Earthquake Engineering Method of Seismic Load Control using Galilean Frame of Reference (Version 4.0 new English – Transfer of Monitor data) (TPD1911050)

2)   Description of Monitors for Vibration: GEAÒ System

Monitoring is performed using the Sequoia GEA System.

The device has a wide range of the recordable value for accelerations, and its precision guarantees the capability of assessing the spectrum of the dynamic mode of vibration during soil consolidation with Soiltac.

Period T is defined, as the time needed to restore the initial configuration after an oscillation, the accelerogram of the input for a FEM analysis is an old record like the one of figure 5. The repetition of the velocity value is very short, than the improvement of the strength is important (linked to the maximum amplitude) but the viscous characteristic of the fluid phase is important too. Non-symmetric acceleration repeated for many cycles of shearing can damage the structure also for low intensity.

In case of a classic building with a perimeter of 20 m length for the maximum dimension, a soil layer with 2D vertical section area: 20 m x 20 m should be compared with the volume of the single shallow foundation of 4 m² (2 meters base of the footing), the ratio between 4m²/(20×20)m²=0.01. It means that the design for static loading uses the 1% of the volume characterized with geophysics, when the waves enter the Index of Risk.

Figure 5, Acceleration records at National Station (INGV).

The proposed treatment of the soil foundation considers material as a porous solid composed by water, solid and gas. This hypothesis can reduce the cost of retrofitting of the original design using the Van der Waals forces: it means to use the adhesion of the water/gas or water/air mix with viscosity:

Equation (5) can be viewed as a probabilistic function using the Boltzmann Entropy:

Maxwell-Boltzmann distribution function describes the N number of moles of water/gas mix that apply the Enthalpy PV on the mass m on a spherical volume. Fixing the PV (enthalpy) of the fluid in the porous network, the number N(v) with kinetic energy ½ mv² increases exponentially with v². The soil beneath the foundation in the first 2 or 3 meters is characterized by a high potential of liquefaction, the far zone is characterized by a smaller probability of damage. This incertitude explains why the geotechnical method to design foundations in seismic areas are empirical.

Earthquake Engineering uses a ‘hybrid’ method based on the monitoring with wave amplitude and frequency analysis. The official website of INGV (Istituto Nazionale Geofisica e Vulcanologia) publishes daily the seismic events also of small intensity in Richter scale with epicenter and depth. The records with GEA system by Sequoia can be referred to the same node of INGV and the records can be compared for two events of same magnitude. The Retrofit is obtained until the required value of safety is reached and then stopped with a maximum efficiency of the investment.

The use of Entropy instead of Elasticity is suggested by the logarithmic nature of deviator stiffness of soils reported in figure 6. The increase of volume of the building/infrastructure suggests that the proposed idea is efficient. Data is reported by the Jardine study on the small strains stiffness for embraced excavation.

Figure 6, Deviator stiffness of soils for different value of strains.

4)   Use of Soilworks (U.S. Patent) fluid SoiltacÒ for improving visco elastic behavior of foundations.

Soiltac can be filtrated as reported in figure 7 or it can be injected with low pressure with same technical method of the expansive synthetic polymers. Companu Systab of Parma has reviewed the idea and confirmed their devices are able to infiltrate the mix Soiltac and water into the ground. Contrary to the expansive polymers used for cohesive soils and for differential settlements, Soiltac acts using viscosity. The dynamic behavior is the characteristic used in seismic design. In order to explain the mechanism of consolidation the gravity percolation is depicted in figure 7. A column generates the hydraulic gradient and the flow is due to gravity into the fringe of capillary zone. The difference in the height is 2 meters and the tube is open at the bottom, a second tube is installed in the right part to check the filtration regime. An increase of the level in the tube represents the flow regime variation. The fluid Soiltac is mixed with water and the effect is monitored with Sequoia GEA System. Percentage of the Soiltac in one liter of water is decided by preliminary shear test on the type of soils (see next paragraph). Assuming a permeability of K = 10^-7 m/s in order to filtrate a molecule of H₂O + product Soiltac^Ò , time will be 10⁷/(3600 x 24) =115 days The regime will be stationary in at least the double of time: 250 days. The filtration can be stopped when the monitors by Sequoia will record a reduction of the amplitude necessary to satisfy the required degree of safety. Use of Monitoring System excludes the instability induced by the Soiltac fluid filtration, because any unforeseen geotechnical incertitude is immediately recorded and the intervention is stopped.Same degree of safety is not possible with structural intervention. In case of use of low-pressure injection, the filtration of mix water/Soiltac will take few days per foundation.

Figura 7: Hydraulic gradient and Soiltac^Ò in the compressed zone of the foundation, (according Terzaghi equation)

5)   Data of unconfined compression of loose dry sand treated with SoilTAC in laboratory SOGEA Roma (SOGEA is a certified laboratory for Geotechnical Tests by MIT Ministero Infrastrutture e Trasporti).

Soilworks, is a United States company based in Arizona, Phoenix (7580 N Dobson Rd #320, Scottsdale, AZ 85256, United States). It provided a sample of their patented fluid to test the efficiency in controlling soil viscous plastic behavior.

Geologist Sergio Rabottino, SOGEA, laboratory of Roma, via Casal Monferrato n.2, and Engineer Roberto Tamagnini, have treated 3 samples of dry sand with Soiltac.

The tests are UCS Unconfined Compression Strength tests in which sample is loaded to reach the ultimate state of failure (figure 8 e 9)

Figura 8 and 9: Laboratory device for the test of soil treated with Soiltac and initial sand (loose – dry)

Soiltac is used to treat dry sand. Dry soil weight was 300 grams, mixed with 3 different percentage of fluid:

1)    Sample 1: 100 grams Soiltac

2)    Sample 2: 75 grams Soiltac + 10 gramms of H₂O

3)    Sample 3: 75 grams Soiltac

Engineer Chad Falkenberg, CEO of Soilworks, has confirmed the data by SOGEA, and the expected values reported in figure 10 are in line with Soiltac characteristics. The fluid is certified by E.P.A. – Environmental Protection Agency (U.S. Agency) and used by the U.S. Army for “dust control” for aircrafts and helicopters landing in arid zones.

Figure 10: Shear strength vs. axial compression for 3 samples treated with Soiltac

Results of figure 10 show that Soiltac effect is a remarkable increase in soil stiffness and strength. Maximum value obtained is 700 KPa (for 75 grams of Soiltac plus water, 10 grams). Company Soilworks uses the formula of their product to protect soil embankment from erosion; in this case, the ratio between fluid and water is ¼. In case of seismic wave control, the percentage could be higher. Consistency of the treated samples confirms that a loose sand has become a weak rock slightly cemented.

An extensive Report on the mechanical behavior of the treated sand is attached in Copy: Laboratory Engineering Data.

6)   Example of Retrofit for an old building (Certification by a chartered engineer of Ordine degli Ingegneri di Roma for Fiscal SismaBonus DM 2017 MIT).

From the website of the Italian INGV, Istituto Nazionale di Geofisica e Vulcanologia, it is possible to access the records of the strong motion network in Richter scale, recorded every day, in many nodes. As example, the link to the Amatrice node is below:

http://cnt.rm.ingv.it/events?starttime=2019-10-03+00%3A00%3A00&endtime=2019-10- 10+23%3A59%3A59&last_nd=365&minmag=2&maxmag=10&mindepth=- 10&maxdepth=1000&minlat=35&maxlat=49&minlon=5&maxlon=20&minversion=100&limit=30&orderby=ot- desc&tdmt_flag=-1&lat=42.63&lon=13.29&maxradiuskm=30&wheretype=pointradius&box_search=Italia

The list of seismic events can be downloaded from the website. The value of Richter is ML (es. il 2019-10-07 at 15:13:31, earthquake had a magnitude ML 2.0 Epicenter 4 KM from Norcia (PG)).

Indirizzo u_ciale: http://terremoti.ingv.it

Personalizza Ricerca Mappa

Fuso Orario: Italia Ultimi 365 giorni

Magnitudo: 2+

Punto: (42.63, 13.29) – Raggio: 30 km

Visualizzati terremoti da 1 a 30 dei 242 trovati Esporta lista (UTC)

Dal 19 giugno l’INGV pubblica in questo spazio, come sul canale Twitter @INGVterremoti, le localizzazioni

preliminari dei terremoti calcolate in modo automatico. Data e Ora (IT) Mag Zona

2019-10-07 15:13:31 ML 2.0 4 km N Norcia (PG)

2019-10-05 15:50:08 ML 2.1 8 km W Accumoli (RI)

2019-10-03 04:34:23 ML 2.0 3 km E Norcia (PG)

2019-09-29 00:18:01 ML 2.7 5 km W Montemonaco (AP)

2019-09-28 22:57:20 ML 2.0 4 km W Arquata del Tronto (AP)

2019-09-25 18:03:03 ML 3.3 6 km W Montemonaco (AP)

2019-09-25 12:41:44 ML 2.6 8 km E Norcia (PG)

2019-09-23 23:38:59 ML 2.0 2 km E Norcia (PG)

2019-09-23 19:49:41 ML 2.1 4 km E Norcia (PG)

2019-09-23 08:33:48 ML 2.1 4 km W Torricella Sicura (TE)

Same magnitude ML 2.0, was verified also in other dates, for example, the 2019-09-23 at 23:38 – 2Km from Norcia.

With coordinate:

Point: (42.63, 13.29) – Distance 30 km.

Referring to the measuring points of chapter 1 on the church, it is possible to obtain the difference of velocities between the epicenter and the nodes of the Church with the Galileo frame of reference, it means:

Monitor A1 records V₁ at 15:13:31 of the day 2019-10-07, and the INGV (Istituto di Geofisica e Vulcanologia), records the value V₂that it publishes on the website as ML 2.0, at 4 Km from Norcia

V₂ – V₁ = V_a1is the velocity of the frame of reference of the POINT: (42.63, 13.29).

The day 2019-09-23 at 23:38:59 at 2 km E from Norcia (PG), the V2 is recorded and V₂– V₁

=V_a2. Va₂ gives the attenuation of the Seismic Load on the Frame due to Soil Improvement, it should be = or < of Va₁, the previous record. Magnitude of the two days is the same: ML 2.0 and the effect of Soiltac has improved the ground response to dynamic wave shaking. From the correction obtained by the product Soiltac:

DVa = V_a1 (2019-10-07) – V_a2 (2019-09-23) = X

Is the value of the RETROFIT.

After the consolidation the value of Vs30 and Nspt, are repeated and the Standard EC8 are used to submit the Retrofit and the Fiscal TAX refund.

With 2 classes of reduction of the Risk Index the owner can have a detraction of taxes equal to 96.000 Euro. Bonus is for each apartment of the Building.

7)   Engineering Design of Retrofit according EC8.

In this example, the soil data are published by N.G.I. Norwegian Geotechnical Institute, (figure 1.1 provided by Jorg Johansson – N.G.I). Samples are chemically treated with salt. The data are selected because they are depicted using the velocity instead of deformation or strains. The speed is the derivative with respect to time of the strain measure. Comparison of the two concentration gives the different shape of the soil stress-strain behavior. This result is useful to understand the change of convex/concave shape. Figure on the right in 1.1, explains the Retrofit with Soiltac treatment and Sequoia monitors. Test performed at SOGEA are obtained by a constant rate of shearing. The data by N.G.I. are quite different and they shear soils with increasing rotation speed. SOGEA is performing other tests changing concentration of Soiltac quantity to assess viscous – plastic behavior. In situ measure will be obtained by accelerometers. Structural concrete or masonry could also be restored with Self-Healing concrete to avoid corrosion of rebar.

The following mathematical development is an explanation of the EC8 and the classic pseudo static computation with handle calculation for dynamic load.

Figure 11 represents the classic frame of a building or the Church of figure 1.

Figure 11, frame loaded by an earth-quake

The first principle of dynamics supposes that the sum of the active force is equal to the mass of the material point time the acceleration: F=ma, Equation of the sum of the unbalanced forces is:

F(t) = F_I(t) + F_D (t) + F_E (t) (5)

In which:

F_I(t) = m × u” (t) Is the inertial force.

F_D(t) = m × u· (t) Is the viscous force into the concrete

F_E(t) = k × u(t) Is the elastic force, that is used for dimensioning If the equilibrium holds:

F(t) = F_I(t) + F_D (t) + F_E  (t) = 0   → F_I(t) = −F_D (t) − F_E (t)                                                                                                       (6)

In engineering, stress is computed as s=F/A, with A the area of the section. In standard practice, the forces are computed at nodes with a simple method of pins and the soil is considered un-deformable.

 

Innovation is based on the hypothesis that ground improvement is beneficial at least with the same efficiency of the structural one.

The stress into the beams due to the pseudo static force is computed solving a system of equation and computing the samm. There are simple subroutine and freeware that can solve the problem easily knowing the INGV input, for Pushover Analyses. This analysis requires inputs only for the construction material. Their validity in the frequency domain is quite questionable; the experience suggests that increasing mass of the building, especially of old masonry, was an unsuccessful approach. The Report for the Retrofit and Fiscal SismaBonus includes the Pushover Analysis to have a comparison of the Amplitudes recorded with SOGEA, but the masonry works will not be designed on these Numerical Data. Figure 12 explains the method that combines soil consolidation and monitoring system. The nodes of the frame can be re mapped back to the original position before the seismic wave transit. The inertia into the piezo electric GEA system records the evolution in time of the Forces F₁ and F₂. The forces are due to the deformation of the foundation during quake. Difference between F₂-F₁ is the deviator stress into the soil layer. Looking at the figure 1.1, the data by NGI on clays treated with salt, it is clear that the improvement of shear strength is due to chemical reaction. In the Earthquake Method, Soiltac obtains the improvement. The flex of the right test in figure 1.1 indicates a condition in which the rate of the F₂ – F₁ increases with velocity, changing curvature from concave to convex. This is naturally not possible, because gravity acceleration is constant. The behavior is due to the reduction of horizontal F1 rather that an increase of vertical F₂ with to different rates, leading to the condition of 2^nd order instability described by Euler. The equation of motion is: (see figure 12):

Figure 12 Inertial force Monitored and reported at the nodes with Sequoia GEA.

Second Principle of dynamics gives the wave input and the unbalanced force into the ground:

In figure 9 is reported the oscillation with dumping of the node of the frame.

Fig. 9, Viscous effect due to direction change.

The damaging force –c x du(t)/dt, will be smaller if the soil is incompressible but second derivative can produce the effect of figure 1.1 right with a FLEX. Increasing the mass, the effect on the c coefficient is the denominator under square, but on the left is the multiplier of u_t: the seismic load.

The pseudo static force can be expressed as:

The EC8 Euro code 8 – Seismic Design gives an expression similar to the analytical solution:

NTC2018 (Italian law that reports the EC8) gives the Force to compute the dynamic load for the structure with Q_max, from the knowledge of ratio a/g taken by INGV website for the considered area, as:

S: is the Geotechnical coefficient used in the EARTH QUAKE ENGINEERING METHOD:

S_T depends on the topography (plane, hill, etc.) and S_s from the classes A-E S1-S2, described below:

From the table is possible to reduce the Force from a value Max of 1,00 (class A) to Min. of 1,80 (class D) . Increasing the value of the Force for the Computation, the Index of Risk changes of 80% fixing S_T. In order to reduce the pseudo static force, the value of S is obtained from N_spt as in Tab.3.2. V.

N_spt, from 15 to 50 corresponds to a change from D to B. S_ve (T) changes 1,20/1,80 = 0,66 that is the 66%.

From graph, the value of S can be changed from 3.5 (classe A) to 2.5 (classe E) with a change of 40%, at peak, but increasing T from T = 1 to 3 (class A to class D), the reduction is of 200%, see equation (3).

Fig.13 Spectral Analysis according NTC2018, increase of 200% at T=1 from A to D

8)   Results by R. Tamagnini (2011) that demonstrate the effectiveness

Geotechnical scientific publications rarely report a measure of fluid phase compression, because water liquid is considered uncompressible in fully saturated sands. Numerical and geotechnical analysis of a constant volume test for nuclear waste management is reported in Tamagnini (2011). Paper shows feasibility of the proposed technology. The two clay samples (then with a cohesive matrix) are compressed with the air pressure to verify the confinement for the water flow impermeability. Changes in thermal value of T, the temperature, is due to the amount of stocked nuclear fuel. The vapor – water phase % changes during air decompression and the re compression, the second compression simulates the Entropy cycle. Phase transformation gas-liquid does not allow an increasing in the thermal value of T. This is convenient for the Retrofit, because old designs are Formula without Temperature. Data are obtained during the HADES Project, financed by UE, on the Thermal behavior of the Boom clay; Boom is the region of Mol in Belgium, where the SCKN research center is located. Results are depicted in figure 14

Fig.14 Test for constant volume test on Boom clay. Romero (1999) [7]

Pressure wave applied by seismic event can be assessed by suction cycles 500/0 – 0/500 KPa, the vertical axis of the upper diagram. Suction and capillary stress is represented by the difference in the applied air/gas pressure u_a and water pressure u_w: (u_a – u_w). The second parts of the tests: A1-A2 and B1-B2 show irreversibility in the records of the Net mean stress. Entropy is a state variable only and only if irreversibility does not occur. The nonlinear hysteretic data shows that sample has changed position during a phase transition. This is due to the fusion of gas in liquid vapor; the process is not reversible without heating the sample with a source. Confinement is reported by the value of Net stress between 0 and 500 KPa: with an increase of the 20% of density (from 13.7 KN/m³ to 16.7 KN/m³) the sample has shown mechanical stability. Test with “loose” at 13.7 KN/m³ shows that the suction cycle, and then the seismic wave transit, has produced a condition in which shear decreases (Dev. measure) in both cycles compression – decompression, and softening occurred. Confinement is Net mean stress = 0 KPa at the end of the second cycle. The end of the second cycle is the Liquefaction in Earthquake Engineering – FEM modelling.

Entropy of Boltzmann:

At the suction values of 1000 KPa and 2 KPa, in the first cycle of decompression,

Confinement is:

Net stress = 120 KPa, test loose (13.7 KN/m3) – 1000 KPa of suction Net stress = 360 KPa, test dense (16.7 KN/m3) – 1000 KPa of suction Maximum is for the double of the phase space W=2W, the Net stress: Net stress = 240 KPa test loose (13.7 KN/m3): 120 x 2 KPa

Net stress = 720 KPa test dense (16.7 KN/m3): 360 x 2 KPa Value of Entropy:

In the two cases: the uplift of the foundation starts at 1000KPa. In the first (13.7 KN/m³) the double of the phase space W = 120 x 2 = 240, has produced Liquefaction or Friction Sliding, in the second test dense (16.7 KN/m³); g (gravity acceleration) has produced only a radial deformation, and it occurred in the first cycle, corresponding to 180 KPa of deviator strees. Second cycle of recompression does not increase softening for 16.7 KN/m3.</sup>

To obtain the same result with a Frictional test the weight of the building should increase of 3 times, this is why the increase of Period in figure 13 increases of 200% the displacement or reduces of 2 times the force.

In case of use of Soilworks – Soiltac, increase of strength is obtained with the increase of fluid density, passing from gas to liquid. In case of partially saturated sands, the matrix is compacted removing the capillary forces induced by menisci. In saturated sands the effects is induced with the viscosity of fluids. Thermal capacity of sand grains is higher than atmosphere, after permeation the fluid mixed with water exchanges heat with solid grains and cooling induces increase in viscous – plastic response (see test by SOGEA) . Reducing the Reynolds number of 1000 times:

The coefficient 2,3 is the change of base from 2,76 to 10:

Oedometric settlement are monitored and the expected value is in the order of:

Where, 50 KPa indicatively is the vertical pressure applied to sand by foundation and -100 KPa is the maximum capillary tension due to partial saturation.

9)    Example of measures and Retrofit

The difference F1 – F2 = Q is the deviator stress in the column. The monitors are depicted in figure 14, the type of output in figure 15 by the Sequoia GEA System. Difference from horizontal F1 and vertical F2 velocity is reported in blue and red.

Figure 14 Node of the Frame with Monitor and Inertial Direction

Figure 15 Example of acquisition by GEA System

Result shows that difference from blue and red start after the zero. Acquisition performed with same ML, Richter value, after the consolidation period should reduce the deviator peak Q.

 

Figure 16 : 3D FE model used to investigate the caisson load-deflection behavior; and b) verification of the Winkler spring SSI model bay comparison to 3D FE continuum model After H. Law et al. (2011)

An example of classic Pushover Analysis is reported in figure 16. Study is for the analysis of load displacement of a bridge foundation by Earth Mechanics.

Using FEM analyses, Retrofit would be obtained comparing a prevision of displacement induced by the Seismic Force provided by the INGV. The Return Period and the actual condition of the building are the input. The Theoretical Force from the curve gives the displacement without dynamic inertia: the one of the I_SLVin the Macro Area of the Building. Cost of site investigation does not allow reducing the Risk Index without introducing Complex Analyses with FEM.

The frame should be characterized with constitute parameters: stiffness as well as strength and the soil too. Generally, these analyses are required for Strategic Structure as Bridge or Dams. In the Method Proposed by Earthquake Engineering, the Return Period is used as the Interest of the Investment. It means, if the Probability of occurrence is 1 time at least in 750 years, means that the money invested will be useful at least 1 time in 750 years for an existing Building. However, the verification of the Investment can be verified only with the Reference Earthquake of the Area. Otherwise, the scale of the “sample” can be the Building itself, if it is monitored day by day with a very sensible device. Non Linearity is recorded with the GEA System for same excitation ML. Increasing in deflection – rotation will be not possible from the time of installation for same value of ML. Plastic threshold can be measured with records like the one in the N.G.I. in data of figure 1.1. If ML is compared with speed N=5 RPM, the event of ML=4 of same duration should detect the instability at N=10 RPM. Quantity of Treatment, i.e % of Salt, is for the Volume, but not for the Mass. It means that Records are function of the Treated Volume so ML does not only affect Absolute Records with ML but also with Time, because 2.5 g/l for 1 m³ is 1.0 g/l for 0.4 m³. Convexity is detected. Partial Saturation is the KEY. 1 g/l is not applicable to a just existing 2 meters strip footing. A bigger volume of soil controls it.

This is the characteristic of Entropy. It is statistically linked to the Mass because is an Energy. This is the advantage of the use of Temperature rather than Deformation in a point.

Pushover Analyses will be provided anyway without visco-elasticity.

10)       References for the Innovation Technology.

(1)    P. Riva, Comportamento delle Strutture in C.A. in zona sismica, Dispense corso di Ingegneria Sismica Università di Bergamo (resource on line)

(2)    Eurocodice 8, UNI EN 1998-1: Progettazione delle strutture per la resistenza sismica.

(3)    REGIONE LAZIO – DIPARTIMENTO ISTITUZIONALE E TERRITORIO Direzione Regionale, AMBIENTE Area: DIFESA DEL SUOLO ELENCO PROGRAMMATICO DELLE STRUTTURE STRATEGICHE O RILEVANTI ELABORATO IN BASE ALL’INDICATORE DI RISCHIO PER LA SALVAGUARDIA DELLA VITA (IRSLV).

(4)    R. Tamagnini (2004), An extended Cam-clay model for unsaturated soils with hysteresis, Geotechnique, 54(3), pp 223-228

(5)    J.A. Fernandez Merodo, M.Pastor, P.Mira, L.Tonni, M.I.Herreros, E.Gonzalez and R.Tamagnini (2003) Modelling of diffuse failure mechanisms of catastrophic landslides, Computer Methods in Applied Mechanics and Engineering. Special Publication. Ed. R.J. Borja, vol. 193, 2911-2939

(6)    J.A. Fernandez Merodo, R.Tamagnini, M.Pastor and P.Mira (2005) Modelling damage with generalized plasticity, Italian Geotechnical Journal, vol. 4, pp 32-42.

(7)    R. Tamagnini (2011) On the effective stress principle in unsaturated soils, Italian Geotechnical Journal, vol 3, pp 21-27

(8)    E. Soranzo, R. Tamagnini and Wu. W. (2016) Face Stability of shallow tunnels in partially saturated soils,

Geotechnicque 65(6) pp. 454-467

(9)    SOILWORK.COM Website for Industrial PATENT

(10)  Soil-Structure Interaction for Gravity Caissons in Bridge Seismic Design (2011) Hubert Law, Ph.D., P.E.¹, I. Po Lam¹, P.E., G.E., and Patrick Wilson, Ph.D., P.E.¹

1Earth Mechanics, Inc., 17800 New Hope Street, Suite B, Fountain Valley, CA 92708; PH (714) 751-3826; email: H.Law@earthmech.com