Down-hole Seismic Test.
This article covers the procedures for conduct down-hole
Seismic testing for borehole to determine compressional and shear wave
velocities in soil and rock as a function of depth, which in turn, can be used
with density to derive the dynamic soil parameters (Elastic Modulus (E), Shear
Modulus (G) and Poisson's Ratio (ν)). These properties are the key parameters
in predicting the response of soils and soil structure systems to dynamic
loading.
The method requires one borehole per test location. The
borehole is PVC-cased and grouted.
- Equipment.
The present Down Hole Seismic Test (DHST) has been conducted
with Geode Ultra-Light Exploration Seismograph system manufactured by
Geometrics, Inc. (San Jose, U.S.A). The system consists of Geode seismic
recorder 24 channel seismic records, trigger extension Cable 120 m, hammer
switch, strike plate (25x25x3) cm, sledgehammer (12)Kg, in addition to
Wall-Lock Borehole Geophones manufactured by Geostuff, Inc. (Grass Valley, CA
95945 USA), the system of borehole geophones consist of geophones (3-component
tri-axial sensors) and control unit for borehole geophones model BHGC-4. Figure
1 below shows the equipment used for DHST.
- Field procedure.
The test consists of lowering a geophone (motion transducer)
to a specified depth in the borehole and
clamping it to the casing. An energy source is placed at the surface, near the
top of casing. Generally, the source is
a sledgehammer which is struck vertically onto a steel plate (compressional or P wave source) or,
alternatively, horizontally onto a steel plate (shear or S wave source). The source is struck for P wave
transmission as well as for S wave transmission, and travel time from the moment of source
initiation until reception at the geophone is recorded. The geophone is moved to a new depth and the
process is repeated. Interval velocity
(instantaneous velocity over an interval) is determined by comparing
successive readings. This procedure is
repeated at a specified depth interval from the bottom of the hole to the
top.
- Data processing.
- First arrival picking.
First arrival picking is the method that is extensively used
for velocity calculations in Down Hole
Seismic techniques. Following completion, the field work, the recorded
digital records from each depth were
transferred to a personal computer for analysis. Seismic data records were
depth- sorted and spatial information
were assigned to each record. Then, first arrival times of the seismic waves were determined by manual
picking using Reflex –Win Version 4 (Sandmeier - Germany).
- P-Wave Analysis.
First arrival time
are related to the seismic compression P-wave velocity, which is the most common seismic parameter to describe sediment
properties. Travel times of subsequent shots
were loaded, compared to adjacent waveforms and if needed corrected
during the travel time picking
procedure. The recorded digital records were analyzed to locate the first
minima or first arrival on the vertical
axis records, indicating the first arrival of P – wave energy. The seismic data showed excellent quality throughout all
measurements.
- S-Wave Analysis.
The digital records
are studied to establish the presence of clear S-wave pulses, as indicated
by the presence of opposite polarity
pulses on each pair of horizontal records. Ideally, the S-wave signals from the 'normal' and 'reverse'
source pulses are very nearly inverted images of each other.
The first maxima are
picked for the 'normal' signals and the first minima are picked for the 'reverse' signals, although other points on
the waveform were used if the first pulse was
distorted.
- Velocities Calculations.
The travel times of the P and S waves are derived from the
first arrivals identified on the seismic
trace by manual/ automatic picking using Reflex –Win Version 4, for
shear and compression- waves, for each
depth measurements (Z) and used with the known Source – Receiver distances (R) to calculate the velocities (P and S) for
depth by dividing the difference in travel path between two depths by the time
difference between the two signals recorded.
The elapsed time between arrivals of the waves at the receivers (Z2-Z1) is used to determine the average velocity of a 1-meter-high column of soil around the borehole.
- Calculate Dynamic Soil Parameters.
This process returns five formula logs: Poisson's Ratio (v), Elastic Modulus, E, Shear and Modulus, G. To calculate these five logs, three well logs are needed: Compressional wave velocities (VP), Shear Wave velocities (VS), and Bulk density (ρ). If the Bulk density log is not available, only the Poisson’s ratio can be calculated.
The dynamic soil parameters (Elastic Modulus, E, Shear Modulus, G and Poisson's Ratio (v) were derived from data measured in Full Wave Form Sonic test. These parameters were calculated from the velocity of compressional (VP), shear (VS) waves and Bulk Density (ρ) using the following relationships.
- Poisson’s ratio (v).
It is fundamental parameter that is difficult to measure and is usually estimated in engineering calculations. The ratio of horizontal to vertical strain is required to relate the modulus and strains in a soil body. A typical range of values for Poisson ratio for soil is from 0.3 (for stiff soil) to 0.45 (for soft soils), in general. When both the P-wave and S-wave velocities are known, Poisson’s ratio (v) can be calculated from the equation.
Where Vp denotes P-wave velocity and Vs denotes shear wave
velocity.
Where k is the modulus of incompressibility, µ is the
modulus of rigidity or shear modulus and ρ
is the density of the medium through which the wave propagates.
The minimum and maximum values of Poisson’s ratio are 0 and
0.5. Low values of V imply solid and
hard rock whereas high V represents a weaker and less consolidated rock. If
Poisson’s ratio is 0.33, the S-wave
velocity is half the P-wave velocity. In a fluid zone where shear waves cannot propagate, Poisson’s ratio equals to
0.5. If the lithology is homogeneous the results from Poisson’s ratio can determine the
location of fractures relative to the un-weathered and un-fractured rock.
- Shear Modulus (G).
It is the ratio of
the applied stress to the distortion (rotation) of a plane originally
perpendicular to the applied shear
stress. It is also termed as Modulus of Rigidity.
The shear modulus is used to perform more advanced soil
modeling, and dynamic response analysis
of soil- structure interaction. Shear modulus at low strain levels as measured
by geophysical techniques will provide
the elastic parameter that can be used to establish the variation of modulus degradation versus
strain model for the soil behavior. This parameter is used in defining the stiffness matrices for
finite element analysis of earth structures and
foundations on soils.
When the P-wave, S-wave velocities, and Bulk Density (ρ) are
known, Shear Modulus (G) can be
calculated from the equation:
Where, ρ is the density of the medium through which the wave
propagates, Vs: Shear wave velocity; ρ:
Unit weight of the soil, and g: acceleration of gravity.
- Young Modulus (E).
Stress/strain is the ratio of the applied stress to the
fractional extension (or shortening) of
sample length parallel to the tension (or compression). Stress is force
/ unit area and strain is the linear change
in dimension divided by the original length.
Also, when the P-wave, S-wave velocities, and Bulk Density (ρ)
are known, Young Modulus (E) can be
calculated from the equation:
In which Vs is the shear wave velocity, and v is the
Poisson’s ratio, and ρ is the bulk density.
- Results and Presentation.
The example results of Down Hole Seismic Test (DHST) are
shown in Figure below, which include
velocities of P-wave & S-waves, and the interpreted dynamic parameters
(Elastic Modulus, E, Shear Modulus, G,
and Poisson’s Ratio (v), in graphical and tabular forms.