### Shallow Foundation Risk Analysis with Soiltac

###### Roberto Tamagnini, Eng. M.Sc. Ph.D.

*2020-04-23*

**STARTUP Earthquake Engineering Lab. Test**

DATA ON: Shallow Foundation Retrofit by Nano Technology

Soilworks Soiltac with Monitors GEA by Sequoia

The foundation is treated with Nano polymer Soiltac and the GEA piezo electric accelerometer is at the top of the column. It is set with a threshold to acquire data after a certain value of Richter ML. In sake of simplicity, only the horizontal force is described.

DATA BY GEA CELL

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.

The pre and post processing of data are obtained by software SW GeaLab and GEAReport.

Figura 2 GEAII Sensor

Figure 3 Signal in the domain of time

Figure 4 signal in the domain of frequency

EFFECT OF POLYMER SOILTAC

The horizontal displacement is monitored together with the vertical one. This means that the variation of Amplitude and Frequency during one-year period of consolidation is studied with a 3D wave trace that allows computing the inertial energy transferred with friction to the building. The application of the same Earthquake Force: F describes a Retrofit when DL decreases. This happens because the drag force of the vapor/water mix during the quake input reduces the flow rate from the porous network thanks to the Soiltac treatment. The logarithmic nature of the shear stiffness shows that the flow rate of the fluids is fundamental for the response of the soils boundary. The solid matrix composed by grains has a density higher and it is un-deformable.

Theoretical Stiffness for an elastic continuum can be rearranged to show the influence of the frequency:

Kinetic Energy for unit volume V:

Deriving:

First term is the variation of the kinetic energy of 1 cubic meter when the length is changed at constant frequency. It is a Pressure Kg/m^{2} multiplied by the frequency with quadratic expression.

This term was investigated in Laboratory of SOGEA, Roma, see figure 1

CONSTANT FREQUENCY

Figura 1 SAMPLES WITH CURING TIME SHEARED AT CONSTANT SPEED OF PUSHING PISTON dL

CONSTANT DISPLACEMENT

Figura 2 SAMPLES WITH CURING TIME SHEARED AT CONSTANT SPEED OF PUSHING PISTON WITH 1 WEEK PERMEATION

Second term is the variation of the kinetic energy of 1 Kg on 1 meter of displacement in 1 second. It is a Pressure Kg/m/sec. This term was investigated in Laboratory of SOGEA, Roma, see figure 2. It is the amount of internal energy U released in 1 week when the boundary was at 100% of Humidity, compared with the internal energy of the cured samples at 40% of Humidity.

CONSTANT SHEARING WITH QUADRATIC TIME OF VAPOR CONTROL – JUMP IS HEAT TRANSFER

Graphic means: after 40 days of reaction, the maximum infiltration obtainable with a vertical displacement of water is a reduction of : from 5000 KPa to 1200 KPa, inertia cannot induce Liquefaction because 1,2/5 = 0,29 (0 is liquid chemical heat of Soiltac is released in the environment). A reduction of 29% of safety factor is obtained by inertia of liquid phase. At 60 days it is 9000 to 3300 is 0,37 or 37% (10% increased). Applying a boundary condition of 100% of humidity the frequency of exchange of heat is 7 x 24 x 60 x 60 =604.800 seconds. Then 1/T=0,6 x 10^{-6}, Darcy is 1m/T = k Grad Pw. Horizontal q flow at liquefaction is undefined.

FLUCTUATION OF THE EQUILIBRIUM DUE TO DENSITY VARIATION (LIQUEFACTION)

Considering the cyclic motion of the foundation, the waves should be analyzed including the variation of water/gas density:

s,w and g are solid water and gas

Kinetic Energy for unit volume V:

Deriving:

Equating the first 2 terms, at equilibrium without changes in H , the elevation:

Including the deformability (fluctuation):

Fixing the acceleration, a or a/g, the Energy Balance is obtained when the log variation of density is equal to the sum of the log of f frequency and L length.

This explain the data of Romero 1999. Gas speed records are for the different frequencies and length in horizontal and vertical direction, otherwise the records in the linear regime were insignificant.

For the Seismic Retrofit increasing the density by surfactants the 2^{nd} order equilibrium condition is function of:

**Increasing soils weight is beneficial for the static equilibrium: case of loose dry sand. Retaining water improves inertial response. (Case of Romero is the 20% , it means from 16 KN/m3 to 19.2 KN/m3 : from dry to wet sand)**

**Compaction or Densification is an increase of dW (disorder). Sign convention for soil mechanics.**

**Liquefaction is a jump with dr=0, it is the phase transition of gas in liquid. The second derivative of Gibbs energy includes an undefined condition of equilibrium. Radiation of Energy.**

**Tests of laboratory are valid for 1 point, with the GEA System the Foundation is monitored for the whole soil structure interaction.**