element will switch to the opposite corner within an exciter vibration period. 
     Due to the eccentric force application point, the contact element experiences an additional rotational acceleration that counteracts the mass inertia of the contact element. 
     It has turned out that contact surface parameter α can advantageously be determined according to the following equation: 
                   α   =     1     γ   ·     r   hyd                 (   9   )               
where γ is a value in a range from 1.5 to 2.7, in particular is 2.1, and r hyd  represents the hydraulic radius of comparison, and can be calculated from the actually effective contact surface A C  according to the equation:
 
     
       
         
           
             
               
                 
                   
                     r 
                     hyd 
                   
                   = 
                   
                     
                       
                         A 
                         c 
                       
                       π 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Here, in order to determine contact surface parameter α the center of gravity of the actual contact surface of the contact element with the soil can be determined, which itself is determined from a force application point of contact force F. Contact force F is a surface load that acts on the contact surface of the contact element. It can be modeled by a resultant force that is applied at the resultant force application point. This force application point can be regarded, in a first approximation, as identical to the center of gravity of the actual contact surface. In order to correct the deviation of the actual force application point from the center of gravity of the contact surface, a correction factor can be introduced that is determined for example by means of simulation. 
     In a specific embodiment of the present invention, the movement of the contact element during soil contact is acquired by measurement sensors. On the basis of the information determined by the measurement sensors, and on the basis of contact force F, the position and dimension of the actual contact surface, situated within the base surface of the contact element, and/or the force application point of the resultant contact force can be determined. 
     The measurement sensors should be sensors that are capable of acquiring the linear and/or rotational movements of the contact element relative to various degrees of freedom. 
     A measurement sensor can be provided with which a pitch rotational acceleration, caused by contact force F, of the contact element is determined relative to a pitch axis (y axis) that stands transverse to the direction of travel of the soil compaction device. 
     In some circumstances, the pitch or roll acceleration (about the x axis) caused by the contact force must be calculated from the measured rotational accelerations, with knowledge of the moment of excitation. Analogously, in order to acquire a roll rotational acceleration of the contact element relative to a roll axis (x axis) extending in the direction of travel, a suitable measurement sensor can also be provided. The pitch axis and the roll axis each preferably pass through the center of gravity of the contact element. In order to measure the pitch and roll rotational accelerations, however, it is also possible to use three sensors that are not situated on one line, but whose measurement direction is oriented in the direction of the contact normals (as already described above). 
     In addition, it can be useful if, in order to measure a translational movement of the contact element in the direction of contact force F, a corresponding measurement sensor is present. 
     On the basis of the movements of the contact element measured by the measurement sensors, in particular on the basis of the rotational accelerations about the pitch and roll axis, three rotational impulse balances can be set up about the pitch axis and about the roll axis, from which the contact torques, caused by contact force F, about the pitch axis and the roll axis can be determined, taking into account the exciting torques, due e.g. to an exciter and the internal moments to the rest of the machine. 
     On the basis of the contact torques, determined in this way, and the already-known contact force F, the lever arms of contact force F relative to the pitch axis and to the roll axis, and thus the position of the force application point of contact force F, can be determined. 
     As a first approximation, the position of the force application point of the contact force can be regarded as the position of the center of gravity of the contact surface, so that in this way the position of the surface center of gravity is also known. 
     On the basis of the position of the center of gravity of the contact surface, or on the basis of the force application point and a prespecified relation, contact surface parameter α can be determined. The relation between contact surface parameter α and the position of the surface center of gravity, or of the force application point, can be determined in advance by the manufacturer of the soil compaction device through trials, in order to obtain a diagnostically effective equation. The specification of this relation can be stored in the form of a table, or as an equation for calculation. 
     In this way, contact surface parameter α can be determined during each compaction cycle of the contact element, and can be constantly adapted as a function of the size or position of the contact surface. 
     After both the contact surface parameter α and the dynamic rigidity k dyn  have been determined in this way, dynamic modulus of deformation E V,dyncompaction  can be determined according to the formula stated above. 
     If required, calibration measurements can be used to create a connection between dynamic modulus of rigidity E V,dyncompaction  determined in this way and the moduli of deformation that can be determined using conventional measurement modules. For example, as a function of particular soil conditions tables can be created that permit the dynamic modulus of rigidity determined using the method according to the present invention to be transferred to other moduli of deformation that have been determined using standardized measurement methods. 
     According to the present invention, a soil compaction device is also indicated having a vibration exciter driven by a drive, a contact element charged by the vibration exciter that, during a vibration cycle, contacts the soil in phases or constantly, and is capable of briefly lifting off of the soil being compacted, and having a measurement system for determining a soil parameter that has at least one measurement sensor for acquiring a movement characteristic of the contact element. According to the present invention, the soil compaction device is characterized in that the measurement system is operated according to the above-indicated method of the present invention. 
     Advantageously, the soil compaction device is a vibrating plate or a tamper. However, an application to rollers is also possible in principle. 
     These and additional features and advantages of the present invention are explained in more detail below on the basis of an example, illustrated by the accompanying Figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1   a ) shows a schematic side view of a vibrating plate having a contact element, a vibration exciter, and an acceleration sensor; 
         FIG. 1   b ) shows the contact element of  FIG. 1   a ) with a schematic representation of the imbalance shafts of the vibration exciter; 
         FIG. 2  shows a perspective view of the contact element of  FIG. 1 ; 
         FIG. 3  shows a phase diagram indicating the contact force F contact  and the vibration path s over time; 
         FIGS. 4   a ) and  b ) show a contact element during operation with a small contact surface; 
         FIGS. 5   a ) and  b ) show a contact element during operation with a large contact surface; 
         FIG. 6  shows a schematic representation of forces and moments on a contact element (simplified); 
         FIG. 7  shows geometric relations on a contact element with a two-shaft vibration exciter; 
         FIG. 8  shows a contact element having a triangular contact surface; 
         FIG. 9  shows the contact element of  FIG. 8  in a top view; 
         FIG. 10  shows a contact element having a quadrangular contact surface; 
         FIG. 11  shows the contact element of  FIG. 10  in a top view; 
         FIG. 12  shows a top view of a contact element having a pentagonal contact surface; and 
         FIG. 13  shows a schematic side view of a vibrating tamper used as a soil compaction device. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       FIG. 1  shows, in a highly simplified schematic representation, a vibrating plate acting as a soil compaction device, having a contact element  1 . Contact element  1  can also be, in a similar manner, a component of a vibrating tamper. The contact element, acting as a soil contact plate in this way, transfers, in a known manner, vibration forces produced by a vibration exciter  2  into the soil being compacted. 
     As is shown in  FIG. 1   b ), vibration exciter  2  can be made up, in a known manner, of two imbalance shafts  3  that are capable of rotation in mutually opposite directions, and whose phase position to one another can be adjusted in order to achieve steerability, or change of direction, of the soil compaction device during traveling operation. 
     Contact element  1  is connected via a spring device  4  to an upper mass  5  so as to be capable of motion. A drive for vibration exciter  2  is standardly housed in upper mass  5 . Moreover,  FIG. 1   a ) shows a measurement sensor  6  that can be formed for example by an acceleration sensor. Measurement sensor  6  can be attached to vibration exciter  2 , or can also be attached directly to contact element  1 . 
       FIG. 2  shows a part of the design of  FIG. 1   a ) in a perspective view. 
     Here, contact element  1  is shown in a highly simplified manner as a rectangular plate. Instead of a single measurement sensor  6 , six measurement sensors  7 , which can likewise be realized as acceleration sensors, are situated on contact element  1 . 
     In addition,  FIG. 2  shows a pitch axis  8  (y axis) that extends transverse to a direction of travel X, and a roll axis  9  (x axis) that extends in direction of travel X. Pitch axis  8  and roll axis  9  intersect at a center of gravity  10  of contact element  1 . Acceleration sensors  7  are each situated at a distance from pitch axis  8  and roll axis  9  in order to be able to acquire rotational movements relative to pitch axis  8  and to roll axis  9 , in particular angles of rotation or rotational accelerations. 
     The present invention also relates to a measurement method for determining a dynamic modulus of deformation of the soil being compacted at that moment by the soil compaction device. For this purpose, the movement characteristic of contact element  1  is measured and is evaluated in suitable form, as described below. However, because the measurement method has also already been explained in detail above, in the following only the essential aspects of the measurement methods are summarized. 
     The dynamic modulus of deformation is determined by the equation: 
     
       
         
           
             
               
                 
                   
                     E 
                     
                       v 
                       , 
                       dyncompaction 
                     
                   
                   = 
                   
                     α 
                     - 
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           F 
                           contact 
                         
                       
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             s 
                             contact 
                           
                         
                         
                           ︸ 
                           
                             k 
                             dyn 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Here, k dyn  is the dynamic rigidity of the soil. Contact surface parameter at takes into account, as a geometric factor, the characteristic size of the contact surface, and in particular the deviation of the position of the force application point relative to the overall base surface of the contact element. Both dynamic rigidity k dyn  and also contact surface parameter cl can be determined during each load phase, so that a constantly current evaluation of these parameters, and thus of dynamic modulus of deformation E V,dyncompaction , is possible. 
     In order to determine dynamic rigidity k dyn , first contact force F contact  and the path S contact  traveled by contact element  1  during the contact phase, i.e. during contact with the soil being compacted, must be determined. 
     Contact force F contact  is determined from the center of gravity principle relative to a coordinate system fixed on contact element  1 . For this purpose, in addition to the acceleration of the center of gravity and the known mass of the contact element, the direction and magnitude of the exciting forces produced by vibration exciter  2 , the direction and magnitude of the internal forces to the rest of the machine, the weight forces, and the normal acceleration forces resulting from the rotational speeds must be determined. 
     In particular, contact force F contact  is calculated in simplified form for the case of the vibration plate shown in  FIG. 1 , as:
 
 F   contact   =m   L   ·{umlaut over (z)}   L   −F   ECC   (5)
 
     where m L  is the mass of contact element  1 , {umlaut over (z)} L  is the acceleration of contact element  1  in the direction of the contact normals, and F ECC  is the exciting force of vibration exciter  2  charging contact element  1 . 
     Translational acceleration {umlaut over (z)} L  of contact element  1  in the direction of the normal to the contact surface can be measured for example via measurement sensor  6  (acceleration sensor) in center of gravity  10  of contact element  1  (cf.  FIG. 1   a ). 
     Alternatively, the translational and rotational accelerations in the contact normal direction and in the direction of the pitch and roll axes can also be measured with the aid of the six measurement sensors  7  (acceleration sensors) attached for example around center of gravity  10  of the contact element, in the manner shown in  FIG. 2 . 
     In addition, the acceleration in the direction of the contact normals can also be determined in contactless fashion, for example using optical laser sensors, or with the aid of the Doppler effect, corresponding measurement sensors  6   a  preferably being attached to upper mass  5  of the soil compaction device for this purpose. 
     The exciting force F ECC  required for the calculation of contact force F contact  in the above equation can be calculated in simplified fashion using the following equation:
 
 F   ECC   =EM·Ω   2 ·cos(φ Phase /2)·cos(Ω·t)
 
where EM is the resultant mass of rotating imbalance shafts  3 , Ω is the exciting frequency of vibration exciter  2 , and φ Phase  represents the phase angle between the two imbalance shafts  3 .
 
     Phase angle φ Phase  can be varied as a function of the operator settings. It relates to the relative position of the two imbalance shafts  3  to one another, and can therefore be modified according to the operator&#39;s desired direction of travel (forward or backward). A measurement of phase angle φ Phase  is possible for example using inductive or capacitive proximity switches or Hall sensors. It is also possible to set the phase position of imbalance shafts  3  using a regulating valve, so that reliable information about phase angle φ Phase  is also available. 
     If, for the time elapsed during a load cycle, contact force F contact , calculated according to equation (5), is plotted over vibration path s, the typical contact force/vibration path phase diagram shown in  FIG. 3  is obtained.  FIG. 3  distinguishes two phases of a movement cycle of contact element  1 , namely an airborne phase (also called a flight phase), and a contact phase that has a load phase and a relief phase. During the airborne phase, contact element  1  is in the air over the soil being compacted, while in the contact phase a mutual action takes place between contact element  1  and the soil. 
     The point at which vibration path s=0 is regarded as the null point. Starting from this point, the imbalance effect of vibration exciter  2  presses contact element  1  into the soil, so that, corresponding to the climbing branch (cf. direction of arrow in  FIG. 3 ), as the vibration path increases an increase in contact force F contact  takes place. After a maximum has been reached, contact element  1  is relieved of load due to the imbalance action, so that the phase curve reaches the decreasing branch of the contact phase, until finally there is no longer contact with the soil (at s=2 in  FIG. 3 ). 
     The imbalance action lifts contact element  1  off the soil being compacted, and contact element  1  moves through the air over the soil, with no contact and therefore no contact force. 
     After a change in the direction of the vibration, contact element  1  again reaches the null position in the airborne phase, so that a new compaction cycle begins. 
     The vibration path s in the contact phase is designated contact path s contact . It can be computed through double integration of the acceleration of the contact element. As explained above, the translational and rotational movement components should be taken into account here, i.e. during the integration as well. 
     For the determination of the dynamic rigidity k dyn  of the soil, a plurality of measurement point pairs (contact force F, contact path s) can be determined in the load phase, and their gradient dF/ds can be determined. For this purpose, for example the curve can be approximated by a polynomial, using the least squares method. The gradient of the approximated curve can then be analytically calculated fairly easily from the polynomial coefficients. 
     The dynamic rigidity k dyn  is then determined by averaging the various gradients over the overall load phase, so that finally for a load cycle a k dyn  value can be found, as a measure of the dynamic rigidity, that represents an essential portion of the dynamic modulus of deformation E V,dyncompaction  according to equation (1). 
     In order to determine contact surface parameter α, first the following set of problems must be noted: 
       FIG. 4   a ) shows, in simplified form, soil contact element  1  during operation, compacting soil  11 . Due to the action of vibration exciter  2 , contact element  1  is positioned obliquely relative to soil surface  11 , so that only a rear part of contact element  1  contacts soil  11 . Correspondingly,  FIG. 4   a ) shows a contact surface  12  that reproduces the actual contact of contact element  1  with soil  11 . In contact surface  12 , contact forces  13  act as surface load. 
     In  FIG. 4   b ), contact forces  13  are combined as resultant contact force  14 , which acts in the direction normal to the contact surface at a force application point  15 , and which corresponds to the above-named contact force F contact . Force application point  15 , at which contact force  14  is applied to contact element  1 , has distance a from center of gravity  10  of the contact element. 
     For center of gravity  10  of contact element  1 , the mass of contact element  1  and of vibration exciter  2  are taken into account. 
     It can be seen clearly that force application point  15  does not coincide with a center of gravity of a base surface of contact element  1  that would result if contact element  1  was completely in contact with the soil. Rather, contact force  14  acts asymmetrically, or eccentrically, on the center of gravity of the surface of contact element  1 , and also on the overall center of gravity  10  of contact element  1 . 
     Analogously to  FIG. 4 ,  FIG. 5  shows a contact element  1  that acts on soil  11 , contact surface  12  being significantly larger here (see  FIG. 5   a )). This is the case for example if the soil is softer than in  FIG. 4   a ). 
     As can be seen from  FIG. 5   a ), force application point  15  of resultant contact force  14  is then moved closer to center of gravity  10 , so that distance a is reduced. 
     In order to determine contact surface parameter α, the position of force application point  15  of contact force  14  relative to the position of center of gravity  10  of contact element  1  can now for example be used. This approach is based on the consideration that given almost constant soil rigidity along the compaction path, the center of gravity of a large contact surface  12  ( FIG. 5   a )) is situated closer to center of gravity  10  of contact element  1  than is the case given a smaller contact surface ( FIG. 4   a )). 
     In order to determine the center of gravity of actual contact surface  12 , first the rotational accelerations, caused by contact force  14 , about the pitch and roll axes ( 8  and  9  in  FIG. 2 ) are determined. From the knowledge of the respective momentary resultant contact force  14 , and the torques caused thereby, force application point  15  can be calculated. For this purpose, the translational movement, the pitch movement, and the roll movement of contact element  1  must be determined using measurement sensors. For this purpose, for example measurement sensors  7  shown in  FIG. 2  are suitable. 
     The rotational movements that occur as a result of the contact, in particular the pitch and roll movement of contact element  1 , can be determined from the rotational impulse balances in the pitch and roll direction with knowledge of the mass inertia moments (known a priori) of the contact element on contact element  1 , so that the contact torques, caused by contact force  14 , about pitch axis  8  and about roll axes  9 , can be calculated, as is explained below. 
     From the contact torques, with knowledge of contact force  14 , or F contact , the lever arms of contact force  14  in the roll and pitch direction, and thus the position of force application point  15 , can in turn correspondingly be determined. Here, the position and geometry of the contact surface are inferred from the knowledge of the center of gravity of the contact force. Because the soil may be uneven, this is not unambiguously possible in all cases. However, it is technically sufficient to create a relation through suitable trials and statistical evaluation of the load cycles. 
     The relations are shown in simplified form in  FIG. 6  for the case of a vibrating plate. 
     In general, in order to calculate contact surface parameter at first the position of the theoretical force application point  15  must be calculated: 
     Using the principle of conservation of angular momentum, the rotational accelerations in the center of gravity of a moved body, or of a coordinate system fixed in the center of gravity, is calculated from the sum of the acting external torques, according to:
 
 I   X   ·{umlaut over (X)} +( I   Z   −I   Y )·{dot over (Φ)} {dot over (N)} −( {umlaut over (N)}+{dot over (X)}{dot over (Φ)} )· I   XZ +( {dot over (N)}   2 −{dot over (Φ)} 2 )· I   YZ +( {dot over (X)}{dot over (N)} −{umlaut over (Φ)})· I   XY   =ΣM   X  
 
 I   Y ·{umlaut over (Φ)}+( I   X   −I   Z )· {dot over (N)}{dot over (X)} −( {umlaut over (X)}+{dot over (Φ)}{dot over (N)} )· I   XY +( {dot over (X)}   2   −{dot over (N)}   2 )· I   ZX +({dot over (Φ)} {dot over (X)}−{umlaut over (N)} )· I   YZ   =ΣM   Y  
 
 I   Z   ·{umlaut over (N)} +( I   Y   −I   X )· {dot over (X)} {dot over (Φ)}−({umlaut over (Φ)}+ {dot over (X)}{dot over (N)} )· I   YZ +({dot over (Φ)} 2   −{dot over (X)}   2 )· I   XY +( {dot over (N)}{dot over (Φ)}−{umlaut over (X)} )· I   ZX   =ΣM   Z   (11)
 
     The moments of inertia of contact element  1 , I X , I Y , I Z , etc., can be determined from CAD data, or may be determined experimentally. The rotational accelerations can be determined using suitably positioned acceleration sensors  7  as described above. 
     The components of the applied torques result from internal moments M U  to the rest of the soil compaction device (upper mass), the moments M C  caused by the soil contact force, and the moments M ECC  exerted by vibration exciter  2  about the respective axes x, y, and z, according to:
 
Σ M   X   =M   C,X   +M   ECC,X   +M   U,X  
 
Σ M   Y   =M   C,Y   +M   ECC,Y   +M   U,Y  
 
Σ M   Z   =M   C,Z   +M   ECC,Z   +M   U,Z   (12)
 
     For torques M C,1  effected by soil contact force components F C,1 , the following may be used:
 
 M   C,X   =F   C,Z ·r C,Y   −F   C,Y ·r C,Z  
 
 M   C,Y   =−F   C,Z ·r C,X   −F   C,X ·r C,Z  
 
 M   C,Z   =F   C,Y · C,X   −F   C,X ·r C,Y   (13)
 
where r C  represents the coordinates of the force application point relative to the center of gravity of contact element  1 .
 
     r C  are therefore the coordinates that define the position of force application point  15  relative to the center of gravity of contact element  1 . They can be determined by solving the above equation system (13), taking into account equation systems (11) and (12). 
     The following thus results for coordinates r C  of force application point  15 : 
     For the case of a contact element whose excitations lie in the xz plane of the center of gravity (i.e., F C,Y ≈0), there results for the lever arms: 
                     r     C   ,   Y       =       M     C   ,   X         F     C   ,   Z                 (   14   )                 r     C   ,   X       =       -     [       M     C   ,   Y       +       F     C   ,   X       ·     r     C   ,   Z           ]         F     C   ,   Z                 (   15   )               
r C,Z  is the z coordinate of the underside of contact element  1 , and is known e.g. from CAD data.
 
     For the case in which the vibration exciter has two shafts rotating in opposite directions, having equally large imbalance masses, whose axes of rotation have the same orientation as the y axis of contact element  1 , and whose phase position to one another is adjustable, the components of the exciting torque about the axis (pitch moment) M ECC,Y , relative to the stationary coordinate system on the contact element can be calculated as a function of time t in simplified form using the following equation:
 
 M   ECC,Y   =EM·Ω   2   ·[e   Z ·(sin φ V +sin φ M )− r   S ·(cos φ V +cos φ V )]  (16)
 
     EM is the resultant mass of rotating imbalance mass  3 , and Ω is the exciting frequency of vibration exciter  2 . The angles φ V  and φ H  represent the momentary phase angles of the front and rear exciter shafts relative to the vertical (z axis). They can be determined separately, for example using proximity switches on each exciter shaft. r S  represents half the distance between the exciter shaft midpoints, and can be taken from CAD data or can be measured directly. e Z  is the distance of the exciter shaft center of gravity from the overall center of gravity of the lower mass in the z direction, and can likewise be determined from CAD data. 
     The relations are shown in  FIG. 7 . 
     For the case in which the center of gravity of the two exciter shafts in the x and y direction agrees with the center of gravity of the contact element, the exciter does not produce any additional exciting torques about the x axis and about the z axis. The torque components M ECC,X  and M ECC,Z  are then zero. For all other cases, the torques can of course be calculated by computer from the momentary position of the imbalance masses. 
     In the following, as an example a method is explained for the approximate determination of actual contact surface  16  for the case of a rectangular contact element  1  and a flat one: Due to the pitch and roll movement of the contact element, contact will always begin from a corner or edge of the contact element. 
       FIG. 8  shows a schematic perspectival view of a contact element  1  whose travel direction is in the direction of the x axis. On contact element  1 , a triangular contact surface  16  with straight boundary edges is shown in broken lines. The outer boundary lines here are known from the known outer geometry of contact element  1 . 
     The missing inner boundary line (contact edge  17 ), which in the ideal case is straight, is now calculated from the condition that force application point  15  is situated for example in the center of gravity of the triangle forming contact surface  16 . 
       FIG. 9  shows an example of the construction of the missing inner edge of contact surface  16 ; in this example, the contact begins at a corner  18  (point of intersection of edges I and II of contact element  1 ). 
     From the knowledge of the center of gravity of the surface (which should be identical to force application point  15 , so that the above-determined coordinates r C  hold) and the condition that the two straight lines g 1  and g 2  intersect in the center of gravity of the surface, and given the known coordinates of the two edges I and II of contact element  1 , a system of two equations can be created and solved for the desired unknown intersection points (x s1 , y s1 ) and (x s2 , y s2 ) of the inner edge of triangular contact surface  16 . The procedure is analogous if the contact begins at a different corner of contact element  1 . 
       FIG. 10  shows a case in which one of the points of intersection calculated in this way according to  FIG. 9  goes beyond the actual geometry, i.e. in particular goes past the relevant edge of contact element  1 . In this case, the calculation of inner contact edge  18  is then carried out again, under the assumption that contact surface  16  is now quadrangular. For quadrangular contact surface  16 , from the known position of the surface center of gravity (coordinates r C  of force application point  15 ) and the geometric construction rules, an equation system can now likewise be set up and solved in order to determine the unknown points of intersection with the contact element edges (edges I and II). 
       FIG. 11  shows the geometrical determination of center of gravity  15  of a trapezoidal, quadrangular surface. 
       FIG. 12  shows a case in which, on the basis of the superposition of the rotational and translational speed components in a part  16   a  (dotted surface) of contact surface  16 , a speed distribution arises in which this part moves away from the soil. These surface portions should then be given lower value in the calculation of the actual contact surface  16 , because there practically no soil contact forces, or only very low ones, are transmitted. 
     A speed zero line  19  runs between surface part  16   a , which lifts off from the soil and is shown in dotted lines in  FIG. 12 , and surface part  16   b , shown with hatching in  FIG. 12   b , which moves toward the soil and thus transmits soil contact forces. 
     The presence and the position of a zero line  19 , at which the speed of the contact element in the normal direction changes its sign, can be calculated from the kinematic relations, given known translational and angular speed of the center of gravity of contact element  1 . For the overall speed at a point (r x , r y ) of contact element  1 , given pure translational movement in the z direction and superposed pitch/roll movement, there results:
 
ν P,z   =ż   S   +{dot over (X)}·r   y   −{dot over (Φ)}·r   x  
 
     Setting the speed to zero then yields the relevant linear equation for speed zero line  19 , according to: 
     
       
         
           
             
               
                 r 
                 y 
               
               ⁡ 
               
                 ( 
                 
                   r 
                   x 
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     Φ 
                     . 
                   
                   · 
                   
                     r 
                     x 
                   
                 
                 - 
                 
                   
                     z 
                     . 
                   
                   S 
                 
               
               
                 X 
                 . 
               
             
           
         
       
     
     Because speed zero line  19  is always a straight line, in the worst case there results a pentagon for the relevant contact surface (hatched surface  16   b ), as  FIG. 12  shows.  FIG. 12  shows the resulting contact surface when speed zero line  19  is close to a corner  20 . Because the center of gravity of the triangular surface that is to be drawn away (dotted surface part  16   a ) is known, the center of gravity of dotted triangular surface  16   a  plus the hatched actual contact surface  16   b  can be calculated as a summed center of gravity. For the resulting quadrangular overall surface (surface parts  16   a  and  16   b ), the missing contact edge  17  can then be calculated again according to the method described above. 
     The definition of the one-dimensional modulus of elasticity in soil mechanics is as follows: 
     
       
         
           
             E 
             = 
             
               
                 
                   ( 
                   
                     1 
                     - 
                     
                       υ 
                       2 
                     
                   
                   ) 
                 
                 · 
                 
                   1 
                   
                     2 
                     · 
                     r 
                   
                 
               
               ⁢ 
               
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   F 
                 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   s 
                 
               
             
           
         
       
     
     Here the soil is loaded by a circular, rigid plate having radius r and constant distribution of pressure. F describes the applied force, and s describes the sink-in depth. For cohesionless soils, Poisson&#39;s ratio υ is approximately constant, and is for example always used with υ=0.212 in the evaluation of the static load plate trial. 
     Gradient ΔF/Δs was already determined above, so that for contact surface parameter α the following formulation is to be used (with υ=0.212): 
     
       
         
           
             α 
             = 
             
               
                 1 
                 
                   2 
                   , 
                   
                     1 
                     · 
                     
                       r 
                       hyd 
                     
                   
                 
               
               . 
             
           
         
       
     
     In this definition, the above-named value γ is set to 2.1, which yields suitable results. However, it has turned out that Poisson&#39;s ratio υ can vary given different soil qualities. Correspondingly, the factor γ can lie in a range from 1.5 to 2.7. 
     r hyd  represents the hydraulic comparison radius, and can be calculated according to 
               r   hyd     =         A   c     π             
from contact surface A C  (reference character  16 ), whose determination was explained above.
 
     In order to enable dynamic modulus of rigidity E V,dyncompaction  to be compared with moduli of deformation determined using conventional, e.g. standardized, measurement methods, calibration measurements can be carried out, or calibration tables can be evaluated. 
     The method according to the present invention, or a soil compaction device such as a tamper or a vibrating plate operated using the method according to the present invention, make it possible to determine the soil rigidity, or the dynamic modulus of deformation of the soil, during compaction. The method is particularly well-suited for soil compaction devices in which the contact element executes relatively long airborne phases, and in which, due to significant rotational movement components, the contact force and the contact path often have unpredictable, changing directions. The method is also well-suited for taking into account different contact geometries or different effective actual contact surfaces. This is a significant difference from previously known measurement methods used in particular with soil compaction rollers, in which the contact surface and also the direction of the dominant contact force to the soil is essentially constant, or can be reliably predicted a priori. 
     Soil compaction devices having short airborne phases, or no airborne phases, can however also determine the soil rigidity and the dynamic modulus of soil deformation using the method according to the present invention. 
       FIG. 13  shows, in a side view, a typical vibrating tamper in which the method according to the present invention can be used. 
     Machines in which an essentially constant contact characteristic can be assumed (vibrating rollers) can also use the method described herein to determine the soil rigidity and the modulus of soil deformation.