Civil Engineering R esearch January 2005 69 GEOTECHNICS Model Tests on Passive Piles in Soft Clay Goh Teck Chee Anthony ([email protected]) Miao Lingfeng ([email protected]) Wong Kai Sin ([email protected]) Teh Cee Ing ([email protected]) Introduction The majority of piles are designed to support loads that are applied directly to the pile head by a structure. However in some cases piles are subjected to lateral soil pressures as a result of lateral soil movements. Typical examples of these “passive” piles are piles adjacent to tunnelling and excavation, existing piles adjacent to pile driving, piles used to stabilise slopes, and piles supporting bridge abutments adjacent to approach embankments. A critical factor in the design of the passive piles is the ultimate soil pressure p u , which is defined as the maximum value of the limiting soil pressure along the length of the pile shaft when piles are subjected to large soil movements. A specially designed laboratory apparatus was used to carry out a series of tests on single piles and pile groups in soft clay undergoing lateral movements. Experimental apparatus The apparatus is illustrated in Figure 1. It was designed to apply a uniform rectangular profile of lateral soil movement on the rigid piles with pinned head and tip conditions to obtain the ultimate soil pressures. The model circular piles of 16 mm diameter and 150 mm embedded length were installed in a clay sample with the undrained shear strength of 24 kPa. The clay samples were prepared from a kaolin slurry by consolidating the slurry in a consolidometer of 400 mm diameter. The piles were instrumented with button load cells to measure the ultimate soil pressures acting on the piles. The assembled apparatus prior to testing is shown in Figure 2. Results and discussion For the test on a single circular pile, the normalized ultimate soil pressure p u /c u was found to be 11.1. It is within the range of 9.14~11.94c u suggested by Randolph and Houlsby (1984) and a little higher than the value of 10.6c u obtained by Pan et al. (2000) for a rectangular pile. A number of tests were conducted on different pile group configurations to investigate the reduction of the pile group capacity. Some results are shown in Figure 3 for a two-pile group. The group factor F p is defined as F p = p ui / p us (1) in which p ui is the ultimate soil pressure for an individual pile in a group and p us is the ultimate soil pressure from the single pile test. S h and S v are the pile center-to-center spacing and d is the pile diameter. Generally, the group factors for two-pile groups were smaller than 1.0 and increased with larger pile spacing. For two piles in a row of 6d spacing, the F p was very close to 1.0. It indicated that the piles for a two- pile group in a row behaved like isolated single piles when the pile spacing was 6d or larger. For two piles in a line, the group factor of the “front” pile was always larger than that of the “back” pile in a group. For the “front” pile, the F p slightly increased with increased pile spacing, and all values of F p were close to 1.0 (with maximum difference of 13%). For the “back” pile, even at a pile spacing of 6d, the F p was 0.76. It indicated that the group effects still existed when the pile spacing was 6d for a two-pile group in a line. When the pile spacing was 3d or smaller, shear failure between two piles in a line was observed on the soil surface, as shown in Figure 4. The shear failure may have caused significant reductions of p u for the “back” piles in a two-pile-in-a-line group. Figure 1. Elevation sketch of apparatus Figure 2. View of assembled apparatus prior to testing
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Civil Engineering Research
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GEOTECHNICSModel Tests on Passive Piles in Soft Clay
The majority of piles are designed to support loads that areapplied directly to the pile head by a structure. However insome cases piles are subjected to lateral soil pressures as aresult of lateral soil movements. Typical examples of these“passive” piles are piles adjacent to tunnelling and excavation,existing piles adjacent to pile driving, piles used to stabiliseslopes, and piles supporting bridge abutments adjacent toapproach embankments. A critical factor in the design of thepassive piles is the ultimate soil pressure pu, which is definedas the maximum value of the limiting soil pressure along thelength of the pile shaft when piles are subjected to large soilmovements. A specially designed laboratory apparatus wasused to carry out a series of tests on single piles and pilegroups in soft clay undergoing lateral movements.
Experimental apparatus
The apparatus is illustrated in Figure 1. It was designed toapply a uniform rectangular profile of lateral soil movementon the rigid piles with pinned head and tip conditions toobtain the ultimate soil pressures. The model circular pilesof 16 mm diameter and 150 mm embedded length wereinstalled in a clay sample with the undrained shear strengthof 24 kPa. The clay samples were prepared from a kaolinslurry by consolidating the slurry in a consolidometer of 400mm diameter. The piles were instrumented with button loadcells to measure the ultimate soil pressures acting on thepiles. The assembled apparatus prior to testing is shown inFigure 2.
Results and discussion
For the test on a single circular pile, the normalized ultimatesoil pressure pu/cu was found to be 11.1. It is within the
range of 9.14~11.94cu suggested by Randolph and Houlsby(1984) and a little higher than the value of 10.6cu obtainedby Pan et al. (2000) for a rectangular pile.
A number of tests were conducted on different pile groupconfigurations to investigate the reduction of the pile groupcapacity. Some results are shown in Figure 3 for a two-pilegroup. The group factor Fp is defined as
Fp = pui / pus (1)
in which pui is the ultimate soil pressure for an individualpile in a group and pus is the ultimate soil pressure from thesingle pile test. Sh and Sv are the pile center-to-center spacingand d is the pile diameter. Generally, the group factors fortwo-pile groups were smaller than 1.0 and increased withlarger pile spacing. For two piles in a row of 6d spacing, theFp was very close to 1.0. It indicated that the piles for a two-pile group in a row behaved like isolated single piles whenthe pile spacing was 6d or larger.
For two piles in a line, the group factor of the “front” pilewas always larger than that of the “back” pile in a group.For the “front” pile, the Fp slightly increased with increasedpile spacing, and all values of Fp were close to 1.0 (withmaximum difference of 13%). For the “back” pile, even ata pile spacing of 6d, the Fp was 0.76. It indicated that thegroup effects still existed when the pile spacing was 6d fora two-pile group in a line. When the pile spacing was 3d orsmaller, shear failure between two piles in a line was observedon the soil surface, as shown in Figure 4. The shear failuremay have caused significant reductions of pu for the “back”piles in a two-pile-in-a-line group.
Figure 1. Elevation sketch of apparatus
Figure 2. View of assembled apparatus prior to testing
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Figure 3. Group factors for two-pile groups(with pile spacing in brackets)
Figure 4. Observed shear failure for two pilesin a line with 3d spacing
References
[1] Pan JL, Goh ATC, Wong KS and Teh CI, 2000, Modeltests on single pile in soft clay. Canadian Geotech. J.,37: 890-897.
[2] Randolph MF and Houlsby GT, 1984, The limitingpressure on a circular pile loaded laterally in cohesivesoil. Geotechnique, 34(4): 613-623.
Effect of Joint Number and Distributionon Moment Induced in Tunnel Lining
The use of precast segmental lining in tunnelling projectshas become increasingly popular in recent years. However,in the design of precast segmental lining, the influence ofjoints between the lining segments on the stresses induced inthe lining is often ignored.
A numerical study to investigate the effect of both the numberand orientation of joints on the moment induced in the liningwas performed. In this paper, some of the results obtainedare summarised and a simple design methodology todetermine the moment induced in the jointed tunnel liningwithout incorporating the joints in the analysis is proposed.
Methodology
The two-dimensional finite element program PLAXIS wasadopted in this study. Typical lining parameters of North-East Line MRT Tunnels in Singapore were adopted. Table 1summarises the properties of tunnel lining. The analysis wasperformed on a tunnel of 6.0m in diameter (D) with a cover-to-diameter ratio (H/D) of 2, where H is the depth of thetunnel measured from ground surface to the centre of thetunnel. The main analysis was performed on soil propertiesof Bukit Timah Residual Soil, as given in Table 2.
Influence of number and orientation of joints
This study was performed to investigate the effect of thenumber and orientation of joints on the moment induced inthe tunnel lining. The joints were evenly distributed aroundthe tunnel and various orientations of the joints were adoptedin order to obtain the critical and the most favourable joint
Table 1. Properties of elastic tunnel lining(after Sebastian and Nadarajah, 2000)
Parameter Symbol Value Unit
Thickness t 0.275 m
Weight w 6.6 kN/m/m
Young’s modulus El 32000 MN/m2
Poisson’s ratio vl 0.2 -
Table 2. Properties of Bukit Timah Residual Soil(after Karr Winn et. al., 2001)
Parameter Symbol Value Unit
Unit weight γ 18 kN/m3
Coefficient of earthpressure at rest Ko 0.5 -
Young’s modulus Es 8250 kN/m2
Poisson’s ratio vs 0.495 -
Shear strength Cu 55 kN/m2
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Figure 2 shows the variation of moment induced in the liningdue to various joint orientations of the 4-joint lining. Thelocation of the joints in the tunnel with respect to the crownwas measured by an angle “θ”. An angle θ of 0o representsthe locations of joints at 0o, 90o, 180o and 270o with respectto the crown of the tunnel, while an angle of 45o representsthe location of joints at 45o, 135o, 225o and 315o with respectto the crown of the tunnel.
orientation that would induce the maximum and minimummoment in the lining respectively.
Figure 1 shows the variation of maximum bending momentwith number of joints (critical orientation). It can be seenfrom Figure 1 that as the number of joints increases, themoment induced in the lining decreases and reaches a smallvalue when the number of joints is greater than 8. This canbe attributed to the fact that the span of the beams (liningsegments) is shorter for the larger number of joints andtherefore induces lower moment in the lining.
Figure 1. Variation of moment in tunnel liningwith number of joints (critical orientation)
Figure 2. Variation of moment in 4-joint tunnel liningwith different joints orientation
It can be seen from Figure 2 that by orienting the joints fromθ = 45o to θ = 0o, the values of the moment induced in thelining is reduced by 8 times. This is a considerably largereduction in moment and can lead to a large reduction incosts.
For design purpose, one can obtain Ie,min which representsthe most favourable orientation for minimum moment in thelining as shown in Figure 3. The corresponding effectivethickness can then be calculated. The calculated effectivethickness can then be used to compute the flexibility ratio ofthe lining as defined by equation (1):
Flexibility Ratio = ... (1)
where Es is the Young’s modulus of soil, El is the modulusof elasticity of the lining, t is the thickness of lining, vs is thePoisson’s ratio of soil, vl is the Poisson’s ratio of the liningand Il is the moment of inertia of the cross section per unitlength along the axis of the tunnel.
One can then proceed to Figure 4 which shows the influenceof flexibility ratio on the moment coeficient to determine themoment induced in the jointed tunnel lining.
Conclusion
A numerical study on the bending moment induced in jointedtunnel lining was carried out. The influence of both thenumber and orientation of joints on the moment induced injointed tunnel lining were studied in detail. From the studyperformed, the following conclusions can be made:
Simplified design methodology
A simplified design methodology is proposed in order tofacilitate the determination of bending moment induced injointed tunnel lining without incorporating the joints in theanalysis.
An equivalent tunnel is defined as the unjointed tunnel thathas a lining thickness that gives the same maximum momentas the jointed tunnel lining. The equivalent of the jointedtunnel is thus established for the moment as shown in Figure3, where Ie,max and Ie,min are the effective second moment ofinertia of the lining for the critical and the most favourableorientation of joints respectively and I is the second momentof inertia for non-jointed tunnel lining.
Figure 3. Equivalent I of jointed shallow tunnels
Ie/I
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Figure 4. Variation of moment coefficient inunjointed shallow tunnel lining with flexibility ratio
(a) The number and orientation of joints in the lining havesignificant effects on the bending moment induced inthe lining.
(b) The increase in the number of joints in the mostfavourable orientation will reduce the bending momentin the lining significantly.
(c) The most favourable orientation of 4 joints can reducemoment in the lining up to 8 times as compared to thecritical orientation of the 4 joints.
(d) A simplified design methodology to determine themoment induced in jointed tunnel lining withoutincorporating the joints in the analysis is proposed.
References
[1] Karr Winn, Rahardjo, H and Peng, S.C. (2001).Characterization of residual soils in Singapore.Geotechnical Engineering Journal of the South-East AsiaGeotechnical Society, 32 (1), 2001, 1-13.
[2] Lee, K.M. and Ge, X.W. (2001). The equivalence of ajointed shield-driven tunnel lining to a continuous ringstructure. Canadian Geotechnical Journal, 38 (3), 2001,461-483.
[3] Muir Wood, A.M. (1975). The circular tunnel in elasticground. Geotechnique, 1, 1975, 115-127.
[4] Peck, R.B., Hendron, A.J. and Mohraz, B., 1972. State ofthe art of soft ground tunnelling. 1st North A M. RapidExcavation and Tunnelling Conference, Chapter 19.
[5] Sebastian, P. and Nadarajah, P., 2000. Construction of NorthEast Line tunnels at Singapore River Crossing. Tunnellingin soft ground. Proceedings of the international conferenceon tunnels and underground structures, Singapore, pp.191-198.
Effect of Rock Mass Properties onTunnelling Boring Machine Excavation
The tunnel boring technology has been improved over thepast years. This includes the significant advances of TBMson the capacities of thrust and torque as well as thedevelopment of large diameter rolling cutters with a constantsection profile. Such cutters are capable of dealing with thehigh cutter loads required for hard rock and keeping aconstant production and high abrasion resistance. Hence,TBMs are extensively utilized in tunneling and the effect ofrock mass properties on TBM excavation has become animportant topic for project planning and choice of economictunneling methods. In this study, a series of two dimensionalnumerical modeling were performed using the discreteelement method (DEM) to explore the effect of rock massproperties including rock material brittleness index, jointspacing and joint orientation on TBM excavation.
Model configuration
The dimension of the model was 0.6×0.6 m. The cutter was
modelled by a normal force applied at mid height of the leftboundary through a contact thickness of 15 mm. The rollingforce acting on the cutter was not taken into considerationin the two dimensional model. The upper, lower and rightboundaries were regarded as fixed displacement boundaries.There were three types of rock mass conditions modeled.Type 1: only rock material brittleness index varied form11.41~29.52. Type 2: one set of vertical joints was includedin the rock mass and the joint spacing varied form 10 mmto 500 mm. Type 3: one set of joints with a fixed spacing of200 mm was included in the computation model. The dipdirection of the joint set was assumed to be in the samedirection as the cutting load, and the joint dip angle variedfrom 0º~90º. The rock blocks between the joint set werediscretized with fine finite difference meshes, namely zonesin UDEC. The zone size in the blocks was set to 5 mm andthe damping value 0.1.The rock material modeled is typicalgranite found in Singapore (Zhao, 1996). The intact granitewas assumed to be the Mohr-coulomb material and itsproperties are listed in Table 1, while all joints satisfy theCoulomb slip model with the properties summarized inTable 2.
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Effect of rock mass propertieson TBM excavation
The rock mass breakage process under TBM rolling cuttersmay be divided into two stages. The first is that the rollingcutters are pressed into rock surface which cracks the rockimmediately beneath the cutter. This process is termed asindentation. The second stage is that cracks between twoadjacent cutters propagate across the distance between twoneighbouring cutters, and then chips are formed. The rockstrength affects the rock behaviour under compression. Whenthe rolling cutter indents the rock, it must exert a stress morethan the rock strength. Thus, the rock strength is directlyrelevant to the excavation of TBM. Some models forpredicting TBM performance show the relationship betweenthe penetration rate and rock uniaxial compressive strength(Hughes, 1986). Generally, the penetration rate decreaseswith the increase of rock uniaxial compressive strength.
The brittleness, which the rock exhibits when subjected to theindentation test and chip formation, is important to the TBMpenetration. It affects the formation and propagation of cracksinside the rock. In this paper, the brittleness index (BI) isdefined as the ratio of the uniaxial compressive strength to theBrazilian tensile strength. Based on the simulation results,with the decrease of the brittleness index, the crushed zonedecreases and the number and length of the main cracks outsidethe crushed zone also decrease. It is obvious that with anincrease of the rock brittleness index the cutter indentationprocess gets easier. The variation of the failure element numberat the different rock brittleness index is shown in Figure 1.With the increase of the brittleness index, the failure elementnumber increases linearly.
It has been well recognized that joints and fractures have animportant effect on the TBM performance. From the viewpointof either energy or fracture propagation, it is easy to understandthat discontinuities should facilitate rock breakage, becauserock mass with many discontinuities has more surface energythan that of the same volume of rock material. The simulation
Table 1. Properties of intact granite
Property Value
Bulk density (kg/m3) 2600
Bulk modulus (GPa) 55
Shear modulus (GPa) 32
Cohesion (MPa) 66
Friction angle (°) 31
Tensile strength (MPa) 11.3
Dilation angel (°) 10
Table 2. Properties of joints
Property value
Normal stiffness (GPa/m) 10
Shear stiffness (GPa/m) 5
Cohesion (MPa) 1.5
Friction angle (°) 25
Tensile strength (MPa 0.04
results of the effect of joint spacing on TBM excavation areshown in Figure 2. In the figure, Ps denotes the penetrationrate as the joint spacing is equal to S, and P0 denotes thepenetration rate without joints. With the increase of the jointspacing, the penetration decreases. The results are comparedwith the field measurements by Bruland (1998) shown inFigure 2. The curve shape of the simulated results showsgood agreement with that of the field measurements.
The effect of joint orientation on TBM excavation mainlyconcentrates on the changes of the rock chipping process.The simulation results are shown in Figure 3. In the figure,Pα denotes the penetration rate as the angle between the tunnelaxis and the joint plane is equal to α, and P0 denotes thepenetration rate at α =0. As the angle α increases, thepenetration increases until α reaches 60º, then the penetrationrate decreases with the increase in α. The results show a goodagreement with the in situ measurements by Bruland (1998).
Figure 1. Failure element variation at the different BI
Figure 2. Effect of the joint spacing on the TBM penetrationrate (St denotes fissures and Sp denotes joints)
Figure 3. Effect of joint orientation on theTBM penetration rate
Rock mass properties are the main factors influencing TBMexcavation. Generally speaking, with the increase in the rockstrength, the penetration rate decreases. Higher rockbrittleness index leads to an increase in the TBM penetrationrate. With the increase of joint spacing, the penetrationdecreases. In practise, when the joint spacing is too small,the tunnel face may not be stable during excavation and thepenetration rate may decrease. The influence of jointorientation shows a curvilinear relationship. When the angleα is equal to 60º, the penetration rate reaches the maximumvalue.
References
[1] Zhao J., 1996. Construction and utilization of rockcaverns in Singapore Part A: The Bukit Timah granitebedrock resource. Tunnelling and Underground SpaceTechnology, Volume 11, Issue 1, pp. 65-72.
[2] Hughes H. M., 1986. The relative cuttability of coalmeasures rock. Mining Science and Technology, Vol. 3,pp. 95-109.
[3] Bruland A., 1998. Hard rock tunnel boring. DoctoralThesis, Norwegian University of Science andTechnology, Trondheim.
Hydrofracturing in Situ Stress Measurementsin Singapore Granite
Recently, Singapore has been extensively exploring thepossibility of underground space development to free someof the surface land. The first set of caverns in Singapore isnow under construction in the Bukit Timah Granite. Extensivesite and laboratory investigations have been carried out priorto the construction phase. In situ stress tests have beenperformed in the Bukit Timah Granite using the hydraulicfracturing technique. These hydraulic fracturing tests are thefirst in situ stress measurements to be carried out in rocks inSingapore.
Geology features of the Bukit Timah Graniteand surrounding formations
The Bukit Timah Granite is the base rock formation inSingapore and it outcrops in about one-third of the mainSingapore Island and the whole of Pulau Ubin. Granite is aMesozoic rock formation formed during the Triassic period.The dominant granite component is grey and medium tocoarse grained (2~5 mm) and consists of cream or pale yellowfeldspar (60~65%), smoky quartz (30%), and smallerproportions of reddish-brown biotite and hornblende.
Generally, there are three to four sets of joints in the graniterock masses with predominantly sub-vertical joint sets,accompanied by a sub-horizontal set. The strike of thedominant sub-vertical joint set is NNW-SSE, with secondarysets at NNE-SSW and NW-SE, measured in the Mandaiquarry. Investigations also reveal that the faults and the shearzones are generally sub-vertical.
The Bukit Timah granite is mainly covered by the JurongFormation on the southwest and the Old Alluvium on theeast. The Old Alluvium is a Cenozoic semi-consolidatedsediment, mainly flat-lying sand and sub-ordinate pebblysand and gravel. The Old Alluvium has no significant bearingon the in situ stress in the Bukit Timah granite and therefore,is not elaborated here. The Jurong Formation is a Mesozoicformation deposited during late Triassic to early Jurassictimes. It covers south, southwest and west Singapore with avariety of folded sedimentary rocks. A variety of folds havedeveloped in the Jurong Formation. It was suggested [1] thatthe folding of the Triassic sedimentary pile started beforethe cessation of sedimentation in early Jurassic times bysliding of the sedimentary pile to the NE against the BukitTimah granite. The folds range in style from open throughvertical isoclinal to isoclinal over-folds. The strikes aregenerally NW with dips varying from 10 degrees to thevertical. The lateral compression from the main range graniteblock is believed to be the source of tectonic stress generatingfolding in the Jurong Formation and possibly high in situstress in the Bukit Timah granite. The strike of the basin isin the direction of NW-SE, and the folding is along themaximum tectonic stress acting in NE direction.
In situ stress measurementin the Bukit Timah Granite
A total of 8 hydrofracturing tests were carried out in 2boreholes (BH8 and BH17), at depths between 60 and 120m below the ground. The tests followed the standard testset-up and procedure [2]. The test procedure, which involvessealing a section, hydrofracturing the rock, re-opening the
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fracture, recording the key pressures, and mapping thefracture orientation, is listed below:
a) The test interval was selected based on borehole log.
b) Straddle packers were lowered down in the borehole tothe selected test depth.
c) The straddle packers were inflated to seal the testinterval. The pressure in the packers was set at about 7-8 MPa.
d) Water was pumped with rapid flow rate into the testinterval. Pressure increased until “breakdown” occurred(i.e., occurrence of a hydraulic tensile fracture on theborehole wall) at pressure Pc. Pumping was thenimmediately stopped, to obtain the “shut-in” pressurePs.
e) After the water pressure stabilised at the ambient porewater pressure (Po), fracture re-opening test was carriedout. Water was pumped into the test interval again toincrease the pressure until the tensile fracture was re-opened with a “re-opening” pressure Pr. Pumping wasthen stopped immediately to obtain the “shut-in” pressurePs. Re-opening tests were usually repeated for 3-5 cyclesto ensure good test records.
f) After the hydraulic fracturing tests, fracture impressionswere mapped by impression packer tests. Orientation ofthe fracture was determined from the impression.
A summary of the breakdown pressure Pc, interpreted shut-in pressure Ps, reopening pressure Pr, and ambient pore waterpressure Po for each test is given in Table 1. The breakdownpressure is interpreted as the peak value of the pressure inthe first cycle. The reopening pressure is taken as the averagevalue of the peak pressures in the re-opening cycles. The
ambient pore water pressure is taken as the water pressureafter it is stabilised. The shut-in pressure is determinedgraphically using two methods: the pressure decay rate (dP/dt) versus pressure (P) method and the inversed pressuredecay rate (dt/dP) versus pressure (P) method. These arestatistical analysis procedures applied to digitally recordedfield pressure and flow rate data, aiming to improve theobjectivity of Ps [2]. As can be seen from Table 2, in generalthe two methods yield close values.
Because the fractures induced by the tests are generallyvertical, the vertical stress σv is assumed as one of theprincipal stresses and the maximum σH and minimum σh
horizontal stresses are calculated using the followingequations [2].
σh = Ps (1)
σH = 3σh – Po – Pc + T (2)
where T is the tensile strength of the rock. The tensile strengthcan be estimated from the hydraulic fracturing test data asthe difference between the breakdown pressure and reopeningpressure. It can also be obtained through laboratory tensiletesting. The values of the initial stresses and their orientationsin the ground as interpreted from the hydraulic fracturingtests are summarized in Table 3.
Conclusion
Results of the stress measurements indicate that the ratio ofσv:σh:σH is approximately 1:2:3. The maximum horizontal insitu stress is in the direction of NNE-SSW. This direction ofmaximum horizontal stress is in correlation with local
Table 1. Key pressures for the derivation of horizontal in situ stresses
Borehole Test No. Depth (m) Pc (MPa) Po (MPa) Pr (MPa) Ps (MPa) Thf (MPa) Tlab (MPa)
geological setting. The Bukit Timah Granite is against thelateral deformation and folding in the Jurong Formation inthe direction of NE~NNE. The regional maximum horizontalstresses are also in the direction of NE~NNE, as influencedby the Sumatra-Java trench. The high horizontal stressesprovide general favourable condition for the construction ofthe proposed cavern complex as the cavern designed is oflarge arch span and relatively small height.
[1] Public Works Department. The geology of the Republicof Singapore. Public Works Department, Singapore,1976.
[2] Hamison BC. The hydraulic fracturing method of stressmeasurement: theory and practice. Comprehensive RockEngineering, Editor-in-Chief: Hudson JA, 1995; Vol.3,395-412.
Continuous Surface Wave Measurementfor Site Characterization
Geophysical techniques have been used to characterize theearth’s surface for decades. The great advantage ofgeophysical techniques is that they can be performed rapidlyand cover large areas. Geophysical tests using surface wavehave become popular recently in geotechnical sitecharacterization. There are two different geophysicaltechniques using surface waves: Spectral Analysis ofSurface Wave (SASW) method which uses hammer blowsas an energy source and Continuous Surface Wave (CSW)method which uses a steady-state vibrator as an energysource. The CSW method overcomes the frequencyresolution problem of the SASW method by using a vibratorthat can create surface waves with known frequencies.Although surface wave survey methods have shown greatimprovement in the ease of conducting the test, there isstill ambiguity in the interpretation of surface wave testswhich is the primary concern of this article. In this article,the interpretations of CSW tests for two sites in NTU arepresented.
Continuous Surface Wave System and fieldexperimental procedures
The Continuous Surface Wave System (CSWS) developedby GDS (GDS Instruments Ltd., 1998) was used for thefield experiment. Details of CSWS and test procedures aregiven in Anand et al. (2001) and will not be repeated here.CSW tests were conducted at two sites in NanyangTechnological University (NTU) Jurong campus. Site 1 islocated behind the School of Civil and EnvironmentalEngineering and Site 2 is located near the NTU Jalan Baharentrance (opposite to graduate hall).
Analyses of CSW tests
The data collected from the CSWS were retrieved for furtheranalysis. Processing of the data can be divided intocalculation of dispersion curve (plot of phase velocity, Vφ,versus wavelength, λ) and inversion of the dispersion curve.
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The schematic diagram for obtaining the dispersion curveis shown in Figure 1. The dispersion curve is subsequentlyinverted to obtain the shear wave velocity profile using aMATLAB program based on the linear elastic method byLai and Rix (1998). With a given surface wave dispersioncurve and initial soil profile containing information of layerthickness, Poisson’s ratio, unit weight and initial shear wavevelocity of each soil layer as input parameters, the programcontinuously adjusts the shear wave velocity profile tomatch the field dispersion curve in a least square errorsense.
Uniqueness of shear wave velocity profile from theinversion is difficult to prove. Many researches havesuggested examining the shear wave velocity profileobtained from several initial soil profiles to determine thereasonableness of the shear wave velocity profile(Herrmann, 2002; Lai and Rix, 1998). Attempt is made inthis article to optimise the procedure for obtaining the shearwave velocity profile. The shear wave velocity profileobtained is compared with available borehole information.
The initial soil profile has three parameters: thickness (t),unit weight (γ) and Poisson’s ratio (ν). To obtain t, thefactored wavelength method is used. In this method, thenumber of soil layers is obtained from the dispersion curve
Time Series
Dispersioncurve
Phase angleplot
Phase angle
Power spectra
Phase Velocity, Vφ
Wav
elen
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λ
For 15 Hz
Phas
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φ Geophone 1
Distance, d
Geophone 3Geophone 2
2πf/Vφ
Figure 1. Schematic diagram of obtainingdispersion curve from CSW
Figure 2. Dispersion curves for Site 1 and Site 2
(a) Site 1 (b) Site 2
by drawing tangents to the dispersion curve as illustratedin Figure 2. The intersection of two tangents represents achange in the soil stiffness and therefore a different soilstratum. The factored wavelength method suggests that λ/z is constant, where z is depth and λ is wavelength.Literature show that the value of λ/z varies from 2 to 4(Gazetas, 1982). To estimate the thickness of each soillayer from the dispersion curve, λ/z of 2, 3 and 4 wereused. The γ and ν of each soil layer are arbitrarily assignedvalues 18 kN/m3 and 0.3, respectively. The inversionanalyses are then carried out and the root mean square(RMS) errors of the fit of the computed dispersion curveto the measured dispersion curve are compared as shownin Table 1. Using the soil profile with the lowest RMSerror (Trial 2 for both Site 1 and Site 2), the other twoparameters of the soil layer, γ and ν, are then adjusted tosee if a lower RMS error can be obtained as shown inTable 2 as Trials 4 and 5, respectively. It was found fromdifferent trials for both Site 1 and Site 2 that, when onlythe values of γ are varied (γ = 17, 18, 19 kN/m3) and allother parameters remained constant, the RMS value remainsconstant. However, the RMS value decreases and thenincreases with increasing value of ν (from 0.3 to 0.49). ForSite 1, the lowest RMS value was obtained when ν = 0.45.Therefore the final shear wave velocity profile for Site 1 isTrial 5. For Site 2, Trial 5 with ν = 0.4 gave the lowestRMS error. Therefore, Trial 5 was selected as the mostprobable final shear wave velocity profile for Site 2. It ispossible to have different γ and ν for each soil layer. In theabove, both γ and ν were varied similarly for the soil layersso simplify the illustration.
From the final shear wave velocity profile, the shearstiffness of each soil layer can be easily obtained using
G=ρVs2 (1)
where G is the stiffness of the soil, ρ is the mass densityand Vs is the shear wave velocity. The stiffness profile ofSite 1 and Site 2 are compared with the available boreholeinformation in Figure 3. The comparison shows goodagreement with the stratification given by the boreholeinformation.
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Table 1. Effect of thickness of soil layer on inversion analyses
Current technology for surface wave measurements is welldeveloped. However, the uncertainty in the interpretation ofthe surface wave tests still exists. In this article, a procedureof obtaining a consistent shear wave velocity profile fromthe surface wave test is presented. The procedure appears togive shear wave velocity profile in good agreement withborehole information. Ongoing research effort is made tofurther improve the procedure.
References
[1] Anand, S., Leong, E.C. and Cheong, H.K., 2001,Theuse of a continuous surface wave measurement systemfor in-situ characterisation of soil, Proceedings ofInternational Conference on In Situ Measurement of SoilProperties and Case Histories, Bali, Indonesia, May 2001,pp. 139-144.
[2] GDS Instruments Limited, 1998, The GDS ContinuousSurface Wave System: User Handbook, GDS InstrumentsLtd., Surrey, UK.
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(a) Site 1 (b) Site 2
Figure 3. Results of inversion analysis for Site 1 and Site 2
[3] Gazetas, G., 1982, Vibrational characteristics of soildeposits with variable velocity, International Journalfor Numerical and Analytical Methods in Geomechanics,Vol. 6, pp. 1-20.
[4] Herrmann, R.B., 2002, Computer Program inSeismology, Version 3.20, Department of Earth andAtmospheric Sciences, Saint Louis University, USA,August 25, 2002.
[5] Lai, C.G., and Rix, G.J., 1998, Simultaneous Inversionof Rayleigh Phase Velocity and Attenuation for Near-Surface Site Characterization, Report No. GIT-CEE/GEO-98-2, Georgia Institute of Technology, School ofCivil and Environmental Engineering.
The small land size and high population density inSingapore, coupled with the industrial development andeconomic growth, increase the need to utilise poor soilsfor foundation support and earthwork construction. Besidesthis need, extensive land reclamation programmes havebeen carried out by the Singapore government to meet thedemand for more land. An example of the past reclamationprojects that used sand as the fill material to reclaimthe low land or sea area are Punggol and ChangiAirport.
In fact, the poor ground conditions of the marginal andreclaimed land lead to the need for soil improvement. Soilimprovement utilises the poor ground −by modifying orstabilising it− without the use of pile foundations. In manycases, it is more practical and economical to enhance themechanical properties of the poor soil by soil improvementrather than to ignore the problem and design the structureswith pile foundations. Dynamic compaction, as one of themethods to improve engineering properties of soil, is adeep improvement method mainly for granular soil.Dynamic compaction, for example, was used extensivelyfor the densification of the hydraulic fills in the site for thedevelopment of the Changi airport.
How does dynamic compaction work? Dynamic
compaction is a soil improvement method in which a largepounder is repeatedly dropped from a certain height ontothe ground surface by using a crane; it intends to compactmainly granular soil in-place without the need of removal.During the dynamic compaction process, the potentialenergy of the pounder is converted into impact energythat is produced by dropping the pounder onto the groundsurface. Normally, dynamic compaction is performed witha regular pattern in order to densify the granular soil. Theprimary goal of dynamic compaction is to change a poorgranular soil into one that has better engineering properties,such that the soil strength is increased, and itscompressibility is decreased, as the result of thedensification process.
Dynamic compaction produces impact stress on the groundsurface, and as a result of the impact stress, thedisplacements −usually seen as craters− are produced atthe ground surface. The stresses during impact have asignificant role in the process of densification, and there isnot much information about the lateral stress in the soildue to the impact. Therefore, the objective of this researchis to investigate the effect of the initial dry density of sandand the impact energy of the pounder on the impact andlateral stresses due to one dimensional dynamic compaction.The study was experimental, and the scope of theexperiments was one-dimensional laboratory dynamiccompaction on a dry sand column.
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Figure 1. Impact testing set-up
Experiments and results
As the continuation of the past research performed by Low[1], a laboratory dynamic compaction was conducted on adry Ottawa sand column under various dry densities. Thedry sand column was prepared by raining and dry pluviationmethods so that various densities could be obtained. Thedetails of the experiments can be found in Chua and Chua[2]. A set up of the equipment system to produce an impacton the sand column is shown in Figure 1. A free fallingpounder was dropped several times onto the surface of thesand column, and the deceleration of the pounder duringimpact was measured by an oscilloscope through a signalconditioner. In addition, lateral stresses in the sand columnduring impact were also measured by pressure transducersat 150 mm and 300 mm below the sand surface.
Figure 2 shows typical variation of impact stress and thelateral stresses with time for loose sand condition underthe impact energy of 34 Nm. Impact stress can be definedas the vertical stress acting on the surface of the sand columndue to the impact of a free falling weight, and lateral stressis the radial stress induced in the sand column as the resultof the impact. Firstly, Figure 2 indicates that the impactstress has relatively higher amplitude than that of the lateralstresses. In fact, the deeper the location in the sand column,the smaller the amplitude of the lateral stress is; this isprobably because of the decreasing impact energy withdepth due to the loss of the impact energy along the sandcolumn. Secondly, Figure 2 also illustrates that there is atime lag for the lateral stresses, due to the time taken bythe stress wave travelling down the sand column.
Accordingly, Figure 3 shows the impact stress versus timeunder various pounder drops. Figure 3 indicates that theimpact stress of the first drop has a relatively smallamplitude with longer impact duration, whereas the impactstress after the fifth drop shows a quite high stress amplitudewith relatively shorter impact duration. According toWibawa et al. [3], the difference of the stress amplitudes isdue to a higher sand density which resulted after the firstdrop. The loose sand becomes denser because there is ahardening effect after dropping the pounder repeatedly.During the first drop, the damping effect is probably the
Figure 2. Stress vs. time profiles of drop 5 for loose sandwith impact energy of 34 Nm
largest since the density of the sand is in the loosest state.Thus most of the impact energy is cushioned by the sandmass; however, as the sand density increases, the amplitudeof the impact stress increases as well. Figure 4 shows thelateral stress versus time under various drops. The patternof the lateral stress for various drops is quite similar to thatof the impact stress.
Discussion
Since the stresses in the sand column are closely related todisplacement, the effect of the initial dry density and impactenergy on the impact and the lateral stresses will be
Figure 3. Impact stress profiles for loose sandwith impact energy of 34 Nm
Figure 4. Lateral stress - time profiles for loose sandwith impact energy of 34 Nm
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Figure 5. The amplitude of impact and lateral stressesvs. dry density
Finally, the effect of impact energy on the amplitude of theimpact and the lateral stresses of sand will be discussed.Figure 6 shows the relationship of impact and lateral stressesand applied impact energy. Figure 6 indicates that, firstly,the amplitude of the impact stress is linearly related to theapplied impact energy because higher impact energy causeslarger impact on the sand column, especially the surface,resulting in the higher impact stress. This finding is alsoconsistent with the previous experiment in Wibawa et al.[3]. Secondly, the amplitude of the lateral stress is smallerthan the impact stress’ amplitude; the difference of the stress’amplitude is due to the different depths. Lastly, theamplitude of lateral stresses is also linearly related to theimpact energy.
discussed. Figure 5 shows the amplitude of the impact andthe lateral stresses versus dry density at the energy level of34 Nm. The first finding, as shown in Figure 5, is that theamplitude of the impact and the lateral stresses increasesnonlinearly with the dry density of sand. This is probablybecause loose sand absorbs more impact energy than sandof higher density, and as a result, the stress amplitude issmaller. Secondly, Figure 5 also indicates that the impactstress’ amplitude is higher than that of the lateral stressesfor the density range in the experiments. This is probablydue to the different depths and the decreasing impact energywith depth − caused by energy loss in the sand column.
Figure 6. The amplitude of stress and energy relationshipsfor loose sand
Conclusion
Based on the experimental results and the discussion above,for the particular impact energy range in the experiments,it can be concluded that:
a. The amplitude of impact stress and the lateral stressincrease nonlinearly with the dry density of sand.
b. The amplitude of impact stress and the lateral stressincrease linearly with the applied impact energy of thefree falling pounder.
References
[1] Low, P. C., “Dynamic Compaction of Sand Column,”M.Eng Thesis, Nanyang Technological University,Singapore, 1995
[2] Chua, S. S. and Chua A. H., “Laboratory DynamicCompaction on Dry Cohesionless Soil,” Final YearProject Report, Nanyang Technological University.Singapore, 2004
[3] Wibawa, B., Bay, H. S. and Ng, Y. K., “Impact Stresson Dry Sand due to Dynamic Compaction,” CivilEngineering Research, No. 17, Nanyang TechnologicalUniversity, Singapore, 2004
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