DISCUSSION of: Ground Improvement Using Preloading wit Prefabricated Vertical Drains Full Reference: Dar, A.S., Siddique, A., Ameen, S.F., (211). Ground Improvement using Pre-loading wit Prefabricated Vertical Drains. International Journal of Geoengineering Case Histories,, Vol.2, Issue 2, p.86-14. doi: 1.4417/IJGCH-2-2-1. Bengt H. Fellenius, Dr. Tec., P.Eng., Canada; email: bengt@fellenius.net KEYWORDS: Ground improvement, immediate compression, consolidation settlement, secondary compression, wick drains, drain spacing, smear zone, preloading future maintenance. INTRODUCTION Te autors ave presented a straigtforward case istory on settlements measured for a wick drain preloading project; not from a specific researc project but from an actual engineering project. Te latter fact makes up for some lack of details. Neverteless, it would be desirable if te autors could supply te following additional information. 1. a delineated figure similar to autors' Figure 2 sowing wic part about a tird of te total project site tat was included in te reported measurements. 2. a delineated figure similar to autors' Figure 11 sowing te locations of te 12 settlement observation bencmarks included in te autors' Figure 13. 3. a table indicating te measured or estimated tickness of te clay layer for eac of te 12 settlement bencmarks. 4. an estimate of te immediate settlements of te four soil layers due to te placing of te surcarge tat preceded te consolidation settlement of te clay layer. Te autors report, tat te first survey of te bencmarks was taken before te 3.-m surcarge was placed across te test area. Te first day of settlement measurements for te twelve bencmarks was te date of te second bencmark survey, wic was carried out only wen all of te surcarge ad been placed to te full eigt over te test area. Te time between te first and second surveys and te placing of te surcarge ranged from a few days to twenty days. Because te times between te placing of te surcarge and te second survey differed for te bencmarks, te amount of settlement tat ad occurred at te time of te second survey also differed between te bencmarks. Tis explains some of te significant scatter displayed in te autors' Figure 13. I ave re-plotted te measured settlements in Figure 1 to a common starting point at te average start settlement of 16mm and added 1 days to te autors' measurement days to indicate te average duration of placing te surcarge, wic took place before te second survey. During tis time, immediate compression and some consolidation will ave occurred. As indicated, I estimate te immediate compression to be about 5 mm. I ave also added an average curve and extrapolated it back to te origin (te average excludes te two outlier records). All bencmarks appear to sow tat most of te consolidation ad developed at te time te last survey was made. Submitted: 6 Marc 214; Publised: 31 Marc 214 Reference: Fellenius B.H., (214). Discussion of Ground Improvement Using Preloading wit Prefabricated Vertical Drains. International Journal of Geoengineering Case istories,, Vol.3, Issue 2, p.67-72. doi: 1.4417/IJGCH-3-2-1 International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 67
SETTLEMENT (mm) SETTLEMENT (mm) 5 Estimated immediate compression due to te placing of te surcarge Consolidation settlement Average Placing surcarge 35 4 Average day of start of placing surcarge Day of second survey 1 days added to Day in paper TIME (days) Figure 1. Settlement measured at te bencmarks sifted 1 days. Figure 2 sows te measured final settlements are normalized to te average final settlement (28 mm). Tere is still muc scatter between te curves, but now te approximate start date for eac curve can be obtained by sliding te curves left or rigt until te best agreement to te average curve is obtained as sown in Figure 3. Te removal of muc of te scatter te agreement between te time-settlement curves is of course to some extent fictitious as te bencmark measurements cannot be expected to be all tat similar; a natural variation must ave taken place, not least wit regard to te tickness of te soft clay layer. However, I believe tat te figure suggests a reasonably realistic day for te start of placing te surcarge. 5 Settlement vs. days after start of placing surcarge normalized to average end value 35 Average Placing surcarge 4 Average day of Day of second survey TIME (days) start of placing 1 days added to surcarge Day in paper Figure 2. Settlement measured at te bencmarks normalized to te average end values. International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 68
SETTLEMENT (mm) 5 Settlement vs. days after first survey normalized to te average end settlement wit time adjusted to fit eac curve to te average curve Average 35 4 First survey Range of duration of placing of te te surcarge and range of TIME (days) bencmarks days added to Day in paper Figure 3. Settlement measured at te bencmarks adjusted to obtain te approximate start day. Te average curve sown in Figure 3 can now serve as reference to a back-calculation of te time-settlement development for te wick-drain project to determine compressibility and coefficient of consolidation of te soil layers. Te backcalculation consists of applying te teory of pore pressure dissipation in fine-grained soils (consolidation) due to radial flow (Barron 1948, Kjellman 1948, and Hansbo 196; 1979) is based on radial flow toward a circular drain in te center of a cylinder of omogeneous soil wit an impervious outer boundary surface). Te teory is summarized in te Kjellman- Barron formula, Equation 1. Te Kjellman-Barron formula is based on te assumption of orizontal (radial) flow only and a omogeneous soil. t 2 D D [ln 8c d.75] ln 1 1U (1) were t = time from start of consolidation (s) D = zone of influence of a drain (m) d = equivalent diameter of a drain (m) U = average degree of consolidation for radial (orizontal) flow (--) c = coefficient of orizontal consolidation (m 2 /s) (1 m 2 /s = 3.2 x 1 8 m 2 /year) Equation 1 can be rearranged to give Equation 2, te relation for te average degree of consolidation, U, wic is te same equation as te Autors' Equations 4 and 5 wit te portions on smear and discarge capacity (well resistance) removed. International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 69
8 c t U 1 exp (2) 2 D D (ln.75) d Te orizontal drainage acieved by installing vertical drains will accelerate te consolidation settlement to a approximate factor equal to te square of te ratio between te tickness of te soil layer and te spacing of te drains, times te ratio of te vertical and orizontal coefficients of consolidation. Of course, te vertical drainage occurs togeter wit te orizontal drainage. Asaoka (1978) presented a relation for te combined effect as quoted in Equation 3. Usually, te tickness of te consolidating soil layer is many times larger tan te spacing of te vertical drains. Te vertical drainage is ten omitted from te analysis. U c = 1 - (1 - U )(1 - U v ) (3) were U c = average degree of consolidation, combined U = average degree of consolidation, orizontal only U v = average degree of consolidation, vertical only Te teory of consolidation applied to vertical drains is based on te assumption of a circular drain. In applying it to a wick drain, wic is a bandsaped drain, te drain must be converted to a virtual "sand" drain, tat is, to a circular sape. Tis is usually, as reported by te autors, done by te input of an equivalent diameter, "d", wit a circumference equal to te total circumference of te wick drain. Te autors applied tis definition, wic results in a 66-mm equivalent drain diameter. However, oter approaces for determining te equivalent diameter ave been proposed, e.g., assuming tat "d" is equal to te average of te widt and tickness of te wick drain, resulting in a 52mm diameter for te subject drain. Or, tat te equivalent sand drain diameter of te wick drain is tat of a drain wit te same open area as its virtual sand drain (Fellenius 1977). Te ratio of open and obstructed area of a sand drain is equal to te porosity of te sand, about.4. Te wick drain as a muc larger open surface ratio tan a sand drain, te ratio is about.7, depending on wick drain type. Accordingly, for te subject drain, te equivalent gross sand drain diameter would be equal to 28x.7/.4π = 116mm. As te autors report, te widt of te smear zone reported in different studies ranges significantly between various writers. Te zone is a function of several factors, not least te gross cross section of te installation mandrel as opposed to te drain cross section, wic te autors report to ave been 7cm 2, as opposed to te 4cm 2 drain cross section. On witdrawal of te mandrel, te soil tat was displaced and "smeared" by inserting te mandrel is assumed to flow back against te drain and, in te process, te permeability of te soil is reduced in a zone, te smear zone, nearest te drain. However, it as been argued tat, in some soils, te displacement and flow-back result in opening up of fissures in te soil tat provide improved passages for te water and, terefore, te "disturbance" actually increases te flow caracteristics of te soil. Te relative importance of te smear zone is also a function of te drain spacing and reduces wit increased spacing. A 1.4-m drain spacing may well result in about te same time development as a 1.-m spacing. Te former would require only alf as muc total lengt of drain as te latter. Te questions of te widts of te equivalent sand drain and te smear zone are not possible to assess in a field study unless te study includes different size drains and different spacing between te drains. Te subject study involves no suc parameter variation and can terefore neiter be used to draw any conclusions as to a correct equivalent drain diameter nor tickness of smear zone to use wen back-calculating te results to find te soil compressibility and coefficient of consolidation. Moreover, te measurements do not separate te immediate compression from te consolidation settlement and te fact tat te actual tickness of te soft clay layer ranged from 3 troug 7m make for a source of additional uncertainty in using te records for detailed teoretical assessment. For te back-calculation, I ave assumed a 5-m tickness of te clay layer. I also applied a 66-mm equivalent circular drain diameter. I believe tat a reasonable, albeit approximate, modulus of immediate compressibility of te four soil layers is about 3MPa, te same for eac layer, wic results in an immediate compression of 5 mm, as indicated in te figures. (Settlement due to secondary compression will ave been negligible). Tus, te measured average consolidation settlement is 23mm, occurring only in te soft clay layer. Te back-calculated Janbu modulus number for te soft clay is 18, caracterizing it as moderately compressible. Te autors indicate an average value of, C c, for te clay of.3. Combining International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 7
SETTLEMENT (mm) tis wit te back-calculated modulus number, results in a void ratio of 1.38, wic lies witin te 1.4 troug 1.62 range of void ratio presented by te autors. Te next step of back-calculation was fitting calculated development of settlement over time to te measured settlement. I assumed tat te surcarge (stress) was placed in four steps of 14kPa, te first step coinciding wit te placing of final -mm of te drainage blanket and te oter tree loading events following every two to tree days later. A next to perfect fit was obtained wit a c -coefficient of 11 m 2 /year combined wit a c v -coefficient of 7.5 m 2 /year (te latter is te autors' laboratory value. However, including te vertical drainage or excluding it made very little difference to te fit). All calculations were made wit te UniSettle4 software (Goudreault and Fellenius 211). Te results of te back calculation are sown in Figure 4 togeter wit te average curve of te measurements. In order to sow te sensitivity of te clay layer tickness and modulus number, te figure also sows te final settlement for soil layer tickness ranging from 3 troug 7m and te final settlement resulting from modulus numbers of 15 and 21. Te figure also sows te settlement during te first 6 days tat would ave occurred ad tere been no wick drains (for tis input, I used te autors' 7. 5m 2 /year c v -coefficient). 5 35 4 Calculated for 5 m of soft clay c v = 7.5 m 2 /year c = 11 m 2 /year m = 18 Start day Surcarge is assumed placed in 4 steps 2 days apart Estimated immediate compression due to te placing of te surcarge Consolidation settlement Measured average normalized TIME (days) Figure 4. Average measured and calculated settlements. Witout wickdrains m = 21 m = 15 Range of bencmark settlements Clay layer tickness Considering tat my data reduction is quite different to tat of te autors, my back-calculated c -coefficient (11m 2 /year) agrees well wit te autors' laboratory-establised value (14m 2 /year). Te difference could be taken to represent te effect of a smear zone. However, considering all te uncertainties involved, I believe te agreement to be entirely fortuitous. I must empasize tat witout te support of data from measurement of areas wit different spacing of drains, drains of different sizes, and different surcarge level, conclusion regarding te smear effect cannot be drawn. I do recognize, of course, tat te autors ave presented te results from an engineering project and te study was not a specifically designed researc project, but limited to te details recorded for te project. Te autors ave indicated te final settlement is % degree of consolidation. Tis is not correct; it is % of te measured settlement. At Day 5 (or 4 in te autors count), about 85 to 9% of te consolidation ad occurred. Te remaining amount, small as it is, will take considerable time to develop. International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 71 3 m 4 m 5 m 6 m 7 m
A final point is tat I am surprised tat te surcarge was designed to correspond to te exact load expected from te containers to be stored at te site. Sooner or later, te site will ave to be upgraded, say, for reasons of adjusting to te final portion of te consolidation settlement, about 4 mm and secondary compression of about te same magnitude, wic means tat additional fill will be placed. Tis fill will start a new consolidation. If te surcarge ad included an extra, say,.5 m of fill, suc maintenance would ave resulted in stress canges witin te preconsolidation range establised by te preloading and practically eliminated any future settlement due to te maintenance. REFERENCES Asaoka, A., (1978). Observational procedure of settlement prediction. Soils and Foundations, te Japanese Geotecnical Society, JGS, 18(4) 67-11. Barron, R.R., (1947). Consolidation of fine-grained soils by drain wells. Proceedings of te ASCE 73(6) In Transactions of te ASCE 1948 (113) 718-742. Fellenius B.H., (1977). Te equivalent sand drain diameter of te bandsaped drain. Discussion. Proc. 9t ICSMFE, Tokyo, July 1-15, Vol. 3, p. 395-396. Goudreault, P.A. and Fellenius, B.H., (211). UniSettle Version 4 tutorial wit background and analysis examples. UniSoft Ltd., Ottawa. [www.unisoftltd.com]. 85 p Hansbo, S., (196). Consolidation of clay wit special reference to influence of vertical sand drains. Swedis Geotecnical Institute, Stockolm, Proceedings No. 18, 16 p. Hansbo, S., (1979). Consolidation of clay by band-saped prefabricated drains. Ground Engng, London, 12(5) 16-25. Kjellman, W., (1948). Accelerating consolidation of fine-grained soils by means of cardboard wicks. Proc. 2nd ICSMFE, Rotterdam, Vol. 2, pp. 32-35. International Journal of Geoengineering Case Histories, Vol. 3, Issue 2, p. 72
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