In recent decades, the bender element (BE) test has been used to estimate the seismic wave velocity in the laboratory due to several advantages; simplicity, versatility, fastness, inexpensiveness, and non-destructive nature. However, even with the advanced usage of BE in the laboratory, there has been little effort to use the BE in the field. In this article, the BE was used on a physical model at a multilayer mixture soils system and using different methods, patterns, and wave path lengths to evaluate the BE technique in the simulated field. The results indicated that the cross-hole pattern was the most suitable pattern to implement the BE test on the simulated field. BE results were highly influenced by the boundary condition when the distance between the sensor and hard boundary is less than 0.3 of the wave path length. BE sensors were able to detect seismic wave velocity at a ratio of the wave path length to sensor length up to 200 times.
In the last decades, the bender element (BE) test has been used commonly in the laboratory to estimate the seismic wave velocity and predict the maximum modulus. BE had several advantages in the laboratory due to simplicity, versatility, fastness, inexpensiveness, and non-destructive nature [1,2,3]. However, despite the advantages of using BE in the laboratory, a little effort had been done to develop the application of BE techniques in the field [4,5], particularly in a small range of multilayer soil systems (compacted layers and pavement). At this small range, the seismic methods such as seismic refraction (SR) and multichannel analysis of surface waves (MASW) could be subjected to uncertainty due to the low resolution of the seismic data because of the thin layers [6,7,8,9]. For example, Kang et al.  installed a pair of BE in the sand to develop Portable Bender Element-Double Cone Penetration. Another trial by Hlasko and Zeng  established the usage of BE in the field through the development piezoelectric probe on a mono system of soil using Nevada sand and coarse-grained separately. Jung et al.  developed a probe called MudFork which has been used as a field BE and the pattern of seismic cross-hole (CH) was implemented in the evaluation of natural soft soil. Later Kim et al.  tried to expand the efficiency of MudFork by correlating the shear wave velocity to silt properties. Lee et al.  used a pilot BE on a shaking table, which had been filled with sand to evaluate the shear wave velocity. Zhou et al.  implemented the surface embedded technique of BE sensors to do a horizontal measurement of the shear wave velocity. Yoon and Lee  used a field velocity resistivity probe on a single layer of sand–clay mixture in the calibration chamber to measure stiffness. Jang et al.  prepared a prototype of in-hole type CPTu using the BE sensors and tested it on a layer of kaolin. The Norwegian Public Roads Administration has recently established a method to measure the dynamic properties of the soil in field and lab using seismic CPTu (SCPTu) and BE, respectively . Refereeing to the previous researchers, it can be recognized the following (a) the heterogeneity of the soil was ignored which can exist in the case of a small range of compacted soils and pavement, (b) no comparison between different arrangements of sensor, and (c) the boundary condition effect in the present of multilayer soil system was not assessed.
In this article, BE was used in a physical model of a multilayer system of sand–kaolin mixtures with different densities, moisture content, and percentage to evaluate the efficiency of BE in the simulated field and provided the suitable procedure for field BE. The results were verified using SR and MASW methods. In addition, BE test was used to assess: (1) The effect of the wave path length between the sensors; (2) the effect of the variation in the medium using different patterns: CH, multilayer cross-hole (CHm), downhole (DH), and suspension (SS); (3) the boundary effect in variable wave path lengths.
2 Materials, model construction, and principles
2.1 Materials properties
A multilayer system made of different soil mixtures was developed to simulate the field condition and assess BE efficiency in the physical model. The soil mixtures of sand–kaolin were (a) 80–20% for the top layer, (b) 30–70% for the middle layer, and (c) 40–60% for the bottom and base layers. The sand had a particle size of less than 3.35 mm (Figure 1), and the kaolin properties were as follows: (a) the product name was kaolin–AKIMA 45, (b) more than 40% of the particles had a diameter <2 μm, and (c) less than 0.05% of the particles had size >45 μm.
2.2 The model simulation
To build an appropriate model for the simulated field test, several layers were subjected to laboratory pre-evaluation. Then a simulation of the predicted behaviour of the refracted seismic wave path was developed to estimate the suitable model dimension, layers sequence, layers thickness, and geophone spacing. To conduct the seismic methods inside the model successfully, (a) the suitable layer sequence was chosen to avoid the blind layer, (b) the correct layer thickness was estimated to avoid the hidden layer, and (c) the proper geophone spacing was selected to assurance receive all refracted waves of all layers [7,8,9,18,19]. If a thin layer (second layer) with a seismic velocity of V 2 is sandwiched between the upper layer (first layer) with a seismic velocity of V 1 and the lower layer (third layer) with a seismic velocity of V 3 where V 1 < V 2 < V 3 as well as there is no big differential between V 2 and V 3, in such case, the refracted waves of the third layer (which had V 3) could have arrived before the one from the thin layer (the second layer with V 2); this phenomenon is called the hidden layer. On the other hand, the blind layer appears when V 1 > V 2 < V 3; in this case, no refraction from the second layer and only the third layer will be recorded (Figure 2).
The laboratory pre-evaluation was conducted on six groups of soil mixtures: 80–20, 70–30, 60–40, 50–50, 40–60, and 30–70% of sand–kaolin mixtures using 34 compacted samples. The sand–kaolin mixtures were compacted via standard compaction ; then, the representative samples with higher maximum dry density and optimum moisture content were subjected to a laboratory BE test to measure both the seismic compression wave velocity (V P) and seismic shear wave velocity (V S). The simulation was applied to the six sand–kaolin mixtures (80–20, 70–30, 60–40, 50–50, 40–60, and 30–70%) using different sequences, geophone spacing, and layers thicknesses. Among the six soil mixtures, the best sequence, thickness, density, and moisture content were adopted (Table 1). In addition, the 100 mm geophone spacing was used.
|Sequence from top to bottom||Layer||Thickness (mm)||Kaolin (%)||Sand (%)||Wet density (g/cm3)||Moisture content (%)|
The simulation depended on (1) Snell’s law (equation (1)) where the behaviour of the refracting the seismic wave depended on the angle of incidence wave (θ i ) and the differential in the dynamic properties of the layers such as elasticity modulus and density. (2) Triangle laws as in equations from (2) to (4) (refer to Figures 3 and 4) [18,21].
where V 1 and V 2 are the velocities of the first and second layers, respectively. A, B, and C are the triangle sides and represented the wave path length, the half of the critical distance, and the depth respectively. While a is one of the triangle angles and represented incidence wave (θ i ) and critical angle (θ c ). According to the simulation results, six seismic wave velocities were concerned (Figure 4), V 1, V 2, V 3, V 4, V 5, and V 6, and represented the simulated velocities of the top layer, middle layer, bottom layer, base layer, isolated sand layer, and tank boundary, respectively. However, the distance–time sketch in Figure 4 showed that both base and isolated sand layers (V 4 and V 5) were blind layers (did not appear in the time–distance sketch) due to their low velocity compared to top, middle, and bottom layers (V 1, V 2, and V 3). Also, within the tank dimension, the refracted wave of the tank boundary (V 6) did not obscure the refracted wave of top, middle, and bottom layers (V 1, V 2, and V 3). According to Snell’s law, at the critical angle (θ c ), the refracted angle is equal to 90° (equation (1)). Thus, the seismic refracted wave arrives before the direct wave in the seismic record at a distance from a source called crossover distance (X cr), which depended on the depth to the surface of the second layer (z) and wave path length (L tt). However, the critical distance (X c) is the minimum required distance to refract the seismic wave when L tt2 = 0 [21,22].
2.3 Model properties and construction steps
According to the simulation results, the multilayer system was constructed in a tank has dimensions 2 m × 1 m × 0.7 m (Figures 5 and 6) from four compacted layers with different components and densities laid over a sand layer with relatively low density. The four compacted layers were subjected to field compaction using the jumper rammer, which was recommended in this case due to the suitability of this tool for compacting the cohesive soil in a small trench .
The sand layer acted as an isolation zone with a thickness of 300 mm at the bottom, 300 mm at the end edges, and 335 mm on both sides of compacted layers (Figure 5). The purpose of the isolated zone was to avoid the unwanted refracted and reflected waves from the tank boundary [24,25,26,27]. The main purpose of the base layer was to minimize the dissipation of the compaction effort during the bottom layer compaction. The base layer held the compaction effort of the bottom layer instead of the low relative density sand, thus avoiding high dissipation of the compaction energy which resulted from the direct compaction over the low relative density sand.
2.4 Acquisition of seismic data
The seismic wave velocities were measured using the seismograph set and the portable BE device. The data from the seismograph were used to analyse both SR and MASW. The primary wave velocity (V P) and shear-wave velocity (V S) were calculated using SR and MASW methods, respectively. Figure 6 shows the layout of the seismic survey inside the model and the offsets to implement the SR and MASW methods using 12 geophones (4.5 Hz vertical geophones) in one spread line. A hammer was used as an impact source (Figure 6). The spacing between the geophones (d 1) was fixed (d 1 = 100 mm), and shot point d 2 had several locations as in Figure 6. The acquisition was conducted using a seismograph called ABEM SeisTW Terralco Mk 6, ABEM Instrument AB, Sundbyberg, Sweden. Data were processed using the software called ABEM SeisTW. The highest setting was used to increase the resolution of the seismic data as follows: (1) the sampling interval was 25 μs, (2) the sampling number was 4,096, (3) the number of stacks was 5, and (4) the data were saved in an SG2 file. The raw data were subjected to filtering to remove the noise level using Interpex seismic shot conversation (IXseg2Segy; an updated version can be found on: http://www.interpex.com/ixseg2segy/ixseg2segy_version.htm).
In the BE test, a series of tests were conducted using pair sensors with length l b = 5 mm, input voltage equal to 15 V, and applied frequency f = 80 kHz to evaluate the seismic wave velocities using the follows:
Constant wave path length (L tt) between the BE sensors for the four layers, both transmitter and receiver inserted on the side of the top, middle, bottom, and base layers and using L tt equal to 100 mm (Figure 7a).
Increment L tt between the BE sensors along the surface of the top layer, the transmitter position was fixed, and the receiver was moved along the surface of the top layer, i.e. L tt increment from 100 to 1,000 mm (Figure 7b).
Constant L tt along the surface of the top layer, both transmitter and receiver were placed at different points (e.g. point 1, point 2, to point n) along the surface of the top layer using constant L tt equal to 100 mm (Figure 7c).
CHpattern: both transmitter and receiver were placed on the same level (same layer). The transmitter is placed on one side of the compacted layers and then the receiver is placed on the other side using L tt = 330 mm (Figure 7d).
CHm patterns: both transmitter and receiver were placed on different levels (different layers). The transmitter is placed on one side of the compacted layers, and then receiver placed on the other side using L tt > 330 mm (Figure 7e).
SS pattern: the transmitter was inserted on the side of the top layer then receiver was moved down to the same side of the middle, bottom, and base layers (Figure 8a).
DH pattern: the transmitter was placed on the surface of the top layer, and then, the receiver was moved down to the side of the top, middle, bottom, and base layers (Figure 8b).
CH at the different L tt, this pattern was only used on the middle and base layers. The transmitter position was fixed on the side of the layer, and then, the receiver was moved laterally at the same side of the layer using L tt equal to 100, 200, and 300 mm (Figure 8c).
However, the experimental procedure was interrupted and delayed for 1 month, which affected the moisture content of the layers (particularly the top layer). Thus, the layer velocities were subjected to variation [28,29]. However, the seismic tests were repeated using the SR and BE methods on the new soil moisture content condition, i.e. after the moisture content was reduced due to the delay in the test procedure.
2.5 Interpreting the seismic measurement
The seismic data from the seismograph were analysed through two paid software (1) SeisOptPicker to interpret SR data and (2) SeisImager/SW to interpret the MASW. At SeisOptPicker, V P was analysed directly via the SR waves (the software can be found on www.optimsoftware.com) while at SeisImager/SW, the phase velocity of the Rayleigh wave was measured and then the shear wave velocity was predicted (the software can be found on https://www.geometrics.com/software/seisimager-sw/). The interpretation of SR data was according to the Snell law (equation (1)) while the MASW depending on the measuring of the phase velocity . The details of the SR and MASW methods were beyond the scope of this article. The arrival time in BE data was analysed using the first-peak method which was the most used method for time-domain interpretation [30,31,32]. The wave path length was considered to be tip-to-tip (tip of transmitter sensor to the tip of receiver sensor) according to equation (5) [33,34,35].
where V is the wave velocity for either P-wave or S-wave, L tt is the wave path length from the tip of the transmitter to the tip of the receiver, and t is the recorded time. Even though the relatively short distance between BE sensors, the trigger time was controlled and the shift phase lag in recorded time was avoided using high-resolution auto triggering.
3 Results and discussion
3.1 Comparison between seismic wave velocities from different seismic methods
The comparison between the seismic wave velocities (V P and V S) from SR, MASW, laboratory BE, and physical model BE at both conditions immediately and after 1 month delay (from the day when the model was constructed) was shown Figures 9 and 10, respectively. The results in Figure 9 showed the same pattern where the velocity increased with an increase in depth. On the other hand, due to a delay in the field test procedure, the moisture content on the top layer was decreased and the layer was subjected to hardening [36,37,38]. Consequently, both V P and V S values were increased and became higher than the beneath layers, while the middle and bottom layers were less affected by the variation in the moisture content . The new sequence in the wave velocity resulted in blind layers, and the underneath layers disappeared from the SR record as shown in Figure 10 [18,19].
The results showed that the BE can be used for the measurement of the seismic wave velocity in the physical model, which is not restricted to the small soil sample only. This result agreed with the outcomes from the following:
Hlasko and Zeng  using sand material, sensor length (l b) = 28.6 mm, and L tt ≈ 100 mm.
Lee et al.  using sand, l b = 6 mm, and L tt ≈ 74 mm.
Zhou et al.  using silica sand, l b = 10 mm, and series of L tt equal to 100, 200, 300, and 400 mm.
Jang et al.  using kaolin and L tt = 150 mm.
Yoon and Lee  using a mixture of sand–kaolin, l b = 2 mm, and L tt = 65 mm.
3.2 Evaluating the simulated field BE test
BE was evaluated in the simulated field to assess (1) the effect of lateral distance, (2) lateral medium variation, and (3) boundary effect as was shown in the next sections. The BE tests were performed on low soil moisture content conditions (after 1 month of construction of the model).
3.2.1 Evaluation wave path length between the sensors
The results of V P and V S showed similar values using constant L tt = 100 mm and increment L tt from 100–1,000 mm (Figure 11). This indicated that BE sensors were able to measure the seismic wave velocity to distance L tt = 1,000 mm, which was equal to 200 times the sensor length l b (i.e. L tt/l b = 200) compared with (a) L tt/l b = 40 by Zhou et al. , (b) L tt/l b = 12 by Lee et al. , (c) L tt/l b = 10 by Yoon and Lee , and (d) L tt/l b = 3.5 by Hlasko and Zeng .
3.2.2 Using different patterns to measure the seismic wave velocity
The results from conducting the BE in the simulated field using different patterns were concluded the following:
Both base and middle layers showed high variations in their velocity measurement compared to the top and bottom layers (Figure 12). Among the four compacted layers inside the model, the base layers showed highest variation in the seismic wave velocity results with a percent difference between the highest and lowest of V S equal to 56% compared to 22% at the middle layer, 13% at the base layer, and 4% at the top layer. The same for V P where the percent differential was 68% for the base layer compared to 20% at the middle layer, 28% at the base layer, and 3% at the top layer.
The top layer has lower variation in the results using CHm, DH, and SS patterns compared to the bottom layer. The variation in the seismic wave velocity results at the bottom layer was due to the variation in the medium of wave path length where the wave travelled through different layers. For example, at CHm, the wave path length from the transmitter at the top layer to the receiver at the bottom layer crossed a longer distance through the middle layer (which had a lower velocity) compared with SS and DH patterns; thus, the seismic wave velocity showed lower value at CHm compared with SS and DH patterns (refer to Figures 7, 8 and 13).
The top and bottom layers which had higher velocities showed no significant variation between the results using different wave path lengths (L tt equal to 100 or 330 mm) in the CH pattern compared with the middle and base layers (Figure 13). This is because the production of refracted wave required rigid boundary, i.e. boundary had higher velocity; however, this condition existed only in middle and base layer cases [7,8,18]. Meanwhile, the slight variation in the velocities of both top and bottom layers was related to the differences in the wave path length in the CH pattern .
Middle and base layers showed lower seismic wave velocities using the CH pattern had L tt ≤ 100 mm compared to CH had L tt = 330 mm, SS, and DH patterns (Figure 13). In CH using L tt ≤ 100 mm, there was no significant influence on the boundaries; thus, the direct seismic waves arrived earlier than the refracted wave due to the short wave path length (L tt ≤ 100 mm) [26,27]. While at CH using L tt 330 mm, the boundary influenced the results because the increasing of the L tt to 330 mm yielded D r/L tt < 0.3 where D r was the distance between the sensors and the hard boundary (Figure 14). At D r/L tt < 0.3, the first arrival corresponded to the refracted wave from the hard boundaries (i.e. top or bottom layer) instead of the direct wave (Figures 13 and 14) [26,27,41,42,43,44].
In the middle and base layers, the CH pattern using L tt ≤ 100 mm showed that the seismic wave velocities were lower than the results from SS and DH patterns. The increasing the seismic wave velocity at SS and DH patterns is linked to the wave path medium. In SS and DH patterns, the seismic wave propagated through two layers that had higher velocity (top and bottom layers); thus, the waves travelled faster than they should be if travelled only in the middle and base layers which had lower velocities. On the other hand, the measured seismic wave from DH was higher than the one from SS for both the middle and base layers.
The CH pattern using L tt ≤ 100 mm was the most reliable pattern to be used in the simulated field BE .
3.2.3 Effect of boundary along wave path
The results in Figure 15 revealed the boundary effect on the detection of the first arrival wave time at middle and base layers. At L tt ≤ 100 mm, the CH was not affected by the boundary where D r/L tt ≥ 0.3 and the first arrival wave time referred to the direct waves, i.e. both direct P-wave and direct S-wave [42,44,45]. Meanwhile, both V P and V S increased with the decrement of the D r/L tt to less than 0.3 using both L tt ≈ 200 mm and L tt ≈ 300 mm. At D r/L tt < 0.3, the seismic waves refracted from the boundary and reached the receiver before the direct seismic wave [42,44,45]. Thus, the first arrival wave time at D r/L tt < 0.3 corresponded to the refracted wave rather than the direct wave [24,25,26,27].
The procedures and efficiency of BE in the simulated field were investigated and verified using different methods, patterns, wave path lengths, and a multi-layer model that had different velocities for each layer. The results showed the following:
BE sensors were able to detect seismic wave velocity at a distance up to 1,000 mm and ratio of the wave path length to sensor length up to 200 times.
The boundary condition had a significant influence on the efficiency of BE measurement when wave path length was higher than 100 mm where the first arrival wave time corresponded to the refracted seismic wave rather than the direct seismic wave. Thus, the distance between the sensor to the hard boundary should be higher than 0.3 of the wave path length to avoid the boundary effect.
The CH pattern using a distance between sensor and hard boundary higher than 0.3 of wave path length (i.e. D r/L tt ≥ 0.3) was the most suitable pattern in the simulated field BE among the CHm, DH, and SS patterns.
Author contributions: Implementation of the experiments and writing the article were done by Badee Alshameri.
Conflict of interest: Authors state no conflict of interest.
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© 2022 Badee Alshameri, published by De Gruyter
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