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EARTHQUAKE ENGINEERING proposes an innovative technique to assess quality of Marble and Travertine and the improvement of quarries management by reduction of water consume using dust control by Soilworks patent Durasoil.

**1) Assessment of the Rock Quality with Vibration Monitoring**

The impact of the rock wall with the ground applies a pressure that breaks the rock and transfers the kinetic energy to the ground at the base of the excavation. The impact is dumped by the presence of a bed of granular material that decreases the acceleration gradually (“baggioli” in Italian). The excavated rock can remain intact if the quality is high or the bench can break into pieces.

Data on the commercialization of Roman Travertine shows that only the 20 – 30 % of the volume of the benches becomes a commercial stone. This means that the other 80-70% is fragmented as a calcareaous granular soil with grains of big dimeter. The definition of a scientific measure of the Rock Quality can be very useful for the owner of the Mining Company because the amount of the material is very large and the variation of a small percentage of the order of 3% can increase the production with a sensible economic difference. The error of 3% on the prediction of a bench value in a volume in which only the 30% is commercially valid means the increase of production of 10% in a single working activity.

The 3% can be valued with an approach based on physics. The energy that is transferred to the base, that the bench exchanges during the impact is:

dU = dl + dQ (1)

The internal energy U changes, because the impact apply an inertial force to decrease the speed of the rock. The impact cracks the massive wall and it creates the parts varying Q, that is the energy that the material has stored during cementation: i.e. the carbonation.

dQ is a chemical process that creates calcareous stone during thousands of years with calcite deposition and CO^{2} storage. The liquid CO^{2} becomes a solid that bonds the grains and transforms a sediment in a solid. Marble is the same rock that is immerged by tectonic activity at many meters depth and the chemical bonds became crystals better ordered giving the stone a typical light reflection.

The breakage of the chemical bonds of the rock is not reversible and then to obtain the amount of energy that is lost during the impact, equation (1) can be transformed removing the elastic reversible deformation. The reversible work of deformation L is computed by:

Where, V1 and V2 are the difference in the volume of the stone due to compression applied by the impact (compression +dV). Part of the elastic work is restituted to the environment as an elastic wave that travels into the excited base. The breakage of the chemical bonds is computed with the variation of the latent heat Q stored into the rock during the diagenesis.

The characterization of the material with a measure like the one in chapter 2 with Sequoia GEA monitors can give a value of Amplitude in m/s, that is the velocity of vibration in time and Frequency in Hz (Hertz) that is the inverse of the wave lenght in seconds s^{-1}. Assigning to the commercialized volume: Amplitude (A) and Frequency

(F) the spectral analysis can be compared with the material extracted in other zones.

The degrees of freedom for the characterization are 2. The maximum value of v is for F max, but comparing 2 different zones with different velocities, the frequency distribution can give an idea of the different quality with the extension:

Comparing the distribution of figure 1, L* is the length necessary to have in the same time interval s1=s* , the velocity of the zone A_{2} equal to v_{1}. L_{1}/L* in equation (4) is the percentage (%) of difference between the qualities of the two benches.

Figure 1 principle of the Rock Quality definition

Figure 1 explains the monitoring assessment of the Rock Quality. The impact produces the inertial Force –F(A) and the weight and gravity the Force +F(A). The two directions changes with a wave function described in the third graph on the right. The first graph is the distribution of the Amplitude with the Frequencies with Gauss function, see the standard output in figure 4 and 5. The two Gauss distributions in

figure 1 corresponds to the different Rock Quality of 2 benches. The highest is for the upper value V_{2} the poorest the one with V_{1}.

It is possible to acquire 2 informations:

a) The ratio between V_{2}/V_{1}, the maximum value of both benches. This gives the **Maximum Strength of the Rock.**

b) The Probability of exceeding the value of F(1/s*) for the second bench, the poorest (the one with V_{2}). The black area. This is the probability that in the highest quality a part of the material has a strength lower than the poorest one. The velocities are not unique for the gauss bell distribution. The black area on the left indicates that for the lower velocities a part of the records can represent a material with higher caracteristics with respect to the second, the one with higher peak value of V. Probability is the ratio between the 1 black portion on the whole gauss of the highest one. The 1 – X(%) is the income of the real value before division in blocks of the second respect the first.

**2) ****Monitoring of Vibrations: GEA System**

The Monitoring is obtained using the Sequoia GEA System. The device has high precision and a wide range of recording values, characteristics are reported in figure 2. The range of characteristics of GEA System allows to apply the piezoelectric sensor to a variety of problems.

In case of the Quarry Records SW GeaLab Software will be used for processing of signals and

GEAReport is the document obtained respecting the legislative limits of Standards.

TABELLA 1 CARATTERISTICHE DINAMICHE G

**3) Boltzmann Entropy as a measure of the Quality of the Rock, how to increase prevision.**

The inertial measure of the example shows the difference between the vertical axis and the horizontal one. This asymmetric behavior is due to the gravity direction. The increase of precision in the estimation of the quality of the 3% is obtainable with a scientific Formula and the record of wave speed.

Formula is the expression of the Boltzmann Entropy S = K logW.

The visual identification of the quality can be assessed only on a 2D face. In the hypothesis that the assessment is totally arbitrary, volume can have the 50% of probability to be classified correctly as a good volume or bad rock. This estimate is the worst estimate for the rock that is not yet reached by the front and then visible.

Immagine to divide the volume of the bench in many small cubes of 3D marble/travertine, the 50% can be statistically a Good Rock and the other 50% of Bad Rock.

If you consider the whole volume as Good or Bad, at 100%, the probability related to the entire volume is the sum of n! (where n is the number of the cubes of the benches) If you consider the probability of 50%, the sum for Bad or Good is : n/2! Economic Value or n/2! Environmental Expense.

Using the Logarithm espression, the difference between the Best Estimate and the

Worst (visual 2D not Excavated) is:

This is the knowledge of the value of the bench without any scientific evaluation, observation is not useful to assess quantitatively Rock Strength, experience of other benches are also not exactly correct because the Marble strength varies depending on diagenentic formation. K is a constant (known as the Boltzmann constant), M is the mass of the bench.

For an high number of n, that means for small cubes, the punctual logarithm is :

With the GEA monitoring system in the 3 directions, the measure allows an increase of the estimation of the quality with an increase of 3 % as a minimum of knowledge.

This result is obtained using the Formula for the Volume of the Bench: (H x B) x D, where D is the dimension of the cut, generally 1.5 – 1.0 meter, the thickness of the bench. The weight of the bench is a medium density time the volume, but the potential energy is MgH, where H is th Height (m), M the mass, and B (m) is the width.

Fixing H, the other two dimensions are characterized by 2N information for the face of the benches. In total the 3N small masses (with equal length) are the object of the analysis. N is the maximum number, with the 3D volume in x,y and z directions.

The ratio between 2N/3N is 2/3 = 0.66. 66% is the probability that the Head of The Quarry (the chief of the workers), can assess perfectly the Quality of the Rock with the observation of the 2D face and the fracturation corresponds to the estimated economic value as foreseen by the business plan of the administration. The 3% of difference between 66% and 69% represents the 10% -15% of the material that can be extracted increasing production by a tipping and controlling the quality in the various part of the quarry. Infact Log (1-0,63) = 1.0, that means 66% +/- 3%, is the best practice of 69% or the misevaluation of the third direction in the 3D Volume. The amount of 10 – 15% is evalued as the increase of 3% of the 30% that is sold.

The variation in the knowledge of the Quality of the Rock depends on the judgment of the whole mass, that means, Prevision of Economic Value is :

In which dn is the increase in the numbers of small cubes that are assessed. The increment of correctness or error is dn on n, because the total Mass M is divided in n small cubes . For a very large number of small cubes n, the error is small but also **the change in right economical prevision is small. Higher is the volume higher will be the convenience.**

**If the 3% of improvement is applied to the AVARAGE of 30% of the WHOLE QUARRY, the improvement of the VALUE of the EXCAVATED ROCK will be:**

In which 0,30 is the commercial Marble or Traverine and 0,03 is the ERROR of 3% that is avoided.

Considering the value of the Area without knowing the Quality before the Marble exposition, Log(1.0)=0.0, means knowledge is 0 or error is 0, minus the real AVARAGE of GOOD ROCK on the entire AREA:

The improvement of knowledge of the 3% of the volume with Inertial Monitoring with a precise scientific measure can double the value of the ROCK reducing it from the COST of Environmental Management with + or -.

**An example:**

the cut is different from the transport of the material but the time needed for the cut of the bench is the same, independently from the quality.

The transport of the 3% for commercially valid Rock or Waste Material, for 10 benches is the 30% of the time used in 2/3 months of the trucks. This extimation is not irrelevant, for 1 year is 200%. 200% is the error for the prevision of time need for wasting excavated rock or 2 benches on 60, means an error of 1 truck that is used to move the COST rather than the PROFIT for the 3% of the material = 2 benches. Being 60 benches, the 30% of the GOOD MARBLE or TRAVERTINE is 18 benches of Good Material, 2 benches is the 11% of the PROFIT of wasted time.

To compute the difference between the coefficient 1.2 and 2.3 in equation (6) and (7), consider 2 parts of the quarry or 2 benches in which the average of the good rock is 30%. The 2 can be characterized by a 60% in one and 0% in the second. Then 1 part of the quarry for 1 year could produce quite zero commercial material and the other year the double of the AVARAGE of the ENTIRE QUARRY. The Management can RISK for the FIRST YEAR to have liquidity problems.

**The measure can be correlated to:**

1) Rock Quality.

2) Volume (W1) Rock that is commercial.

3) Volume (W2) Rock needed for filling the quarry pit after excavation. B-W1=W2. Kowing the Volume of the Bench, the relation is direct.

4) Time to commercialize and to fill the Quarry Volume.

Figure 6 Engineering records of quality with wave speed

To better understand the link between the equation (1) and the method, figure 1 explains the link between the measure and the energy. Subtraction of equation (2) , the elastic work, from equation (1) gives:

Equation (3) is called Enthalpy and it is recorded in point A (see figure 1 ). The pressure wave is vdP and is the maximum recorded by piezoelettric accelerometers by Sequoia. dQ is the vibration of the cristaline structure of the marble, it is the difference between the vertical and horizontal velocity.

The efficiency of the excavation technique can be obtained by:

a) Limit of vibration imposed by UNI, if the activity affects a civil building near the impact.

b) Limit of vibration due to the Noise, this is the record done by the authority for the workers protection.

The efficeny is not measured as a LEGAL or INSPECTIVE threshold but only to know the margin for the environmental activity.

The vibration mode is referred to the quantity:

dS is the results of our analysis described in a Report with the Spectral Analyses.

**4) Example of the application of the method**

Area of a Quarry is divided in 4 sectors ,dividing the Quarry in the 4 sectors, each zone is characterized by the Sequia Monitors as in the table 1 (higher is the division higher is the quality of the prevision):

From only 1 impact for each zone F the frequency an V the velocity are correlated to the Commercial Volume and the Limit imposed by UNI Norms or Phonometric VALUE limited by Reginal Authority. Assigning to the benches 1,2,3,4; values B_{i} and W_{ij} we can obtain the value : B_{i}-W_{1i} That is the volume needed for Environmental recovery.

Volume/time is B_{1}/t and W_{1i}/t, gives the amount:

W_{1i}/t x Dt e B_{i}/t x Dt in the 4 sectors are an information for the owner that can know the Volume that effectively are Commercialized or Used for The Filling:

The measure has 2 advantages: |

1) Certify to the Administration the Volumes B_{i} and W_{ij}with the vibration records

2) Certify the timing for the Environmental Recovery of the Original Volume.

Following the scheme of the figure 1, an exemple of Quarry Management can be reported in table 2.

First data is for sector 1, from only 1 bench the owner knows that the commercial stone was the 30% and the income 10 euro/100 Kilos (10 euro/ 1 Quintale)

In other sectors the measures are reported in table 2, where (Fi*Vi) is the operation described in figure 1. Suppose that the orders for the next 2 or 3 months are variable and the measure have been verified for the values:

Periods with low demand can be managed with sector 2 and for high demand with sector 4. Inconvenience can be managed with areas of medium efficency of sector 1 or sector 3. Repeating the measures, it can ensure the buyer of another country that the marble is good before his survey. The commercialization can be improved with scientific data of the wave speed by GEA System sent by certified e-mail (PEC in Italy) in his country like: China, Iran, Giordania and in EU countries like Spain, Turchia, etc. Travel cost in the marble selection could be 2.000 or 3.000 euro. A medium dimension Quarry can sell 40 blocks per month. A weight of 400 tons. A profit of te order of 40.000 euro. The cost of the information transport is like 5% of the gross income.

**5) Application of the Product Soilworks (U.S. Patent/ U.S. Army certified) DurasoilÒ for Dust Control and Water Saving.**

The Quarry Production can be increased also reducing the consume of water and the time used to wet the ground for the Dust. Today, synthetic fluids are available on the market. We reports the data provided by SOILWORKS a U.S. Producer.

To wet the ground to control the dust with DURASOILS, cost is:

1 liter/square meter for approximately 1-3 months of longevity without the need to water. Maintenance is typically 30% of the originally treatment volume. Durasoil is approximately $1.35/Liter in 1,041 Liter IBC Totes (plus freight).

For 1000 m2 1.350 dollars (equal to 1.232 euro change 3/10/19). With 2 applications is 2.700 dollari (2.464 euro), for 2 meters of trucks way: it corresponds to 500 meters

Soilworks can give more information: https://www.soilworks.com

**6) Abaco to compute the water management.**

To Compute the Advantage of Dust Control, we propose the method below. From Quarry water supply:

Input: Pressure = X; tube diameter = Y Abaco /see below : Flow = Z(X,Y)

Time of effect of DuraSoil with reference of 3 months = 3 x 24 days x 10 hours =720 hours

Liters for 10% of time of the working day spent for wetting: With volume of H_{2}O time the Flow results Z x 720 x 0,1 = number of liters

Example: Quarry uses 1 bar pressure and wet the roads for 1 hour with a tube of 2 cm diameter (see pag 14, Abaco values) :

From the Abaco ,Volume of H_{2}O = 4826 x 720 x 0,1 = 3.725.627 liters

Equivalence in m3 = 3,725,627/1000 = 3.726 m3 Considering a small pool of 100 m x 20 m = 2000 m2 Area, with: 37.256/2000 = 1,8 m Depth

This water is saved from the counter and the mix dust/water does not exit from the working area reducing the Environmental Charge of Dust,

In Roma ACEA data are circa 3,7 euro per mc , after 200 mc, Saving is 3.726 x 3,7 = 13.800 Euro for only the summer season.

**7) References for Innovation Technology**

R. Tamagnini , Mavroulidou, M, Gunn, M.J. (2010) A constitutive model for unsaturated cemented soils, UNSAT 2010, Barcellona, Spain

R. Tamagnini , Mavroulidou, M , Gunn, M.J.(2010) Implicit integration of a costitutive model for unsaturated structured porous materials UNSAT 2010, Barcellona, Spain

R. Tamagnini, Mavroulidou, M, Gunn, M.J. (2010) Numerical analysis of equilibrium and stability in unsaturated multiphase media, NUMGE 2010, Trondheim, Norway

R. Tamagnini, R.A. Hiley., M. Mavroulidou and M.J. Gunn, (2011)

Thermodynamics of unsaturated soils, AP UNSAT2011, 5th Asian Pacific Conference on Unsaturated Soils

Barbara M. Switala , R Tamagnini , W. Wu and L. Sanavia (2014) implementation of a constitutive equation for the finite element analysis of landslide triggered by rainfall, 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI)

R. Tamagnini & W. Wu Modeling water induced instability in partly saturated soil

(2015) Universität für Bodenkultur, Institut für Geotechnik (IGT), Feistmantelstraße 4,Vienna, Austria

R. Tamagnini, B.M. Switala,, M.S. Acharaya,, W. Wu, F. Graf, M. Auer, L. te Kamp, Finite Element Analyses of Bio- Engineered Slopes (2015) University of Natural Resources and Life Sciences, Vienna, Austria. Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), J.Krismer Handels GmbH, ITASCA Consultants GmbH

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