Vertical Drains 5
Content
Geotextiles and Geomembranes 27 (2009) 493–496
Contents lists available at ScienceDirect
Geotextiles and Geomembranes
journal homepage: www.elsevier.com/locate/geotexmem
Technical Note
New methods for measuring the installation depth of prefabricated vertical drains
Han-Long Liu a, Jian Chu b, *, Zaiyong Ren c
a
Geotechnical Research Institute, Hohai University, Nanjing 210098, China School of Civil and Environmental Engineering, Nanyang Technological University, Block N1, 50 Nanyang Ave, Singapore 639798, Singapore c Zhejiang Binwang Engineering Materials Co. Ltd, Taizhou, Zhejiang Province 318020, China
b
a r t i c l e i n f o
Article history: Received 22 September 2008 Received in revised form 4 May 2009 Accepted 6 May 2009 Available online 7 June 2009 Keywords: Prefabricated vertical drains Quality control Soil improvement
a b s t r a c t
The installation depth of prefabricated vertical drain (PVD) is one of the key factors affecting the outcome of soil improvement when PVDs are used to accelerate the consolidation of soft soil. As PVDs are installed underground, it is difficult to verify the installation depth of PVDs for quality control purpose. In this note, three new methods that have been used in China for measuring the installation depth of PVD are introduced. The working principles of each method are described. The advantages and disadvantages of each method are discussed. An example is also given to illustrate the use of the methods in soil improvement projects. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Prefabricated vertical drain (PVD) has been used widely in soil improvement projects around the world (Holtz, 1987; Holtz et al., 1991; Bergado et al., 1990, 1993a,b, 1996, 2002; Li and Rowe, 2001; Arulrajah et al., 2004; Bo, 2004; Bo et al., 2003; Chai et al., 2004, 2008; Chu et al., 2004, 2006, 2009; Indraratna and Chu, 2005; Shen et al., 2005; Abuel-Naga et al., 2006; Abuel-Naga and Bouazza, 2009; Rowe and Taechakumthorn, 2008; Liu and Chu, 2009; Huang and Han, 2009). PVDs are normally used to reduce substantially the drainage path so as to accelerate the dissipation of excess pore pressures generated by the application of surcharge load. In most of the cases, PVDs are installed through the entire compressible soil layer. If a full penetration of PVDs is assumed in the design and yet the PVDs are not installed to the entire depth of soft clay, the predicted rate of consolidation will be incorrect. Therefore, it is important to measure the real penetration length of the PVD installed on site. Another reason for measuring the installation depth of PVD is to gain a more specific knowledge of the depth of soft soil at the PVD installation locations. The installation depth of PVD is normally specified by the designer. However, when erratic soil profiles are encountered, contractors are allowed to terminate the PVD only when the stiff or hard formation below the soft soil formation is encountered which can be gauged based on the efforts required to penetrate the mandrel. In this case, the thicknesses of the soft soil layer at different PVD installation points can be known
* Corresponding author. Tel.: þ65 67904563; fax: þ65 67910676. E-mail addresses: [email protected] (H.-L. Liu), [email protected] (J. Chu). 0266-1144/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2009.05.001
more precisely. This in turn will result in a more accurate estimation of the ground settlement and rate of consolidation. At the present, the following three methods have been adopted in measuring the penetration depth of PVD as described by Bo et al. (2003): (1) using a meter on the mast; (2) using a dial gauge; and (3) using an automatic digital counter. However, all the three methods measure only the length of the PVDs that pass through the point where the counter or the dial gauge is located, not the real length of the PVDs that has been installed into the soft clay. For this reason, none of the three methods can provide a direct measurement of the PVD installed in the ground. Therefore, none of the three methods is suitable to be used for independent checking or auditing purposes. Without measuring the penetration depth of the PVD directly, it will be impossible to check whether there is any mistake or cheating in the PVD installation records. There were cases where PVDs were not installed deliberately to the required depths. Therefore, a method that can measure directly the installation depth of PVD is required. In the followings, three new methods that can measure the penetration depth of PVDs directly after the PVD has been installed are introduced. These three new methods are digitised PVD, PVD with two wires and PVD with one wire, respectively.
2. New methods 2.1. Digitised PVD The first method is to print a meter scale on the surface of PVD at an interval of 20 or 25 cm so its linear length can be read directly.
494
H.-L. Liu et al. / Geotextiles and Geomembranes 27 (2009) 493–496
An example is shown in Fig. 1. The meter scale can be printed onto the surface of PVD automatically using the computer scale-spattering digital metering technology. When the PVDs are installed by following a given sequence, the differences in the meters printed on top of the current and the last PVD installed will be the installation length of the current PVD. The total length of PVDs used can also be calculated easily. This method is simple and incurs almost no extra cost. However, this method has the following shortcomings. 1) The numbers printed on the filter of PVD become illegible when the PVDs are stored or exposed outside for too long; 2) the readings are affected by the expansion or contraction of PVDs due to temperature variation or wetting; 3) PVDs may be stretched during installation; and 4) the scale printed may not be accurate. Furthermore, it is still not a direct measurement as the length of the PVDs is not measured directly.
2.2. PVD with two wires The second method is to embed two shielded thin copper wires in the PVD, as shown in Fig. 2. This method has been patented (Ren, 2004). The length of the PVD can be calculated by measuring the resistance of the wires. The two wires are embedded along the overlapping joint of the filter as shown in Fig. 2. Before installation, the two wires at the bottom end of the PVD need to be connected together. At the top end of the PVD, the wires are connected to a meter to measure the electrical resistance of the two wires as one loop. A readout unit as shown in Fig. 3 has been specially designed for this purpose. This readout unit can measure the resistance of the wires, convert it directly into length, display and store the readings. This is probably the most direct and reliable method available so far. However, this method also has some shortcomings. Firstly, it incurs extra costs to the PVDs to use two wires. Secondly, the connection of two wires before each installation of PVD is troublesome. Furthermore, the connection has to be done properly otherwise the method will not work. Disputes may rise sometimes on whether the PVD is not installed properly or simply because the wires at the end of the PVD are not connected properly. For this reason, a standard procedure should be adopted. It is suggested to use a minimum connection length of 20 mm. The insulation at the connection must be removed by burning or scratching. The connected portion should be put back into the filter.
Fig. 2. PVD with two copper wires embedded for PVD penetration depth measurement.
2.3. PVD with one wire To overcome the problems associated with the two-wire PVD method, a third method has been developed. This method is similar to the two-wire PVD method, but uses only a single wire. This thin copper wire is embedded along the overlapping joint of the filter as shown in Fig. 4. This method is based on the principle of microwave impedance measurement as explained in detail by Somlo and Hunter (1985). When PVD is installed into the ground, the wire in the PVD and another wire connecting to the ground as provided by the readout unit form a two-wire system. The impedance, Z, at the entrance of this two-wire system is given by the following approximate formula:
Z ¼ 0:5hr ðR þ jX Þ
(1)
where: hr is a parameter dependent upon the characteristic of the soil where the wire is embedded, and R and X are given by:
R ¼ 60fC þ lnðklÞ À Ci ðklÞ þ 0:5 sinðklÞ½Si ð2klÞ À 2Si ðklÞ þ 0:5 cosðklÞ½C þ lnðkl=2Þ þ Ci ð2klÞ À 2Ci ðklÞg (2)
Fig. 1. PVD with scale printed on it for PVD penetration depth measurement.
Fig. 3. Readout unit for the measurement of PVD penetration depth.
H.-L. Liu et al. / Geotextiles and Geomembranes 27 (2009) 493–496 Table 1 Installation depth measured using the one-wire PVD. # 1 2 3 4 5 6 7 8 9 10 11 12 13 Real installation depth (m) 18 18 18 18 18 18 18 18 18 18 18 18 18 Measured installation depth (m) 17.6 17.2 17.5 17.0 17.3 17.4 17.7 17.3 17.6 17.4 17.1 16.8 17.5
495
Error (m) 0.4 0.8 0.5 1.0 0.7 0.6 0.3 0.7 0.4 0.6 0.9 1.2 0.5
Fig. 4. PVD with one copper wire embedded for PVD penetration depth measurement.
n h X ¼ 30 2Si ðklÞ þ cosðklÞ½2Si ðklÞ À Si ð2klÞ À sinðklÞ 2Ci ðklÞ io À Ci ð2klÞ À Ci 2ka2 =l
(3)
where: C ¼ 0.5772, Ci(x) and Si(x) are the cosine and sine integrals, k ¼ 2p/l, l ¼ c/f is the wavelength, c ¼ 3 Â 108 m/s, f is the frequency, a is the radius of the wire, l is the length of the wire embedded in the soil. It can be seen from Eqs. (1)–(3) that the impedance Z is related to the length of the wire embedded in the soil, that is, the length of PVD. In using this method, the relationship between the impedance and the length of a PVD installed for a given site should be calibrated. This is done by measuring the impedance of several PVDs installed with known depths. The impedance of the wire is measured by recording the emitting and receiving time of the microwave. The length of the PVD installed can be estimated based on the impedance measured. A measuring device similar to that shown in Fig. 3 has been specially designed to measure the impedance and convert it directly into length. The measuring error is normally within 20 cm and the maximum error is within 50 cm which is good enough for many projects. The impedance method is new to geotechnical engineers and some experiences may need to be built up before the method can be used with confidence. In this case, the PVD with one wire method can be combined with the digitised PVD, as shown in Fig. 4. In this way, the one wire method can be verified directly using the meter scale.
PVDs were installed through the entire depth of the soft clay in a triangle pattern at a spacing of 1.2 m. The nominal depth of the installation was 18 m. One-wire type of PVDs was used for one part of this project. PVDs were randomly selected to measure the installation depth using the microwave impedance measurement technique. The measured installation depths for 13 PVDs are given in Table 1. During installation, the depths of PVDs were also recorded using a dial gauge installed on the drain installation mask. These values were also given in Table 1 for comparison. The error in the microwave impedance method is taken as the difference between the lengths measured by the dial gauge and that by the one wire method. The maximum error was 1.2 m or 6.7% for an installation depth of 18 m. This amount of error is negligible for the purpose of checking the installation depth of PVD. 4. Summary Three new methods that can be used to measure the penetration depth of PVDs directly are introduced. These are: digitised PVD, PVD with two wires and PVD with one wire. The digitised PVD is to print meter scale onto the PVD so installation depth can be calculated as the difference between the readings at the top of two adjacent PVDs. The PVD with two wires or one wire methods are to embed two or one thin copper wires along the overlapping joint of the filter. The depth of the PVDs is then estimated by measuring the electrical resistance of the wires embedded in the PVD with two wires method or the microwave impedance of the wire in the PVD with one wire method, respectively. All the three methods have been used for soil improvement projects in China. Acknowledgments The writers would like to acknowledge the supports of the National Science Foundation of China No. 50639010, and Provincial Science Foundation of Jiangsu, China No. BK2008040. References
Abuel-Naga, H.M., Bergado, D.T., Chaiprakaikeow, S., 2006. Innovative thermal technique for enhancing the performance of prefabricated vertical drain during the preloading process. Geotextiles and Geomembranes 24 (6), 359–370. Abuel-Naga, H., Bouazza, A., 2009. Equivalent diameter of a prefabricated vertical drain. Geotextiles and Geomembranes Available online 18 January. Arulrajah, A., Nikraz, H., Bo, M.W., 2004. Factors affecting field instrumentation assessment of marine clay treated with prefabricated vertical drains. Geotextiles and Geomembranes 22 (5), 415–437. Bergado, D.T., Alfaro, M.C., Balasubramaniam, A.S.,1993a. Improvement of soft Bangkok clay using vertical drains. Geotextiles and Geomembranes 12 (7), 615–663. Bergado, D.T., Mukherjee, K., Alfaro, M.C., Balasubramaniam, A.S., 1993b. Prediction of vertical-band-drain performance by the finite-element method. Geotextiles and Geomembranes 12 (6), 567–586.
3. Example All the three methods have been used in soil improvement projects in China. A case study on the third method using one-wire PVD is presented here as an example. The case was a road construction project in Nanjing, China. PVDs were used as part of the vacuum preloading method to improve soft ground of an area 13,155 m2. The soil profile at the site consisted of 3 layers. The first layer was miscellaneous fill of 3 m thick in average. It was mainly clay with some gravel and crushed bricks. The second layer was soft clay. The average thickness of this layer was 15 m. The undrained shear strength of the clay varied from 9 to 23 kPa. The soil below the clay layer was silty sand. The ground water table was 0.2–1.2 m below the ground surface.
496
H.-L. Liu et al. / Geotextiles and Geomembranes 27 (2009) 493–496 Holtz, R.D., 1987. Preloading with prefabricated vertical strip drains. Geotextiles and Geomembranes 6 (1–3), 109–131. Holtz, R.D., Jamiolkowski, Lancellotta, R., Pedroni, R., 1991. Prefabricated Vertical Drains: Design & Performance, CIRIA Ground Engineering Report: Ground Improvement. Butterworth-Heinemann Ltd., London. Huang, J., Han, J., 2009. 3D coupled mechanical and hydraulic modeling of a geosynthetic-reinforced deep mixed column-supported embankment. Geotextiles and Geomembranes Available online 25 February. Indraratna, B., Chu, J. (Eds.), 2005. Ground Improvement Case Histories. Elsevier, Oxford, 1115 pp. Li, A.L., Rowe, R.K., 2001. Combined effects of reinforcement and prefabricated vertical drains on embankment performance. Canadian Geotechnical Journal 38 (6), 1266–1282. Liu, H.L., Chu, J., 2009. A new type of prefabricated vertical drain with improved properties. Geotextiles and Geomembranes 27 (2), 152–155. Ren, Z.Y., 2004. A Prefabricated Vertical Drain with Capability for Penetration Depth Measurement, China Patent No. 0119469.0. Rowe, R.K., Taechakumthorn, C., 2008. Combined effect of PVDs and reinforcement on embankments over rate-sensitive soils. Geotextiles and Geomembranes 26 (3), 239–249. Shen, S.-L., Chai, J.-C., Hong, Z.S., Cai, F.X., 2005. Analysis of field performance of embankments on soft clay deposit with and without PVD-improvement. Geotextiles and Geomembranes 23, 463–485. Somlo, P.I., Hunter, J.D., 1985. Microwave impedance measurement. In: IEEE Electrical Measurement Series No. 2. Institution of Electrical Engineers.
Bergado, D.T., Balasubramaniam, A.S., Fannin, R.J., Holtz, R.D., 2002. Prefabricated vertical drains (PVDs) in soft Bangkok clay: a case study of the New Bangkok International Airport project. Canadian Geotechnical Journal 39, 304–315. Bergado, D.T., Manivannan, R., Balasubramaniam, A.S., 1996. Proposed criteria for discharge capacity of prefabricated vertical drains. Geotextiles and Geomembranes 14, 481–505. Bergado, D.T., Singh, N., Sim, S.H., Panichayatum, B., Sampaco, C.L., Balasubramaniam, A.S., 1990. Improvement of soft Bangkok clay using vertical geotextile band drains compared with granular piles. Geotextiles and Geomembranes 9 (3), 203–231. Bo, M.W., 2004. Discharge capacity of prefabricated vertical drain and their field measurements. Geotextiles and Geomembranes 22 (1–2), 37–48. Bo, M.W., Chu, J., Low, B.K., Choa, V., 2003. Soil Improvement: Prefabricated Vertical Drain Technique. Thomson Learning, Singapore, 341 pp. Chai, J.-C., Miura, N., Nomura, T., 2004. Effect of hydraulic radius on long-term drainage capacity of geosynthetics drains. Geotextiles and Geomembranes 22, 3–16. Chai, J.-C., Miura, N., Bergado, D.T., 2008. Preloading clayey deposit by vacuum pressure with cap-drain: analyses versus performance. Geotextiles and Geomembranes 26 (3), 220–230. Chu, J., Bo, M.W., Choa, V., 2004. Practical consideration for using vertical drains in soil improvement projects. Geotextiles and Geomembranes 22, 101–117. Chu, J., Bo, M.W., Choa, V., 2006. Improvement of ultra-soft soil using prefabricated vertical drains. Geotextiles and Geomembranes 24, 339–348. Chu, J., Bo, M.W., Arulrajah, A., 2009. Reclamation of a slurry pond in Singapore. Proceedings of the Institution of Civil Engineers, Geotechnical Engineering 162 (GE1), 13–20.
Contents lists available at ScienceDirect
Geotextiles and Geomembranes
journal homepage: www.elsevier.com/locate/geotexmem
Technical Note
New methods for measuring the installation depth of prefabricated vertical drains
Han-Long Liu a, Jian Chu b, *, Zaiyong Ren c
a
Geotechnical Research Institute, Hohai University, Nanjing 210098, China School of Civil and Environmental Engineering, Nanyang Technological University, Block N1, 50 Nanyang Ave, Singapore 639798, Singapore c Zhejiang Binwang Engineering Materials Co. Ltd, Taizhou, Zhejiang Province 318020, China
b
a r t i c l e i n f o
Article history: Received 22 September 2008 Received in revised form 4 May 2009 Accepted 6 May 2009 Available online 7 June 2009 Keywords: Prefabricated vertical drains Quality control Soil improvement
a b s t r a c t
The installation depth of prefabricated vertical drain (PVD) is one of the key factors affecting the outcome of soil improvement when PVDs are used to accelerate the consolidation of soft soil. As PVDs are installed underground, it is difficult to verify the installation depth of PVDs for quality control purpose. In this note, three new methods that have been used in China for measuring the installation depth of PVD are introduced. The working principles of each method are described. The advantages and disadvantages of each method are discussed. An example is also given to illustrate the use of the methods in soil improvement projects. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Prefabricated vertical drain (PVD) has been used widely in soil improvement projects around the world (Holtz, 1987; Holtz et al., 1991; Bergado et al., 1990, 1993a,b, 1996, 2002; Li and Rowe, 2001; Arulrajah et al., 2004; Bo, 2004; Bo et al., 2003; Chai et al., 2004, 2008; Chu et al., 2004, 2006, 2009; Indraratna and Chu, 2005; Shen et al., 2005; Abuel-Naga et al., 2006; Abuel-Naga and Bouazza, 2009; Rowe and Taechakumthorn, 2008; Liu and Chu, 2009; Huang and Han, 2009). PVDs are normally used to reduce substantially the drainage path so as to accelerate the dissipation of excess pore pressures generated by the application of surcharge load. In most of the cases, PVDs are installed through the entire compressible soil layer. If a full penetration of PVDs is assumed in the design and yet the PVDs are not installed to the entire depth of soft clay, the predicted rate of consolidation will be incorrect. Therefore, it is important to measure the real penetration length of the PVD installed on site. Another reason for measuring the installation depth of PVD is to gain a more specific knowledge of the depth of soft soil at the PVD installation locations. The installation depth of PVD is normally specified by the designer. However, when erratic soil profiles are encountered, contractors are allowed to terminate the PVD only when the stiff or hard formation below the soft soil formation is encountered which can be gauged based on the efforts required to penetrate the mandrel. In this case, the thicknesses of the soft soil layer at different PVD installation points can be known
* Corresponding author. Tel.: þ65 67904563; fax: þ65 67910676. E-mail addresses: [email protected] (H.-L. Liu), [email protected] (J. Chu). 0266-1144/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2009.05.001
more precisely. This in turn will result in a more accurate estimation of the ground settlement and rate of consolidation. At the present, the following three methods have been adopted in measuring the penetration depth of PVD as described by Bo et al. (2003): (1) using a meter on the mast; (2) using a dial gauge; and (3) using an automatic digital counter. However, all the three methods measure only the length of the PVDs that pass through the point where the counter or the dial gauge is located, not the real length of the PVDs that has been installed into the soft clay. For this reason, none of the three methods can provide a direct measurement of the PVD installed in the ground. Therefore, none of the three methods is suitable to be used for independent checking or auditing purposes. Without measuring the penetration depth of the PVD directly, it will be impossible to check whether there is any mistake or cheating in the PVD installation records. There were cases where PVDs were not installed deliberately to the required depths. Therefore, a method that can measure directly the installation depth of PVD is required. In the followings, three new methods that can measure the penetration depth of PVDs directly after the PVD has been installed are introduced. These three new methods are digitised PVD, PVD with two wires and PVD with one wire, respectively.
2. New methods 2.1. Digitised PVD The first method is to print a meter scale on the surface of PVD at an interval of 20 or 25 cm so its linear length can be read directly.
494
H.-L. Liu et al. / Geotextiles and Geomembranes 27 (2009) 493–496
An example is shown in Fig. 1. The meter scale can be printed onto the surface of PVD automatically using the computer scale-spattering digital metering technology. When the PVDs are installed by following a given sequence, the differences in the meters printed on top of the current and the last PVD installed will be the installation length of the current PVD. The total length of PVDs used can also be calculated easily. This method is simple and incurs almost no extra cost. However, this method has the following shortcomings. 1) The numbers printed on the filter of PVD become illegible when the PVDs are stored or exposed outside for too long; 2) the readings are affected by the expansion or contraction of PVDs due to temperature variation or wetting; 3) PVDs may be stretched during installation; and 4) the scale printed may not be accurate. Furthermore, it is still not a direct measurement as the length of the PVDs is not measured directly.
2.2. PVD with two wires The second method is to embed two shielded thin copper wires in the PVD, as shown in Fig. 2. This method has been patented (Ren, 2004). The length of the PVD can be calculated by measuring the resistance of the wires. The two wires are embedded along the overlapping joint of the filter as shown in Fig. 2. Before installation, the two wires at the bottom end of the PVD need to be connected together. At the top end of the PVD, the wires are connected to a meter to measure the electrical resistance of the two wires as one loop. A readout unit as shown in Fig. 3 has been specially designed for this purpose. This readout unit can measure the resistance of the wires, convert it directly into length, display and store the readings. This is probably the most direct and reliable method available so far. However, this method also has some shortcomings. Firstly, it incurs extra costs to the PVDs to use two wires. Secondly, the connection of two wires before each installation of PVD is troublesome. Furthermore, the connection has to be done properly otherwise the method will not work. Disputes may rise sometimes on whether the PVD is not installed properly or simply because the wires at the end of the PVD are not connected properly. For this reason, a standard procedure should be adopted. It is suggested to use a minimum connection length of 20 mm. The insulation at the connection must be removed by burning or scratching. The connected portion should be put back into the filter.
Fig. 2. PVD with two copper wires embedded for PVD penetration depth measurement.
2.3. PVD with one wire To overcome the problems associated with the two-wire PVD method, a third method has been developed. This method is similar to the two-wire PVD method, but uses only a single wire. This thin copper wire is embedded along the overlapping joint of the filter as shown in Fig. 4. This method is based on the principle of microwave impedance measurement as explained in detail by Somlo and Hunter (1985). When PVD is installed into the ground, the wire in the PVD and another wire connecting to the ground as provided by the readout unit form a two-wire system. The impedance, Z, at the entrance of this two-wire system is given by the following approximate formula:
Z ¼ 0:5hr ðR þ jX Þ
(1)
where: hr is a parameter dependent upon the characteristic of the soil where the wire is embedded, and R and X are given by:
R ¼ 60fC þ lnðklÞ À Ci ðklÞ þ 0:5 sinðklÞ½Si ð2klÞ À 2Si ðklÞ þ 0:5 cosðklÞ½C þ lnðkl=2Þ þ Ci ð2klÞ À 2Ci ðklÞg (2)
Fig. 1. PVD with scale printed on it for PVD penetration depth measurement.
Fig. 3. Readout unit for the measurement of PVD penetration depth.
H.-L. Liu et al. / Geotextiles and Geomembranes 27 (2009) 493–496 Table 1 Installation depth measured using the one-wire PVD. # 1 2 3 4 5 6 7 8 9 10 11 12 13 Real installation depth (m) 18 18 18 18 18 18 18 18 18 18 18 18 18 Measured installation depth (m) 17.6 17.2 17.5 17.0 17.3 17.4 17.7 17.3 17.6 17.4 17.1 16.8 17.5
495
Error (m) 0.4 0.8 0.5 1.0 0.7 0.6 0.3 0.7 0.4 0.6 0.9 1.2 0.5
Fig. 4. PVD with one copper wire embedded for PVD penetration depth measurement.
n h X ¼ 30 2Si ðklÞ þ cosðklÞ½2Si ðklÞ À Si ð2klÞ À sinðklÞ 2Ci ðklÞ io À Ci ð2klÞ À Ci 2ka2 =l
(3)
where: C ¼ 0.5772, Ci(x) and Si(x) are the cosine and sine integrals, k ¼ 2p/l, l ¼ c/f is the wavelength, c ¼ 3 Â 108 m/s, f is the frequency, a is the radius of the wire, l is the length of the wire embedded in the soil. It can be seen from Eqs. (1)–(3) that the impedance Z is related to the length of the wire embedded in the soil, that is, the length of PVD. In using this method, the relationship between the impedance and the length of a PVD installed for a given site should be calibrated. This is done by measuring the impedance of several PVDs installed with known depths. The impedance of the wire is measured by recording the emitting and receiving time of the microwave. The length of the PVD installed can be estimated based on the impedance measured. A measuring device similar to that shown in Fig. 3 has been specially designed to measure the impedance and convert it directly into length. The measuring error is normally within 20 cm and the maximum error is within 50 cm which is good enough for many projects. The impedance method is new to geotechnical engineers and some experiences may need to be built up before the method can be used with confidence. In this case, the PVD with one wire method can be combined with the digitised PVD, as shown in Fig. 4. In this way, the one wire method can be verified directly using the meter scale.
PVDs were installed through the entire depth of the soft clay in a triangle pattern at a spacing of 1.2 m. The nominal depth of the installation was 18 m. One-wire type of PVDs was used for one part of this project. PVDs were randomly selected to measure the installation depth using the microwave impedance measurement technique. The measured installation depths for 13 PVDs are given in Table 1. During installation, the depths of PVDs were also recorded using a dial gauge installed on the drain installation mask. These values were also given in Table 1 for comparison. The error in the microwave impedance method is taken as the difference between the lengths measured by the dial gauge and that by the one wire method. The maximum error was 1.2 m or 6.7% for an installation depth of 18 m. This amount of error is negligible for the purpose of checking the installation depth of PVD. 4. Summary Three new methods that can be used to measure the penetration depth of PVDs directly are introduced. These are: digitised PVD, PVD with two wires and PVD with one wire. The digitised PVD is to print meter scale onto the PVD so installation depth can be calculated as the difference between the readings at the top of two adjacent PVDs. The PVD with two wires or one wire methods are to embed two or one thin copper wires along the overlapping joint of the filter. The depth of the PVDs is then estimated by measuring the electrical resistance of the wires embedded in the PVD with two wires method or the microwave impedance of the wire in the PVD with one wire method, respectively. All the three methods have been used for soil improvement projects in China. Acknowledgments The writers would like to acknowledge the supports of the National Science Foundation of China No. 50639010, and Provincial Science Foundation of Jiangsu, China No. BK2008040. References
Abuel-Naga, H.M., Bergado, D.T., Chaiprakaikeow, S., 2006. Innovative thermal technique for enhancing the performance of prefabricated vertical drain during the preloading process. Geotextiles and Geomembranes 24 (6), 359–370. Abuel-Naga, H., Bouazza, A., 2009. Equivalent diameter of a prefabricated vertical drain. Geotextiles and Geomembranes Available online 18 January. Arulrajah, A., Nikraz, H., Bo, M.W., 2004. Factors affecting field instrumentation assessment of marine clay treated with prefabricated vertical drains. Geotextiles and Geomembranes 22 (5), 415–437. Bergado, D.T., Alfaro, M.C., Balasubramaniam, A.S.,1993a. Improvement of soft Bangkok clay using vertical drains. Geotextiles and Geomembranes 12 (7), 615–663. Bergado, D.T., Mukherjee, K., Alfaro, M.C., Balasubramaniam, A.S., 1993b. Prediction of vertical-band-drain performance by the finite-element method. Geotextiles and Geomembranes 12 (6), 567–586.
3. Example All the three methods have been used in soil improvement projects in China. A case study on the third method using one-wire PVD is presented here as an example. The case was a road construction project in Nanjing, China. PVDs were used as part of the vacuum preloading method to improve soft ground of an area 13,155 m2. The soil profile at the site consisted of 3 layers. The first layer was miscellaneous fill of 3 m thick in average. It was mainly clay with some gravel and crushed bricks. The second layer was soft clay. The average thickness of this layer was 15 m. The undrained shear strength of the clay varied from 9 to 23 kPa. The soil below the clay layer was silty sand. The ground water table was 0.2–1.2 m below the ground surface.
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