International Conference on GEOTECHNIQUES FOR INFRASTRUCTURE PROJECTS 27th& 28th February 2017, Thiruvananthapuram
Method for estimation of Deformation Modulus of Granular Pile based on Top Settlements of Granular Piles with different (L/d) Ratios Kota Vijay Kiran
Madhav Madhira
Department of Engineering C.V.R College of Engineering Hyderabad, India. E-mail:
[email protected]
Department of Civil Engineering JNT University & IIT Hyderabad Hyderabad, India. E-mail:
[email protected]
Abstract—The modulus of deformation is among the parameters that best represent the mechanical behavior of granular pile (GP) as it defines the settlement of GP reinforced soft ground. Estimating the deformation modulus of granular pile is a challenging task and no method for estimating it in-situ is currently available. The paper presents a novel method based on settlements measured in field on two different granular piles for different L/d ratios. The method was successfully applied to a selected case study and the limitations of the proposed method are highlighted. Keywords—Granular piles, Settlement ratio, Deformation modulus, Stiffness factor, L/d ratio.
I. INTRODUCTION Reducing long-term settlement of infrastructure and providing cost-effective foundations with sufficient load-bearing capacities are national priorities for infrastructure development in most countries. Vast areas, predominantly along the coast, are covered with dense soft marine clay deposits having very low shear strength and high compressibility. Foundations on these soft soils can cause excessive settlement, initiating failure of the infrastructure if proper ground improvement is not carried out. Therefore, it is imperative to apply adequate ground improvement techniques to the existing soft soils before construction to prevent unacceptable excessive and differential settlement and increase the bearing capacity of the foundations. Among various methods of soft soil improvement, reinforcing the ground by installing stone columns is one of the wellestablished and effective techniques for light to medium heavy structures such as liquid storage tanks, bridge abutments, road/rail embankments, factories, etc. that can tolerate some settlement.
Granular piles transform the original ground into composite mass of densified/reinforced medium resulting in overall increase in shear strength of in situ soil and improved loaddeformation behavior of the foundation – ground system. (Greenwood, 1970, Madhav et al., 2014) A number of theories and correlations have been developed to estimate the bearing capacity and settlement of granular pile reinforced ground considering different mechanisms. Hughes & Withers (1974)and Madhav et al. (1979) established that granular pile fails in bulging and the ultimate capacity of the granular pile is governed the passive lateral resistance offered by the surrounding soils against bulging. Madhav &Vitkar (1978) presented a solution for the ultimate bearing capacity of granular trench reinforced ground considering general shear failure mechanism. Alamgir et al. (1996) established a simple theoretical approach to predict the deformation behavior of soft ground reinforced by granular piles. Poulos and Mattes (1969) describe research into the settlement of single compressible pile. The influence of the compressibility of the pile on the load transfer along and the settlement of the pile are examined. Priebe (1995) estimated the settlement improvement factor, defined as the ratio of the settlements of unimproved to improved ground, of a rigid foundation supported by infinite number of granular piles as a function of area replacement ratio, angle of shearing resistance of granular pile material, ratio of constrained moduli of the surrounding soils and the granular pile. Scott (1981)presented solutions to estimate settlement of a compressible pile. Seo and Prezzi (2007)present a new settlement analysis method for axially loaded piles in multilayered soil using variational principles. Six et al. (2012) investigate elasto-plastic behavior of granular pile foundation by numerical analysis.
Kota Vijay Kiran & Madhav Madhira A significant parameter in predicting the settlement of GP reinforced ground is the deformation modulus, Egp of GP or a relative stiffness factor, K=Egp/Es, defined as the ratio of deformation moduli of GP and of the soft ground, Es. The relative granular pile stiffness factor is often assumed, estimated indirectly from literature or is based on the experience of the geotechnical engineer. This paper outlines a method for estimating the relative stiffness factor, K, and consequently of deformation moduli (E gp) of granular pile based on analysis of settlements of granular pile along its depth. The efficacy of the method is established based on measured settlements available.
Modulus of granular pile cannot be determined from the above mentioned equation of (Poulos & Davis (1980)) as two unknowns, modulus of deformation of soil, Es, and relative stiffness factor, K=Egp/Es are involved. Hence, a method involving ratio of settlements is proposed to estimate the relative stiffness factor, K.
II. SETTLEMENT OF SINGLE GRANULAR PILE A single GP of diameter, d, and length, L, installed in a layer of finite thickness, h, (Fig. 1) with load, P, is considered. Moduli of in-situ soft soil and of granular pile are Es and Egp respectively. A relative stiffness or modular ratio, K, is defined as the ratio of the two moduli as E gp/Es. Settlement profile of single granular pile is estimated using the approach suggested by Seo and Prezzi (2007) for L/d ratios of 5 to 15, relative stiffness, K of 10 to 100 of granular pile, and thickness ratios h/L of 1 (end bearing GP) to 4 (floating GP). ALPAXL (Seo & Prezzi (2007)), a tool, for the assessment of the loadsettlement response of an axially loaded pile, is based on solution using built-in functions (details can be found in the original paper). The soil was assumed to behave as a linear elastic material. The governing differential equations were derived based on energy principles and calculus of variations. The method uses envelopes of unit load transfer curve that describes the axial load transfer mechanism of a single compressible pile embedded in soil. Top displacement of granular pile is also estimated from Poulos and Davis (1980) in terms of the settlement of an incompressible pile in a half-space, with correction factors for the effects of pile compressibility, length to diameter ratio, L/d, finite thickness of compressible layer, relative stiffness of base layer and Poisson’s ratio.
Fig. 1.Definition sketch of granular pile-soft ground system
III. VALIDATION The results from the present study based on Seo and Prezzi’s approach compare (Fig. 2) well with those of Poulos and Davis (1980); and Scott (1981) in terms of normalized pile head stiffness, KN, (KN = Qt/(wtEgpd)), where wt = settlement at the pile head, as a function of normalized pile length (L/d) for an end-bearing pile. The pile-soil modulus ratio Egp/Gs is 3000 and Poisson’s ratio, νs, of soil is 0.5.
A. Floating granular pile: Settlement, ρ, is 𝑃𝐼
ρ=𝐸𝑑
(1)
𝑠
where I = I0RkRhRν, P = applied axial load, I0 = settlement influence factor for incompressible pile in semi-infinite mass for νs= 0.5, Rk = correction factor for pile compressibility, K = Egp/Es, Rh = correction factor for relative thickness, h/L of finite layer and Rν = correction for Poisson’s ratio, νs B. Granular Pile bearing on stiff bearing stratum with deformation modulus, Eb 𝑃𝐼
ρ=𝐸𝑑
(2)
𝑠
where I = I0.Rk.Rb.Rν, with Rb = correction factor for relative stiffness of the base layer, Eb/Es, of bearing stratum. Values of I0, Rk, Rh, Rb and Rv are taken from Poulos & Davis (1980).
Fig. 2.Comparison of Results - Normalized stiffness vs. Normalized length
Kota Vijay Kiran & Madhav Madhira
Fig. 3. Comparison of Settlement influence factors for compressible pile
Fig. 4. Settlement ratio vs. stiffness factor
Settlement influence coefficient, I, from the present approach compares well (Fig. 3) with that of Mattes and Poulos (1969) for compressible pile, the curves straddling on either side with differences less than 5%. Thus, the results based on Seo and Prezzi (2007) agree well with those from the continuum approach. IV. METHODOLOGY A. Settlement ratio (Theoretical) The top settlements of granular piles are estimated theoretically using Eqs. (1) or (2) or by numerical analysis. The settlement ratio, Sr, defined as the ratio of settlement of granular pile with (L/d)1 to that for GP with (L/d)2 as 𝐿 𝑑 1 𝐿 𝑇𝑜𝑝𝑆𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓𝐺𝑃𝑜𝑓( ) 𝑑 2
𝑇𝑜𝑝𝑆𝑒𝑡𝑡𝑙𝑒𝑚𝑒𝑛𝑡𝑜𝑓𝐺𝑃𝑜𝑓( )
Sr =
=
(𝑆𝑜 )1 (𝑆0 )2
(3)
Fig. 5. Schematic of Granular Piles with different (L/d) ratios
C. Estimation of Deformation modulus The settlement ratios calculated for a range of K, plotted in Fig. 4 against pile stiffness factor, K, as a function of Length ratio, (Lr = (L/d)1 / (L/d)2) as illustrated. Sr decreases with increase in relative pile stiffness, K. Thus if two GP with different L/d ratios are tested, top displacements measured, their ratio, Sr, can be used to estimate the relative pile stiffness by interpolation for Fig. 4. B. Field Settlement Ratio Granular piles with two different L/d ratios [(L/d) 1 and (L/d)2] are tested as illustrated in Figure 5. The field settlement ratio, Sr is estimated at a given stress or load level using Eq. (3).
From the value of K estimated, the deformation modulus of GP is determined as the product of relative pile stiffness factor K and deformation modulus of in situ soil, as
Egp= K.Es
(4)
The implication is that, the above expression holds good for homogenous soil with constant Es, along the depth. However, in case the deposit is weighted average of deformation moduli for different soil layers is then adopted.
Kota Vijay Kiran & Madhav Madhira V. APPLICATION To illustrate the efficacy of the method developed it is applied to few load test results of granular piles constructed in soft ground. The test data for the analysis is acquired from Keller Ground Engineering India Pvt. Ltd. Load tests were conducted to assess the load carrying capacity of the isolated vibro-stone columns installed for full and for partial depths in the soft strata. A. Soil Profile The site was near Navi Mumbai, India, where ground improvement works were carried out. The subsoil is divided into four horizons as presented in Table I. The top layer is filled-up soil of thickness 1.0m with gravel as major constituent followed by Brownish soil with pebbles of thickness 2.0m having an SPT N value of 7, followed by Grayish marine clay of thickness 11.0 m with SPT N in the range of 3 to 8, which in turn overlies a stiff clay layer or in some instance by weathered rock. TABLE I.
Fig. 6 Schematic diagram of the test setup for stone column installed up to soft soil (Depth of installation 6m)
SOIL PROFILE OF THE SITE IN NAVI MUMBAI, FROM KELLER
Depth (m) Soil classification
SPT N
1.0
Fill (Gravel)
0
1.0
2.0
Brownish soil with pebbles
1.0
3.0
12.0
Grayish Marine Clay
3.0
12.0
18.0
Weathered Rock/Stiff Clay Layer
12.0
From
To
0
B. Installation of Vibro Stone Columns Granular Piles of diameter 0.9m were installed up to depths of 6.0 m and 12.0 m. Details of both the GPs and test set ups are presented in Figs. 6 and 7. C. Summary & Analysis of Results 1) Vibro Stone Column in Floating condition The floating stone column of length to diameter ratio 6.67, was subjected to a maximum load of 312kN and the corresponding settlement observed was 26 mm. Ultimate load of 165kN was obtained from the load-settlement plot. The safe load is 110kN with a factor of safety of 1.5. The settlement at 100kN load is 4.8 mm. 2) Vibro Stone Column in End Bearing condition Vibro-Stone Column having L/d ratio 13.34 was installed up to stiff clay layer (End bearing GP). The GP was subjected to a maximum load of 380kN and the corresponding settlement was 80 mm. The ultimate load was estimated to be 250kN and the corresponding settlement was 10.0 mm. The settlement at 100kN load is 4.2 mm. The safe load is 167kN with a factor of safety of 1.5.
Fig. 7 Schematic diagram of the test setup for stone column installed up to stiff clay layer (Depth of installation 12m)
The load-test results for both floating and end-bearing granular piles are tabulated in Tables II and III respectively. The settlement ratios, Sr, are calculated from the top settlements conforming to load up to 100kN. TABLE II.
PLATE LOAD TEST DATA FOR 6.0 M STONE COLUMN
Number of
Pressure on
Sl.
divisions on
the test
No
the pressure
plate,
gauge
kg/sq.cm
0 5.9 7.5 11.8 17.5 23.5
0 0.78 1.0 1.56 2.34 3.12
1 2 3 4 5 6
Load, kN
Duratio
Average
n of
settleme
loading,
nt, mm
minutes 0 78 100 156 234 312
0 300 316 360 480 960
0 3.0 4.8 9.3 15.4 26.0
Kota Vijay Kiran & Madhav Madhira
(D) 75 KN
TABLE III. PLATE LOAD TEST DATA FOR 12.0 M LONG STONE COLUMN Number of Sl.
divisions
Pressure
No
on the
on the test
1 2 3 4 5 6 7 8 9 10 11 12
Load, kN
Duration
Average
of
Settlement, mm
pressure
plate,
loading,
gauge
kg/sq.cm
minutes
0 3.0 4.0 7.0 10.0 13.0 17.0 13.0 10.0 7.0 3.0 0
0 0.76 1.00 1.52 2.28 3.04 3.80 3.04 2.28 1.52 0.76 0
0 76 100 152 228 304 380 304 228 152 76 0
K 10 25 50 100
L=6m 5.82 4.25 3.47 2.97
K 10 25 50 100
L=6m 7.75 5.67 4.63 3.97
L=12m 5.71 3.89 2.84 2.06
Sr 0.98 0.91 0.82 0.69
L=12m 7.61 5.19 3.79 2.75
Sr 0.98 0.91 0.82 0.69
(E) 100 KN
0 300 450 780 660 1620 3300 61 61 61 61 391
0 2.8 4.2 10.3 22.4 45.3 88.9 88.9 88.6 87.7 85.8 77.6
The field settlement ratio, Sr, for 6 m and 12 m long stone 4.2 columns at 100 kN load is, (Sr) = = 0.88. Ratio of L/ds of 4.8 the two GPs piles (Lr) is 2. The settlement ratio and the length ratio corresponding to in situ conditions are utilized in estimating K using the method of Seo and Prezzi. The screenshots of spread sheet program are presented in Figs. 8(a) & (b) indicating the input parameters of soil profile for floating and end-bearing piles respectively. Table IV (A-E) presents the settlement ratios estimated for loads 10-100kN. It can be observed from the Tables IV (A-E) that for a constant K, the settlement ratio remains unchanged or has minimal variation with increasing load.
Settlement ratio from field data, KField = 0.88 is interpolated with the settlement ratio values analyzed for different pile stiffnesses at loads of 10, 25, 50, 75 and 100kN. The relative stiffness factors, K, estimated for loads of 10, 25, 50, 75 and 100 kN are K = 33, 32.9, 33.2, 32.9, 32.9 respectively. Thus, the average relative pile stiffness factor, K attained is 33.0. The deformation modulus of in-situ soil of value 5.5 MPa was estimated based on the empirical relation (Bowles (1988)) from average SPT N for the soil profile given in Table I. The deformation modulus of the granular pile, may therefore be calculated as Egp= K.Es (where, Es =5.5 MPa) Egp = 33 x 5.5 = 182 MPa. where Egp = Deformation modulus of granular pile; E s = Deformation modulus of surrounding soil, and K = Relative pile stiffness factor
TABLE IV. ESTIMATED SETTLEMENTS FOR STONE COLUMN USING SEO AND PREZZI METHOD (A) 10 KN K 10 25 50 100
L=6m 0.78 0.57 0.46 0.4
L=12m 0.76 0.52 0.38 0.27
Sr 0.97 0.91 0.82 0.67 (a) For 6m Floating Pile
(B) 25 KN K 10 25 50 100
L=6m 1.94 1.42 1.16 0.99
L=12m 1.9 1.3 0.95 0.69
Sr 0.97 0.91 0.82 0.69
L=12m 3.81 2.59 1.9 1.37
Sr 0.98 0.91 0.82 0.69
(C) 50 KN K 10 25 50 100
L=6m 3.88 2.83 2.31 1.98
(b) For 12m End bearing Pile Fig. 8 Screen-shots of ALPAXL spread sheet program
Kota Vijay Kiran & Madhav Madhira VI. CONCLUSIONS A new method for the estimation of relative granular pile-soil stiffness parameter and the modulus of granular pile is proposed based on load tests on two granular piles of different L/d ratios. The method is illustrated by application to an actual case study.
Acknowledgment The authors wish to express their appreciation to Keller Ground Engineering India Pvt. Ltd. for providing load test results and geotechnical profile of test site.
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