Analytical and numerical solutions for soft clay consolidation using geosynthetic vertical drains with special reference to embankments

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1 University of Wollongong Researc Online Faculty of Engineering - Papers (Arcive) Faculty of Engineering and Information Sciences 25 Analytical and numerical solutions for soft clay consolidation using geosyntetic vertical drains wit special reference to embankments Buddima Indraratna University of Wollongong, indra@uow.edu.au Colacat Rujikiatkamjorn University of Wollongong, colaca@uow.edu.au Iyaturai Satanantan University of Wollongong Moamed A. Sain University of Wollongong, sain@uow.edu.au Hadi Kabbaz University of Wollongong, kabbaz@uow.edu.au ttp://ro.uow.edu.au/engpapers/197 Publication Details Tis conference paper was originaly publised as Indraratna, B, Rujikiatkamjorn C, Satanantan, I, Sain, MA and Kabbaz, H, Analytical and numerical solutions for soft clay consolidation using geosyntetic vertical drains wit special reference to embankments, in Proceedings of te Te Fift International Geotecnical Engineering Conference, Cairo, 25, Researc Online is te open access institutional repository for te University of Wollongong. For furter information contact te UOW Library: researc-pubs@uow.edu.au

2 ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOFT CLAY CONSOLIDATION USING GEOSYNTHETIC VERTICAL DRAINS WITH SPECIAL REFERENCE TO EMBANKMENTS Buddima Indraratna PD, DIC, MSc (Lond.), FIEAust., FASCE Professor of Civil Engineering, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia Tel: ; Fax: Colacat Rujikiatkamjorn BEng (Hons), MEng (AIT), MIEAust Doctoral Student, Civil Engineering, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia Iyaturai Satanantan BEng (Hons) Doctoral Student, Civil Engineering, Faculty of Engineering University of Wollongong, Wollongong City, NSW 2522, Australia Moamed A. Sain BSc, MSc, PD, MIEAust Researc Fellow, Civil Engineering, Faculty of Engineering University of Wollongong, Wollongong City, NSW 2522, Australia Hadi Kabbaz BSc, MSc, PD Researc Fellow, Civil Engineering, Faculty of Engineering University of Wollongong, Wollongong City, NSW 2522, Australia Te Fift International Geotecnical Engineering Conference, Cairo

3 ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOFT CLAY CONSOLIDATION USING GEOSYNTHETIC VERTICAL DRAINS WITH SPECIAL REFERENCE TO EMBANKMENTS Buddima Indraratna 1, Colacat Rujikiatkamjorn 2, Iyaturai Satanantan 2, Moamed A. Sain 3 and Hadi Kabbaz 3 ABSTRACT Good quality geologic materials for construction are also becoming scarce. Due to tese reasons and because of te environmental restrictions on certain public works, ground improvement is becoming an essential part of infrastructure development. As a result, Civil Engineers are forced to utilise even te poorest soft clay foundations for buildings, igways and railway tracks. Terefore, te application of prefabricated vertical drains wit preloading as now become common practice and one of te most effective ground improvement tecniques. Te classical solution for vertical drains (single drain analysis) as been well documented in te literature, were tere are many vertical drains, a true 3-D analysis of te site becomes very difficult. Terefore, equivalent 2-D plane strain models ave been employed, using te metods of geometric and permeability matcing concepts. Te equivalent plane strain solution can now be used as a predictive tool wit acceptable accuracy as a result of te significant process tat as been made in te past few years troug rigorous matematical modelling and numerical analyses. In tis paper, te equivalent 2-D plane strain solution is described wic includes te effects of smear zone caused by mandrel driven vertical drains. Te equivalent (transformed) permeability coefficients are incorporated in finite element codes, employing te modified Cam-clay teory. Numerical analysis is conducted to predict te excess pore pressures, lateral and vertical displacements. Two case istories are discussed and analysed, including te sites of Muar clay (Malaysia) and te predictions are compared wit te available field data. Te researc findings verify tat te impact of smear and well resistance can significantly affect soil consolidation, ence, in order to obtain reliable consolidation predictions, tese aspects need to be simulated appropriately in te selected numerical approac. 1 Professor of Civil Engineering, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia 2 PD Students, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia 3 Researc Fellows, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia Correspondence to: Scool of Civil Engineering, Faculty of Engineering, University of Wollongong, Wollongong City, NSW 2522, Australia, indra@uow.edu.au

4 INTRODUCTION Preloading of soft clay over vertical drains is one of te most well known metods to improve te sear strengt of soft soil and to reduce its post-construction settlement. Since permeability of most soft clays is very low, time required to acieve te desired settlement or sear strengt can sometimes be too long to support te need for rapid construction (Jonson, 197 and Indraratna et al., 1992). Using vertical drains, te drainage pat is reduced considerably from te tickness of a soil layer to alf te drain spacing in te orizontal direction (Indraratna et al., 1997). Furtermore, for most soft clay deposits, te permeability in te orizontal direction is muc iger tan tat in te vertical direction; ence, te consolidation process can be accelerated (Jamiolkowski et al., 1983). Tis system as been employed effectively to improve foundation soils for railway embankments, airports and igways (Indraratna and Redana, 2; Li and Rowe, 22). Te equivalent plane strain solution developed by te primary autor and co-workers can be used as a predictive tool wit acceptable accuracy. In te future te teory will be extended to include cyclic loads and cyclic pore pressures as applicable for busy rail tracks. Te performance of various types of vertical drains including sand drains, sand compaction piles, prefabricated vertical drains (geosyntetic) and gravel piles, as been studied in te past tree decades. Sand drains were firstly introduced in practice around 192 s. Te laboratory and field tests of te sand drain systems ave been conducted initially by te California Division of Higways since te 194 s, and Kjellman (1948) introduced te prefabricated band saped drains and cardboard wick drains for ground improvement. Typically, te prefabricated band drains consist of a plastic core wit longitudinal cannel wick, functioning as drain and filter jacket (fibrous material protecting te core). Basically, te dimensions of most vertical drains are in te order of 1 mm widt and 4 mm tickness. Figure 1 illustrates a typical plan of vertical drain system installation and essential instruments required to monitor te performance of soil foundation beneat an eartfill embankment. Before installing te vertical drains, general site preparations including te removal of vegetation and surficial soil, establising site grading and

5 placing a compact sand blanket, are required. Te sand blanket system is employed to expel water away from te drains and to provide a sound-working mat for vertical drain rigs. C L Inclinometer Bencmark and Dummy piezometer Surface settlement plate Sand Blanket Piezometer Sub-surface settlement plate Figure 1: Vertical drain system wit preloading For a vertical drain system incorporating vacuum preloading, te installation of orizontal drains in te transverse and longitudinal directions is required after te installation of te sand blanket system (Cognon et al., 1994). Subsequently, tese drains can be connected to te edge of a periperal Bentonite slurry trenc wic is typically sealed wit an impermeable membrane. Te trences are ten filled wit water to improve te sealing between te membrane and te Bentonite slurry. Finally, te vacuum pumps are connected to te prefabricated discarge module extending from te trences. Te suction ead created by te pump accerelates te excess pore water pressure in te soil moving towards te drains and te surface. Figure 2 sows a typical embankment subjected to vacuum preloading.

6 C L Vacuum Pump Periperal Trenc Impervious Slurry Wall Geomembrane Sand mat Figure 2: Vacuum preloading system Field instrumentation for monitoring and evaluating te performance of embankments is essential to examine and control te geotecnical problems. Performance evaluation of embankements is also important to improve settlement predictions and to provide sound guidelines for future projects. Based on te construction stages, field instrumentation can be divided into two groups (Bo et al., 23). Te first group is used to prevent sudden failures during contruction (e.g. settlement plates, inclinometers and piezometers), wereas te second group is used to record canges in te rate of settlement and excess pore pressure during loading stages (e.g. multilevel settlement guages and piezometers). DEVELOPMENT OF THE THEORY OF CONSOLIDATION WITH VERTICAL DRAINAGE Barron (1948) presented an original compreensive solution to te problem of radial consolidation by drain wells. He studied two extreme cases, namely, (a) free strain and (b) equal strain. Smear and well resistance effects for te case of vertical strain were considered in is solutions. Subsequently, various solutions incorporating different assumptions and boundary conditions were given in Yosikuni and Nakanodo (1974), Holtz et al. (1991) and Hansbo (1979). Baron (1948) sowed tat te average consolidation obtained in bot free strain and equal strain cases are nearly te same,

7 and te solution obtained from te equal strain assumption is simpler tan tat obtained from te free strain (Barron, 1948). Terefore, equal strain is commonly used in most radial drainage-consolidation analyses. Te average orizontal degree of consolidation, vertical drain (Figure 3) can be expressed by: U, of a soil cylinder wit U and T = 8 1 exp µ (1) µ = π n + k / ln ln( s ). + z( l z ) k k k (2) s k q ( k / k )( n / s ) w were, T = time factor, n = ratio d e /d w (d e is te diameter of equivalent soil cylinder = 2R and d w is te diameter of drain = 2r w ), s = ratio d s /d w (d s is te diameter of smear zone = 2r s ), k = orizontal permeability coefficient of soil in te undisturbed zone, k = orizontal permeability coefficient of soil in te smear zone, z = dept, l = equivalent lengt of drain, wic is equal to alf drain lengt for opened end drains or entire drain lengt for closed end drains and q w = well discarge capacity. A simplified form of µ can be alternatively given by: µ = π n + k ln ln( s). + z( l z ) k 75 2 (3) s k q Considering only te effect of smear, Equation 3 becomes: w µ = n + k ln ln( s) 75. (4) s k Considering only te effect of well resistance, Equation 3 becomes: µ ln( n ). + πz( l z ) k 75 2 (5) q w For an ideal drain (i.e. smear and well resistance are ignored), te above parameter becomes:

8 µ = ln( n). 75 (6) r l z k Drain Smear zone k' r w l rs R Figure 3: An axisymmetric soil cylinder wit vertical drain (adapted from Indraratna and Redana, 1997) Recently, Indraratna and Rujikiatkamjorn (24) introduced te analytical solutions of unit cell incorporating vacuum preloading. Te large-scale laboratory results sow tat vacuum pressure varies along te drain lengt. Terefore, te efficiency of vacuum preloading is taken into account in te analytical solution by considering te vacuum pressure variation along te drain boundary (Figure 4). -p C L Soil element k 1 p Drain interface Figure 4: Vacuum pressure distribution along te drain lengt

9 Based on te above distribution (Figure 4), te analytical solution for vertical drain incorporating vacuum preloading can be given by: U and ( ) T p G( n) p = G n 8 o u exp µ u (7) ( ) G n ( + k ) 1 1 = (8) 2 were, p = applied vacuum pressure at te top of te drain, k 1 = ratio between vacuum pressure at te bottom of te drain and vacuum pressure at te top of te drain and u = initial excess pore water pressure. Most recently, te primary autor and is co-workers on an ongoing researc at Wollongong University made an attempt to estimate te extent of smear zone, caused by mandrel installation using te Cylindrical Cavity Expansion teory incorporating te modified Cam-clay model (MCC). Cavity expansion as attracted te attention of many researcers due to its numerous applications in te field of soft clay engineering. Tis tecnique is commonly employed to analyse pile driving, tunnelling and soil testing. Wen a mandrel is driven into soil, it will initially displace a volume of soil equal to te volume of te mandrel. A eave of soil can occur at te soil surface, up to about ten times te radius of te mandrel. At a greater dept, te soil is displaced predominantly outwards in te radial direction. Terefore, te expansion of a cylindrical cavity wit a final radius equal to tat of te mandrel is appropriate to predict te extent of smear zone. After te initial yielding at te cavity wall, a zone of soil extending from te cavity wall to a radial distance (r p ) will become plastic as te cavity pressure continues to increase (Figure 5). For a soil obeying te MCC model, te yielding criterion is given by: ' p c η = Μ 1 (9) ' p

10 were, η = stress ratio q/p (q is te deviatoric stress (σ 1 -σ 3 )/2 and p is te effective mean stress (σ 1 +2σ 3 )/3), M = slope of critical state line projected to q-p plane and p c = effective preconsolidation pressure. Te stress ratio at te elastic-plastic boundary can be found as follows: q q p η p = = = Μ 1 ' OCR (1) ' p p r= r p were, η p = stress ratio at te elastic-plastic boundary, r = distance from central axis of te drain, q p = (σ 1 -σ 3 )/2 at te elastic-plastic boundary and OCR is te isotropic over consolidation ratio, defined by p c ( ' ' p ' p c is te initial preconsolidation pressure and ' p is te initial effective mean stress). Stress ratio at any point can be determined as follows: 2 2 ( a a ) 2( 1+ ν ) κ κλ ln f (, η, OCR) 2 r = η Μ (11) 3 3( 1 2ν ) υ υμ and f ( Μ, OCR) ( Μ + η) ( 1 OCR 1) ( Μ η) ( 1+ OCR 1) ( OCR 1) 1 η, η = ln tan 1 + tan 1 (12) 2 Μ were, a = radius of te cavity, a = initial radius of te cavity, ν = Poisson s ratio, κ = slope of te overconsolidation line, υ = specific volume and Λ = 1 κ λ (λ is te slope of te normal consolidation line). Finally, te corresponding mean effective stress, in terms of deviatoric stress, total stress and excess pore pressure, can be expressed by te following expressions: Λ ' ' OCR p = p 2 (13) 1+ ( η Μ) ' q = η p (14) r p q 2 q p = σ rp + dr (15) 3 3 r r Employing Equations 13-15, te excess pore pressure due to mandrel driving ( u) can be determined by:

11 ' ' ( p p ) ( p ) u = (16) p were, p = initial total mean stress. Te extent of te smear zone can be suggested as te region in wic te excess pore pressure is iger tan te initial overburden ' pressure ( σ ) (Figure 5). Tis is because, in tis region, te soil properties, suc as v permeability and soil anisotropy, are disturbed severely at radial distance ' were u = σ v. Excess pore pressure Vertical drain Smear zone ' u = σ v r p Distance (r ) Figure 5: Smear zone prediction by te Cavity Expansion Teory PLANE STRAIN CONSOLIDATION MODEL AND THE CONVERSION PROCEDURE Most finite element analyses on embankments are conducted based on te plane strain assumption. However, te consolidation around vertical drains is truly axisymmetric. Terefore, to employ a realistic 2-D finite element analysis for vertical drains, te equivalence between te plane strain analysis and axisymmetric analysis needs to be establised. Indraratna and Redana (1997) converted te vertical drain system sown in Figure 6 into an equivalent parallel drain well by adjusting te coefficient of permeability of te soil, and by assuming te plane strain cell to ave a widt of 2B. Te alf widt of te drain b w and alf widt of te smear zone b s may be kept te same as teir axisymmetric radii r w and r s, respectively, wic gives b w = rw and s rs b =.

12 Indraratna & Redana (1997) represented te average degree of consolidation in plane strain condition as follows: U and u 8T = 1 = 1 exp u o µ p (17) k µ p = α + β θ k 2 ( ) + ( )( 2lz z ) (18) were, u = initial excess pore pressure, u = pore pressure at time t (average values) and T = time factor in plane strain. r l z k ks k w Drain Smear zone k k ' k wp l r w rs R b w b s B a) Axisymmetric b) Plane Strain Figure 6: Conversion of an axisymmetric unit cell into plane strain condition (after Redana, 1999)

13 Indraratna & Rujikiatkamjorn (24) extended te analytical solutions of unit cell incorporating vacuum preloading for te plane strain condition, as follows: u u = p u o 2 ( 1 k ) 8T p p ( 1 k ) exp p 1 + µ p u 2 1 (19) were, k and k are te undisturbed orizontal and te corresponding smear zone equivalent permeabilities, respectively. Te geometric parameters α, β and θ (flow term), are given by: 2 2 2b s bs bs α = B B 3B 2 (2a) β = 2 ( ) + 3 ( 3 ) B b b bs b b (2b) s w w s 3B 2 2k bw θ = 1 (2c) k q B B z were, q z = te equivalent plane strain discarge capacity. At a given effective stress level and at eac time step, te average degree of consolidation for bot axisymmetric ( U ) and equivalent plane strain ( U are made equal, ence: ) conditions U = U (21) Combining Equations 17 and 21 wit equation 1 of original Hansbo teory (Hansbo, 1981), te time factor ratio can be represented by te following equation: T T k R 2 = 2 k B µ = P µ (22) By assuming te magnitudes of R and B to be te same, Indraratna and Redana (1997) presented a relationsip between k and k, as follows:

14 k = k 2 k ( ) ( α + β + θ )( 2lz z ) k n k ln + ln. + s k 2 ( s) 75 π ( 2lz z ) k q w (23) If well resistance is ignored in Equation 23 by omitting all terms containing l and z, te influence of smear effect can be modelled by te ratio of te smear zone permeability to te undisturbed permeability, as follows: k k = k k β n ( ) + k ln ln s 75. α s k (24) If smear and well resistance effects are ignored in te above expression, ten te simplified ratio of plane strain to axisymmetric permeability is readily obtained, as proposed by Hird et al. (1992), as follows: k k. 67 = [ ln ( n) 75. ] (25) Te well resistance is derived independently and yields an equivalent plane strain discarge capacity of drains, wic can be determined from te following equation: q z = 2 πb q w (26) For vacuum preloading, te equivalent vacuum pressure in plane strain and axisymmetric are te same. LABORATORY TESTING USING LARGE-SCALE CONSOLIDOMETER At te University of Wollongong, te effectiveness of prefabricated vertical drains as been extensively studied by employing large-scale laboratory consolidation tests (Figure 7). Initially, tis apparatus was developed by Indraratna and Redana (1995,1998) to study te effect of smear due to vertical drain installation including sand drains and prefabricated vertical drains (PVDs). Te internal diameter and te overall eigt of te

15 assembled cell are 45 mm and 1 mm, respectively. Te loading system was applied by an air jack compressor system via a piston. Te settlement was measured by a Linear Variable Differential Transducer (LVDT) placed at te top of tis piston. An array of strain gauge type pore pressure transducers complete wit wiring to supply recommended 1 V DC supply was installed to measure te excess pore water pressures at various points. It was found tat even toug a larger widt of te drain may cause a greater smear zone, for PVDs, te measurements and predictions indicate sligtly increasing settlements due to te increased surface area, facilitating efficient pore water pressure dissipation. In contrast, for sand drains, increasing drain diameter does not necessarily improve pore pressure dissipation. In fact, a greater diameter increases te overall stiffness, especially for compacted sand or gravel, tereby decreasing surface settlement. Figure 8 sows te variation of te ratio of te orizontal to vertical permeabilities (k /k v ) at different consolidation pressures along te radial distance, obtained from large-scale laboratory consolidation. It can be seen tat te average value of k /k v starts to decrease considerably from 1.65 (outside smear zone) to 1.1 (inside smear zone). It implies tat te permeability ratio between undisturbed and smear zone (k /k ) is approximately 1.5 and te extent of smear zone (r s ) is 4-5 times te radius of te vertical drain (r w ). It sould be noted tat k /k ratio in te field can vary from 1.5 to 1, depending on te type of drain and installation procedures (Saye, 23). At present, te apparatus is furter modified by applying a suction pressure at te top of te drain to study te effect of vacuum preloading. Soil unsaturation due to vertical drain installation is also furter investigated by tis apparatus. It is found tat te vacuum pressure application accelerates te consolidation process by increasing te lateral ydraulic gradient, as sown in Figure 9. It is also found tat te occurrence of soil unsaturation at te PVD boundary due to mandrel driving could retard te pore pressure dissipation in te early stage of consolidation process.

16 Figure 7: Scematic of large-scale consolidation apparatus (after Indraratna and Redana, 1995) 2. Horizontal/Vertical permeability ratio drain Smear zone Radial distance, R (mm) Mean Consolidation Pressure: 6.5 kpa 16.5 kpa 32.5 kpa 64.5 kpa kpa 26 kpa Figure 8: Ratio of k /k v along te radial distance from te central drain (after Indraratna and Redana, 1995)

17 Load (kpa) Witout vacuum pressure Wit vacuum pressure 1 kpa (a) (b) Settlement (mm) Time (days) Figure 9: Soil settlement results from large-scale laboratory tests APPLICATION OF NUMERICAL MODELLING IN PRACTICE AND FIELD OBSERVATION Indraratna et al. (1992 and 1994) and Indraratna & Redana (2) made an attempt to analyse te performance of two embankments constructed by te Malaysian Higway Autority at Muar plain, one built to failure wit no drains, and te oter wit prefabricated vertical drains. At tis site, soft clay foundation is mostly marine, lagoonal or deltaic origin tat is caracterised by ig compressibility, very low permeability and low sear strengt. Terefore, te ground improvement tecniques are necessary to prevent excessive and differential settlements in te field. Te sub-soil profiles and corresponding properties are sown in Figure 1. Te subsoil is relatively uniform and consists of top weatered clay crust (2 m dept) underlain by soft to very soft silty clay layers tat extend to 2 m dept. Underneat te soft clay layers, dense clayey silty sand layer can be found at 2-24 m dept. Figure 1 also illustrates te variation of water content and consolidation parameters wit dept. Te unit weigt of soil is between kn/m 3, except te top weatered crust, wic as unit weigt of 17 kn/m 3. As measured by te field sear vane, te undrained sear strengt was

18 minimum at a dept of 3 m (C u 8 kpa), and tis value increases linearly wit dept. Extensive laboratory tests were also conducted prior to te construction of te embankments including oedometer, Unconsolidated Undrained (UU) and Consolidated Undrained (CU) triaxial tests. Te performance of te two embankments constructed on te aforementioned site, is described below Water Content OCR C / 1 + e C / 1+ e c o r o (%) PL LL Description of Soil Weatered Clay Very Soft Silty Clay Dept (m) Soft Silty Clay Organic Clay Medium dense to dense Clayey Silty Sand Figure 1: Variation of sear strengt and consolidation parameters at Muar plain (after Redana, 1999) PERFORMANCE OF TEST EMBANKMENT CONSTRUCTED TO FAILURE ON MUAR CLAY One of te two test embankments at Muar plain was built to failure for te purpose of comparison wit te oter embankment. Te failure was initiated by te development of a quasi slip circle type of rotational failure at a critical eigt of approximately 5.5 m, wit a prominent tension crack propagating vertically troug te crust and te fill (Figure 11). Indraratna et al. (1992) analysed te performance of te embankment using 2D finite element analysis incorporating two different constitutive soil models, namely, te Modified Cam-clay teory using te finite element program CRISP (Woods, 1992) and te yperbolic stress-strain beaviour using te finite element code ISBILD (Ozawa

19 and Duncan, 1973). Te modes of analysis can be divided into two types: undrained and coupled consolidation. For te undrained condition, it is assumed tat te rate of loading is muc faster tan te rate of drainage. Terefore, excess pore pressures do not ave adequate time to dissipate and will build up during loading and te volume cange is zero. For te coupled consolidation analysis, te excess pore pressures are generated simultaneously wit drainage and volume cange (positive or negative) is developed. Total mean stress may also be different during loading. Soil parameters used for te Modified Cam-clay model (MCC) in CRISP program are sown in Table 1, wic also summarises te values of te bulk modulus (K w ), and te coefficient of orizontal and vertical permeabilities (k and k v ). A summary of soil parameters applicable for undrained and drained analyses by ISBILD is given in Table 2. Te in-situ stress conditions are also incorporated in te numerical analyses and are given in Table 3. Due to insufficient expermental data, te soil properties of te topmost crust are assumed to be te same as te properties of te layer just beneat it. For te embankment surcarge (E = 51 kpa, ν =.3 and γ = 2.5 kn/m 3 ), te sear strengt parmeters, obtained from drained triaxial tests, are represented by c = 19 kpa and φ = 26. Instrumentation points Embankment Crust Soft clay Inclinometer +2.5m +.5m Actual slip surface -5.6m Stiff clay Figure 11: Failure mode of embankment and foundation (modified after Brand and Premcitt, 1989)

20 Table 1: Soil parameters used in te Modified Cam-clay model (CRISP) (Source: Indraratna et al.,1992) Dept (m) κ λ M ν e cs K w 1 4 (cm 2 /s) γ (kn/m 3 ) k 1-9 (m/s) k v 1-9 (m/s) Table 2: Soil parameters for yperbolic stress strain model ISBILD (Source: Indraratna et al.,1992) Dept (m) K c u K ur c (kpa) φ γ (kn/m 3 ) (kpa) (degree) Note: K and K ur are modulus number and unloading-reloading modulus number used to evaluate compression and recompression beaviour of soil, respectively. Table 3: In-situ stress conditions (Source: Indraratna et al.,1992) Dept (m) σ' vo (kpa) σ' o (kpa) u (kpa) p c (kpa) Note: σ' o = orizontal in-situ effective stress, σ' vo = vertical in-situ effective stress, u = pore water pressure.

21 Te finite element descritisations applicable for CRISP and ISBILD are illustrated in Figures 12 and 13, respectively. Te rate of embankment construction is assumed to be.4 m per week. At tis site, various instruments were installed including piezometers, inclinometers and settlement plates (Figure 14). Excess pore pressure variations beneat te embankment, lateral and vertical displacements and mobilized sear stress contour at failure were obtained from te two finite element analyses and some of te results obtained will be descirbed below. Figure 15 sows te comparison between te actual and predicted excess pore pressure results from CRISP at locations P2 and P7. It can be seen tat te undrained analysis overpredicts te excess pore pressure, wereas te corresponding predictions from te coupled analysis are always less tan tose from undrained analysis and close to te field results. It is clear tat te coupled consolidation analysis is more realistic, because te consolidation of te soft clay layer can be promoted during construction, due to te permeable sand deposits beneat it. Figure 15 also sows tat te excess pore pressure diminises along te lateral direction because of te decreasing effect of te surcarge. C L Displacement and pore pressure node linear strain triangle element 22.5 m 8 m 2 m 4 m 52 m 64 m 8 m ` Figure 12: Finite element discretisation of embankment and subsoils for CRISP analysis (modified after Indraratna et al., 1992)

22 CL Displacement and pore pressure node linear strain quadrilateral element 22.5 m 8 m 2 m 4 m 52 m 64 m 8 m Figure 13: Finite element discretisation of embankment and subsoils for ISBILD analysis (modified after Indraratna et al., 1992) C L m Settlement plate S1 S2 S3 S4 H5 Heave marker H4 H3 H2 H1 P1 weatered Crust P2 P5 P7 Very Soft Silty Clay P3 P4 Soft Silty Clay Pneumatic piezometer Inclinometer I3 I2 I1 Clayey Silty Sand Figure 14: Cross section of Muar test embankment indicating key instruments (modified after Ratnayake, 1991)

23 Excess pore pressure (m) Measured Undrained Coupled P2 Excess pore pressure (m) Measured Undrained Coupled P Embankment Heigt (m) Embankment Heigt (m) Figure 15: Variation of excess pore pressure wit fill tickness (CRISP) (original data from Indraratna et al., 1992) In Figure 16, te comparisons between te predicted and measured surface settlement for various fill eigts (2-5 m) are sown. Te predictions were obtained from te modified Cam-clay (CRISP) and yperbolic (ISBILD) models At te initial fill eigt (less tan 2 m), te undrained prediction by ISBILD agrees well wit te field value, except for te area near te centreline of te embankment, wereas oter predictions generally overestimate te vertical settlement. Wen te fill eigt is more tan 2 m, te maximum measured vertical settlement is observed at a lateral distance 8-1 m away from te centreline, rater tan at te centreline. Te predictions from te coupled consolidation analysis yield better agreement wit te measurements at a greater eigt (3-4 m, Figures 16b and 16c). At te failure eigt (Figure 16d), te undrained analysis using te yperbolic stress-strain model (ISBILD) is more appropriate and gives better agreement wit te field measurements.

24 Surface settlement (m) Heigt of embankment = 2m Measured Undrained (CRISP) Coupled (CRISP) Undrained (ISBILD) Coupled (ISBILD). Surface settlement (m) Heigt of embankment = 3m Measured Undrained (CRISP) Coupled (CRISP) Undrained (ISBILD) Coupled (ISBILD) Distance from centreline(m) Distance from centreline(m) (a) (b) Surface settlement (m) Heigt of embankment = 4m Measured Undrained (CRISP) Coupled (CRISP) Undrained (ISBILD) Coupled (ISBILD) Surface settlement (m) Heigt of embankment = 5m Measured Undrained (CRISP) Coupled (CRISP) Undrained (ISBLD) Coupled (ISBLD) Distance from centreline(m) Distance from centreline(m) (c) (d) Figure 16: Surface settlement profiles for various fill eigts (original data from Indraratna et al., 1992) Figure 17 presents te variation of lateral displacements for location I3 for bot te MCC model (CRISP) and te yperbolic stress-strain model (ISBILD) at te critical eigt (5.5 m). As expected, te maximum lateral displacement is in te upper very soft clay layer at a dept of 5 m below te ground surface. Te realistic predictions from te Modified Cam-clay can be obtained in te upper soft clay layer, wereas tey deviate from te field beaviour at greater depts. Te reason for tis discrepency may be attributed to te accuracy of te soil parameters used and te simulation of plane strain condition.

25 Embankment toe Lateral Displacement (m) Dept (m) Measured. Undrained (CRISP) Coupled (CRISP) Undrained (ISBLD) Coupled (ISBLD) Figure 17: Lateral displacement profile at failure (modified after Indraratna et al., 1992) Te zones of yielding and potential failure surface are interpreted based on te boundaries of yielded zone and maximum displacement vectors using te coupled consolidation from CRISP. Te predicted sear band based on te maximum incremental displacement is sown in Figure 18. Te boundaries of yielded zone approacing te critical state are sown in Figure 19, were eac contour indicates te current field eigt. Te yielded zone can be found close to te bottom of te soft clay layer and subsequently develops to te centreline of te embankement. It verifies tat te actual failure surface is witin te predicted sear band. C L Tension Crack Heavily compacted lateritic fill 5.5 m Predicted sear band Weatered crust Very soft clay 2 m 8.5 m Soft clay 18.5 m Stiff sandy clay 2 m 4 m 6 m 22.5 m 8 m Figure 18: Maximum incremental development of failure (modified after Indraratna et al., 1992)

26 C L 5.5 m Actual failure surface Predicted sear band Weatered crust 2 m Very soft clay m Soft clay 18.5 m Stiff sandy clay 2 m 4 m 6 m 22.5 m 8 m Figure 19: Boundary zones approacing critical state wit increasing fill tickness (CRISP) (modified after Indraratna et al., 1992) PERFORMANCE OF TEST EMBANKMENT STABILISED WITH VERTICAL DRAINS ON SOFT CLAY Indraratna et al. (1994) and Indraratna & Redana (2) investigated te effect of ground improvement by preloading over vertical drains at a site located on te Muar plain, Malaysia. Te plane strain analysis incorporating te MCC model considering only te coupled consolidation analysis was employed in te finite element code CRISP. Figure 2 sows te cross section of te embankment, togeter wit te subsoil profile and PVDs installed in a triangular pattern at spacing of 1.3 m. In tis analysis, te soil foundation was descritised using linear strain quadrilateral (LSQ) elements (Figure 21). Te vertical drains were modelled by using a relatively fine mes to prevent unfavourable aspect ratio of te mes. Table 4 gives details of te drain parmeters and Table 5 summarises te Camclay parameters for Muar clay subsoils used in CRISP. Te relevent soil properties were obtained from CU triaxial tests (Ratnayake, 1991). Based on te matcing procedure, expalined earlier and proposed by Indraratna and Redana (1995), te measured orizontal and vertical permeabilies at te in-situ soil condition, and te equivalent calculated plane strain values, are sown in Table 6 (Equations 23-25).

27 C L Loading stages 43 m 4.74 m 3.5 m m 6.7 m P1 P2 weatered clay very soft silty clay 11.2 m P3 soft silty clay Inclinometer P1 P3 = Piezometers Vertical drain at 1.3 m (triangular medium dense to dense clayey silty sand Figure 2: Cross section of embankment wit soil profile at Muar clay, Malaysia (Indraratna and Redana, 2) Table 4: Vertical drain parameters of te vertical drain system of Muar embankment Vertical drain parameter Value Spacing, d (m) 1.3 Equivalent drain spacing, d e (m) Lengt (m) 18 Equivalent drain diameter, d w (m).7 s = d s /d w 5.7 Table 5: Modified Cam-clay parameters used in CRISP (Source: Indraratna and Redana, 2) Dept (m) λ κ e cs M ν γ (kn/m 3 ) Note: * Te values of λ tabulated are for Stage 2 loading. At Stage 1 of construction due to te lower applied load λ values were taken to be λ oc =.16.

28 Drain-soil Interface Piezometer k / k v = 1. 8 Drain Displacement node Pore pressure node 4.74 m Fill Drain Smear zone k / k = 1. v Inclinometer Smear zone k / k = 1. v m 1.5 m 5.5 m 8 m Drains; S=1.3 m m 43 m 18 m 13 m Figure 21: Finite element mes descretisation of te embankment for plane strain analysis, Muar clay, Malaysia (Indraratna and Redana, 2) Table 6: Permebility coefficients used in te finite element analysis (Source: Indraratna and Redana, 2) Dept (m) k 1-9 k v 1-9 k 1-9 k 1-9 (m/s) (m/s) (m/s) (m/s) Te embankment load was applied in two stages. During Stage 1 of construction, te embankment was raised to a eigt of 2.57 m in 14 days. After rest period of 15 days, additional fill compacted to unit weigt of 2.5 kn/m 3 was placed (Stage 2), until te embankment reaced a eigt of 4.74 m in 24 days. Te settlements and excess pore water pressures at te centreline were monitored for more tan a year.

29 Te comparisons between te actual and predicted settlements at te ground surface and at a dept of 5.5 m, are sown in Figure 22. It can be seen tat, for te surface settlement, te predicted results wit smear effect and well resistance quite agree well wit te measured value (Figure 22a). It can also be seen tat te inclusion of smear effect gives more accurate predictions. At 5.5 m dept, te predictions including te smear effect and well resistance, underestimate sligtly te settlements beyond 2 days, wile te results based on no smear condition overpredict te settlements (Figure 22b). Te predicted and measured excess pore water pressures at te centreline and a dept of 11.2 m are sown in Figure 23. It can be noticed tat te inclusion of smear zone predicts accurately te excess pore pressure up to Stage 2, wereas te inclusion of well resistance does not lead to significant improvement. Tis implies tat te well resistance is less important for tese PVDs tan te smear effect. As expected, te perfect drain predictions underestimate te actual excess pore pressures. An inclinometer was installed at 23 m away from te centreline of te embankment. Te measured and predicted lateral displacements at 294 days after te beginning of te embankment construction are sown in Figure 24. It can be seen tat te predicted lateral displacements agree well wit te measured values wen te effects of bot smear and well resistance were included. Settlement (cm) No smear and well resistance Field measurements Finite element analysis: Perfect drain (no smear) Smear only Smear and well resistance (a) (a) Time (days) Settlement (cm) 1 2 Field measurements Finite element analysis: Perfect drain (no smear) Smear only Smear and well resistance (b) (b) No smear and well resistance Time (days) Figure 22: Total settlements at: (a) Ground surface and (b) a dept of 5.5 m below ground level, along embankment centreline, Muar clay (modified after Indraratna and Redana, 2)

30 Excess pore pressure (kpa) Piezometer P6 Field measurements Finite element analysis: Perfect drain (no smear) Wit smear Smear and well resistance No drains No smear and well resistance Time (days) Figure 23: Variation of excess pore water pressures at embankment centreline for piezometer P6 at 11.2 m below te ground level (Indraratna and Redana, 2) (b) Dept (m) No drains (Unstabilised foundation) Field Measurement: monts days Prediction FEM: Perfect drains (no smear) Smear only Smear and well resistance Lateral displacement (mm) Figure 24: Lateral displacement profiles at 23 m away from centreline of embankments after 294 days (Indraratna and Redana, 2) Te performance of te embankments stabilised wit and witout vertical drains was compared based on normalised deformation, as sown in Table 7. Te ratios of te maximum lateral displacement to fill eigt (β 1 ) and te maximum settlement to fill

31 eigt (β 2 ) were considered as stability indicators. In comparison wit te unstabilised embankment constructed to failure discussed earlier (Indraratna et al., 1992), te stabilised foundation is caracterised by considerably smaller values of β 1, igligting te obvious implication on stability. Te normalised settlement (β 2 ) on its own does not seem to be a convincing indicator of instability. Table 7: Effect of ground improvement on normalised deformation factors (Indraratna et al., 1997) Ground improvement sceme β 1 β 2 Embankment rapidly constructed to failure on untreated foundation ( = 5.5m) Prefabricated vertical band drains in triangular pattern at 1.3 m spacing ( = 4.75 m) CONCLUSIONS Preloading tecniques wit vertical drains ave been used widely to reduce post construction settlement and to accelerate te consolidation process in tick soft soil deposits. However, soil unsaturation at te vertical drain boundary due to mandrel driving could delay te excess pore pressure dissipation in te early stage of consolidation process. In addition, te rate of settlements and pore pressures dissipation associated wit vertical drains are difficult to predict accurately. Tis difficulty may be attributed to te complexity of evaluating te correct magnitudes of soil parameters inside and outside te smear zone as well as te unsaturation zone at te soil-drain interface. Terefore, it is crucial to use appropriate laboratory tecniques to measure tese parameters, preferably employing te realistic stress pats. Using a large-scale consolidometer, it was found tat te smear zone radius is 4-5 times te radius of te vertical drain and te soil permeability in te smear zone is iger tan tat in te undisturbed zone by times. Numerical finite element metods ave been increasingly employed to predict soil consolidation beaviour. In te field, were many PVDs are installed, true 3D finite

32 element analysis is difficult and te equivalent 2D plane strain FEM analysis is most convenient given te computational efficiency. However, te classical axisymmetric solutions cannot be used directly in any plane strain finite element analysis witout reasonable simplification. Terefore, te development of equivalent plane strain model tat can provide good matc wit te measured data is necessary. In addition, te accurate predictions of settlements, excess pore water pressures dissipations and lateral movements involve careful evaluation of soil parameters associated wit actual stress pat during loading stages. In tis study, te performance of soft clay subjected to preloading was predicted confidently by te coupled consolidation model in 2D FEM. Te prediction from te undrained analysis gave unreliable results except at te centreline of te embankment. Te finite element analysis also displayed tat te correct mode of failure by considering te incremental displacement vectors and mobilised sear stress contours, can be predicted. It was revealed tat te inclusion of smear effect is more important in predicting te settlements tan te well resistance. Based on te normalised deformation analysis, foundations stabilised by te PVDs minimises lateral movement, tereby increasing te stability of te foundations. ACKNOWLEDGEMENTS Te autors wis to tank te CRC for Railway Engineering and Tecnologies (Australia) for its continuous support and te Malaysian Higway Autority for providing te trial embankments data. Te autors also express teir appreciation to David Cristie (RailCorp, Sydney) for is continuous assistance and advice. In addition, assistance of Prof. A.S. Balasubramaniam (formerly at Asian Institute of Tecnology, Bangkok, Tailand) is gratefully appreciated. A number of past researc students of Prof. Indraratna, namely, Balacandran, Ratnayake, Redana and Bamunawita ave also contributed to te contents of tis keynote paper troug teir researc work.

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