WF Resonant Column Apparatus Combined Resonant Column (RC) & Torsional Cyclic Shear (TCS) Test apparatus to determinate with saturated soil : Shear Modulus Damping Modulus versus Shear Strain

WF Resonant Column Apparatus The base pedestal is fixed (the same as a standard triaxial) but the specimen top cap is free to rotate. A rotational force (torque) is applied to the specimen top by electro-magnetic system which applies the stress or strain loading in frequency up to 250 Hz. Ideal for Research Conforming to ASTM D 4015

The aim Typically small and medium strain levels The WF-Resonant Column allows the investigation of stress-strain behavior in the small shear strains level field Typically small and medium strain levels High accuracy testing systems, suitable for that levels of strains

The aim (% Strain) Dynamic System Ranges 10 10 10 10 1 10 This bottom half graph shows the range of strain encountered from machines or natural causes. The top half shows test systems that can perform these range of strains Dynatriax - Cyclic Triaxial Bender Element Cyclic Simple Shear TCS-Torsional Cyclic Shear Dynamic System Ranges RC-Resonant Column Small Strain Triaxial 10 - 4 - 3 10 - 2 10 - 1 10 1 10 Machine Foundations Causes of Vibrations Ocean Wave Loading Earthquake 10 - 4 - 3 10 - 2 10 - 1 10 1 10 (% Strain)

Stress conditions of soil sample during earthquake The aim before throughout Stress conditions of soil sample during earthquake

Soil response to cyclic vibrations The aim Soil response to cyclic vibrations

The aim Secant shear modulus Secant shear modulus Damping ratio

Strain level and mechanical The aim Strain level and mechanical behaviour Small strain level behaviour Medium strain level behaviour Big strain level behaviour

Strain-dependent shear modulus and damping ratio The aim Strain-dependent shear modulus and damping ratio G0 or Gmax

Local Seismic Response of a real soil The aim Local Seismic Response of a real soil Change of D and G against depth, due to different density g of the soil layers and to different geostatical stress levels Layer 1 Layer 2 Layer 3

The aim Typical range of G/Go curves against shear strain g for gravels, sands and clays

The aim Range of strain Soil strains on site Micro strains Dynamic tests Conventional triaxial tests Large strains Micro strains Small strains Soil strains on site Local measurement of strains

WF Resonant Column Apparatus The test procedure includes a series of measurements of the resonance frequency against the increasing levels of shear strains, in order to define the diagram (g – G). For each level of strain, once the resonance frequency has been measured, the damping ratio is also calculated, in order to define the diagram (g – D).

The System

The Cell double coaxial perspex cell, electromagnetic system: External perspex cell wall double coaxial perspex cell, electromagnetic system: 8 coils encircling 4 magnets connected to the sample upper end, measuring system (axial transducer, proxy transducers, pressure transducers, volume change system) Axial transducer Proxy transducers support coils magnet specimen Internal lexan cell wall

The Cell Parts Double cell Electromagnetic system: fixed part Magnets supporting frame and top cap: moving part Double cell Proxy transducers motion system

The Cell Electromagnetic drive system connects to the specimen top cap Double cell system

How does it work ? The electromagnetic drive consists of eight coils mounted on a drive plate with four magnets positioned on the specimen top cap assembly. When a sinusoidal current is applied to the coils, it pulls the magnets in one direction and reverses the direction as the sine wave changes from positive to negative. The actual rotational movement of the top cap is determined by the stiffness of the specimen being tested. The double cell is to allow us to have water in the inner cell up to the top cap with a layer of silicon oil on top of the water. The outer cell confining pressure is air. The water in the inner cell is to prevent air diffusion through the specimen membrane and the silicon oil is to prevent air entering the water.

The Cell Electromagnetic system fixed to the inner cell top Magnets supporting frame and top cap: free to rotate

The Cell The top picture shows the electromagnetic drive system which is attached to the top of the inner cell. The bottom picture shows the top cap with the four magnets. This is attached to the specimen with a membrane and o rings, the same as a standard triaxial set up. This assembly is free to rotate.

The Cell The inner cell containing the specimen is filled with water with a silicon oil top to prevent air diffusion through the membrane. The outer cell pressure is air which acts on the water producing equal pressure to the inner & outer cell. We use a double cell to separate the air and water when applying cell pressure. The electromagnetic drive system can only run in air. If we used air around the specimen we can have air diffusion through the membrane. This happens in long term tests, so we use de-aired water as in our standard triaxial tests. Double cell

The Measurements Two proximity transducers are mounted on the electro- magnetic drive system to monitor the rotation of the top cap assembly. Proximity transducers are non contact transducers which do not interfere with the rotation of the top cap. Therefore they have no influence on the recorded data.

The Control Box

The Control Box Power Main switch GND Ground Accel Accelerometer Axial Connection to LVDT for measurement of axial compression of the specimen Aux 1 Auxiliary input for further appplications Prox Connection to the couple of the proximity transducers Cell, Pore e Back pressure Serie of 3 connectors for the relevant pressure transducers Volume Connection to the volume change transducers or differential pressure Motion Connection to the motor drivers of the proximity transducers Aux2 Auxiliary input for further appplications Coils Uscita per il collegamento delle bobine del motore di coppia. USB Connection to PC Each cable is fitted with a specific connector for easy installation of the transducers inside the cell body, near the sample.

The test is performed on a cylindrical sample Performing the test The test is performed on a cylindrical sample (50 mm dia, 70 mm available on request), either undisturbed or remoulded The RC system software has the following stages: 1. Saturation 2. Isotropic Consolidation 3. Resonant Frequency 4. Torsional shear As in all standard triaxial tests, we start by saturating the specimen and applying the in-situ effective stress. Then we choose to determine the resonant frequency or the torsional shear strength.

Performing the test Performing the test: Same as in the triaxial test An excitation current is applied to the electromagnetic drive system, to generate a constant torque to the top end of the soil sample. The frequency of this current is increased until the fundamental resonance frequency of the system is achieved. Resonance frequency and relevant acceleration are measured. From these data the G modulus is calculated The damping ratio D is also measured during the “free vibration decay” procedure. Further measurements are performed during torsional tests, where higher levels of excitation current and torque are applied. Saturation Consolidation Measurements 26

Performing the test The dynamic behavior of soils is represented by the Shear modulus G, the Damping ratio D and the Shear Strain g G shear modulus and D damping ratio, are of key importance to determine the mechanical behaviour of soils under small strain cyclic loading conditions

Resonant frequency The excitation Voltage is fixed and the frequency increased in automatic increments or steps. The system records the shear strain and calculates the Fundamental Resonant Frequency corresponding to the maximum shear strain.

Resonant frequency fr Fundamental Resonant Frequency f1 & f2 are the band width frequencies at which the amplitude 0.707 times the amplitude of the fundamental resonant frequency fr Stokoe et al. 1999 Frequency, f (Hz) Shear strain, g (%) Shear strain, g (%) (0.707 x fr) is the average area enclosed by the sine wave. G is the shear modulus or stiffness of the material being tested D is the damping modulus, the rate of which energy decays in the specimen. This can be achieved by free vibration where the power is switched off and the vibrations reduce to zero. Or as shown above by the half power method of 0.707fr to determine points f1 & f2

Torsional shear The test (undrained conditions): Saturation Isotropic consolidation The frequency of the cyclic Torsional shear (sinusoidal, <2 Hz) is constant while amplitude is increased. The system records the Torsional stress & strain values for each amplitude and displays Hysteresis cycle from witch G and D are determined. g is measured through proximity transducers the shear strength t is evaluated through the applied torque

Resonant frequency From the frequency sweep graph the fundamental resonant frequency and Modulus of damping can be determined. In the resonant column test the half power bandwidth method can be used to measure the material damping The bandwidth is the frequency difference between the upper and lower frequencies for which the power has dropped to half of its maximum, the frequencies F1 and F2 at which the amplitude is 0.707 times the amplitude at the resonance frequency Fr.

Resonant frequency From the frequency sweep graph the fundamental resonant frequency and Modulus of damping can be determined. In the resonant column test the half power bandwidth method can be used to measure the material damping The bandwidth is the frequency difference between the upper and lower frequencies for which the power has dropped to half of its maximum, the frequencies F1 and F2 at which the amplitude is 0.707 times the amplitude at the resonance frequency Fr. Consolidation of the specimen prior to either Resonant or Torsional tests

Saturation and consolidation Consolidation of the specimen prior to either Resonant or Torsional tests Graph showing consolidation curve 33

Torsional shear Torsion Shear Test at 0.1Hz, Amplitude 1 Volt