Predicting bending failure of CDM columns under embankment loading

Computers and Geotechnics 91 (2017) 169–178

Contents lists available at ScienceDirect

Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo

Research Paper

Predicting bending failure of CDM columns under embankment loading Jin-chun Chai a,⇑, Sailesh Shrestha b,⇑, Takenori Hino b, Takemasa Uchikoshi c a

Graduate School of Science and Technology, Saga University, Saga, Japan Institute of Lowland and Marine Research, Saga University, Saga, Japan c JIP Techno Science Corporation, Tokyo, Japan b

a r t i c l e

i n f o

Article history: Received 29 January 2017 Received in revised form 15 July 2017 Accepted 21 July 2017

Keywords: CDM columns Bending moment Soft soils Finite element analysis

a b s t r a c t The mechanism of bending failure and the magnitude of the bending moment in a column formed by cement deep mixing (CDM) under an embankment load were investigated by a series of threedimensional (3D) finite element analyses. Based on the numerical results, a design method to consider the bending failure of the CDM column has been established. The usefulness of the proposed methods was verified using the results of two centrifuge model tests of the embankments on the CDM column improved soft model ground model reported in the literature, and the columns had tensile cracks or showed complete failure. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Cement deep mixing (CDM) is a process that normally forms soil-cement columns in the ground and is an effective and economic method to improve soft ground [1–3]. Both the dry mixing (cement powder) and wet mixing (cement slurry) can be used to form the soil-cement columns. The wet mixing under a lower pressure is called slurry double mixing (SDM) [4], and under a higher pressure, it is called jet grouting [5–7]. Current design methodologies for embankments on CDM columns consider only improving the subsoil bearing capacity of the ground and the safety factor against slip circle failure (Fig. 1). However, there are reported results of centrifuge model tests indicating that the bending failure of the columns is an important failure mechanism [8–12]. Fig. 2 shows an example of bending failure of CDM columns from the centrifuge model test by Kitazume and Maruyama [10]. The bending failure of the CDM columns under an embankment load has also been reported by other researchers using numerical analyses [13–17]. The only design method available to consider the bending failure of CDM columns under an embankment loading is that proposed by Kitazume and Maruyama [10]. The method considers the situation where CDM columns are installed only under the toe and a portion of the slope range of an embankment, and assumes that the earth pressure from the centre of an embankment to the block ⇑ Corresponding author. E-mail addresses: [email protected] (J.-c. Chai), [email protected] (S. Shrestha), [email protected] (T. Hino). http://dx.doi.org/10.1016/j.compgeo.2017.07.015 0266-352X/Ó 2017 Elsevier Ltd. All rights reserved.

with the CDM columns is in an active state, and the earth pressure from the surrounding soil outside the toe of the embankment to the block with the CDM columns is in a passive state. For a real field case, neither active nor passive earth pressure can be mobilized before the bending failure of a column. Goh et al. [18] proposed a method to estimate the maximum bending moment of a single pile/column located under the toe of the embankment, which cannot be directly applied for group pile/column cases. Therefore, there is no current rational and practical design method to consider the bending failure of CDM columns under an embankment load. In this paper, a series of 3D finite element analyses were first conducted to investigate the factors affecting the bending failure of the end bearing CDM columns under an embankment load using a verified numerical procedure. Then, based on the results of the numerical investigation, a design method has been proposed to predict the maximum bending moment in the CDM columns under the toe of the embankment. Finally, the usefulness of the design method was verified with the results of two centrifuge model tests reported in the literature.

2. Numerical investigation 2.1. Numerical modelling The numerical investigation was conducted with assumed plane strain type three-dimensional (3D), full-scale embankments. The deformation boundary conditions adopted were plane strain,

170

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

Fig. 1. Slip circle failure of an embankment on the CDM column improved deposit.

had an overall length of 80 m, a width that was 3 times the spacing between CDM columns and a vertical thickness of 35 m from the ground surface. Even though real CDM columns are cylindrical, a square cross-section was used to model the CDM columns to simplify the meshing process. The side length of the cross-section of the square column was determined under an equal bending stiffness condition (EI, E is Young’s modulus and I is the moment of inertia of the cross-sectional area of a column). Referencing CDM columns constructed in Saga, Japan, a diameter of 1.2 m was adopted as a basic case and the corresponding side length of a square section was 1.05 m. The boundary conditions at the left and the right (x direction) and the front and the back (y direction) boundaries vertical displacement was allowed, while the horizontal displacement was fixed. At the bottom boundary both the horizontal and vertical displacements were fixed. Both the ground surface and the bottom boundaries (sand layer) were defined as permeable and other boundaries were defined as impermeable. Ten-node tetrahedron elements with excess pore water pressure degrees of freedom at all nodes were used to represent the foundation soil while similar elements without excess pore water pressure degrees of freedom were used to represent the embankment. For the adopted model, the total number of nodes (vertex plus side nodes) was approximately 182,000, and the total number of elements was approximately 127,000. The Plaxis 3D (2013 version) program was used for conducting the simulation. The detailed geometry of the assumed basic case is shown in Fig. 4. The embankment height was 6.0 m, with a side slope of 1:1.8 (V:H), and the thickness of soft clay layer was 10.0 m. The area improvement ratio (a) of the CDM columns was 30%. For the columns arranged in a square pattern, a is defined as [19]:

a¼ Fig. 2. Centrifuge test results of the bending failure of the model soil-cement columns [10].

but 3 rows of CDM columns were modelled explicitly, i.e., in the model, CDM columns interact with the surrounding soil in a 3D manner. The adopted model is shown in Fig. 3. The modelled area

pD2 4S2

ð1Þ

where D is the diameter of the column and S is the centre-to-centre spacing between the columns. The soft clay was modelled using the Soft Soil Model (SSM) [20], and the embankment and the sand layer were modelled with the linear elastic model obeying the Mohr-Coulomb failure criterion. The CDM columns were treated as a linear elastic material. The

Fig. 3. Plain strain type 3D model of an embankment on the CDM column improved subsoil deposit.

171

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

Fig. 4. Cross-sectional and plan view of the assumed basic case.

stage construction procedure was used to simulate the embankment loading in 12 different phases, and each phase was loaded with a fill thickness of 0.5 m. In the simulation, each phase had a time period of 5 days. The load was increased linearly with time, and the consolidation was simulated simultaneously. After the embankment was constructed, the consolidation was simulated for a period of an additional year. For all cases, the primary consolidation was almost finished one year after the end of the embankment construction. The coupled consolidation analysis with the updated nodal coordinate option was adopted.

The suitability of the numerical modelling procedure and of adopted soil models was verified by simulating a test embankment on a CDM column to improve soft clayey subsoil in Saga, Japan [21] and some laboratory centrifuge model tests reported in the literature [22]. Since this study is focused on the bending deformation of the columns, an example comparison of the measured and simulated profiles of the lateral displacements of a column under the toe of the test embankment reported by Chai et al. [21] is given in Fig. 5. The adopted values of the model parameters for the basic case are listed in Table 1. The values were determined in reference to the soil properties at a test embankment site in Saga, Japan, reported by Chai et al. [21]. The clayey soil deposited at the site is called Ariake clay, which is a marine clay with a natural water content that is normally more than 100%, The value of the slope of compression line (k) in the e-ln(p0 ) plot (e is the void ratio and p0 is the effective compression stress) is approximately 0.4–1.3 (compression index, Cc, of approximately 1.0–3.0) [23,24]. The basic case is considered to represent the weaker soft clay deposit, while the stiffer cases are simulated by increasing the effective cohesion (c0 ) and reducing the value of k, as detailed in a later section. For the soft soil model, the value of the slope of the unloading-reloading line in the e-ln(p0 ) plot, j, was assumed to be 1/10 of k. The value of Poison’s ratio (m) was assumed to be 0.15 for all the soft soil layers and the CDM columns. The values of permeability in the horizontal direction (kh) were set as 1.5 times the corresponding values of permeability in the vertical direction (kv) [25]. The ground water level was assumed to be 1.0 m below the ground surface. The values of the coefficient of the earth pressure at-rest, Ko of 0.6 for the soil layers from the ground surface to a 2 m depth (OCR > 1.5) and 0.5 for the remaining soil layers were adopted. The values of kv and kh listed in Table 1 are initial values, and they were allowed to vary with void ratio e during the consolidation process, according to Taylor [26] equation. The constant Ck in Taylor’s equation was set as, Ck = 0.5eo (eo is the initial void ratio) [27]. The unconfined compression strength (qu) of the CDM column was assumed to be 1000 kN/m2, and the Young’s modulus (E) was estimated as 100qu [28,29]. The

CL 6 m

6.5 m 0

Column

0

Lateral displacement (mm) 20 40 60 80

100

9.5 m -5

Soft clay Stiff clay Sand

I 1 I2

At elapsed time 559 days Measured (I 1) Measured (I 2) FEM

-10

Inclinometer

Stiff clay Sand

-15

Stiff clay To 23 m

(a)

-20

(b)

Fig. 5. (a) Cross-section of the embankment and (b) comparison of the lateral displacement from the FEM 3D with measured data [21].

172

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

Table 1 Model parameters for the basic full-scale embankment. Depth (m)

Soil strata

E (kN/m2)

m

c0 (/0 ) (kN/m2)

j

kb

M

e0

ct (kN/m3)

kv (104 m/day)

kh (104 m/day)

0.0–1.0 1.0–2.0 2.0–5.0 5.0–7.0 7.0–8.0 8.0–9.0 9.0–10.0 10.0–35.0

Surface soil Soft clay-1 Soft clay-2 Soft clay-3 Soft clay-4 Soft clay-5 Soft clay-6 Sand Embankment

– – – – – – – 40,000 3000

0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.10 0.45

5 5 5 5 5 5 5 20 (35) 20 (35)

0.0435 0.0652 0.087 0.0652 0.0521 0.0434 0.0347 – –

0.435 0.652 0.87 0.652 0.521 0.434 0.347 – –

1.64 1.64 1.64 1.64 1.64 1.64 1.64 – –

1.61 1.61 2.86 2.45 2.45 2.12 2.12 0.76 0.5

16.0 16.0 14.0 14.5 14.5 15.0 15.0 19.0 19.0

6.0 6.0 4.4 5.6 5.6 5.6 5.6 2500 –

9.0 9.0 6.6 8.4 8.4 8.4 8.4 2500 –

Note: c = unit weight; m = Poisson’s ratio; c0 = cohesion; /’ = internal friction angle; E = Young’s modulus; kb = value of slope of the consolidation line in the e-ln(p’) plot (e is voids ratio and p’ is effective mean stress) for the basic case; j = slope of the rebound line in the e-ln(p’) plot; and M = the slope of critical state line (CSL) in the p’–q plot (q is deviator stress).

Fig. 6. Yield surface of the Soft Soil Model in the p0 -q plane.

permeability of the columns was assigned the same values as the corresponding untreated soils. From SSM, the undrained shear strength (su) of the soil can be calculated as:

su ¼

M MC 0 p ðOCRe ÞK 2 MC

p0MC ¼ p0e

OCRe ¼

M 2 þ g2e

ð2Þ

!K ð3Þ

M2 þ M2MC r0v OCRð1þ2K nc o Þ 3

þ c0 cot /0

! ð4Þ

p0e

where ge is the initial stress ratio (qe/p0 e), qe is the initial deviator stress, p0 e is the initial mean effective stress, M is the slope of the critical state line (CSL) in the p0 – q plot, MMC is the slope of the Mohr-Coulomb failure criteria in the p0 – q plane, p0 MC is the equivalent mean stress on the MMC line (Fig. 6), K = 1  j/k, OCR is the over consolidation ratio, /0 is the effective internal friction angle of soil, and r0 v is the initial vertical effective stress. In SSM, M is mainly a function of the coefficient of the at-rest earth pressure at the normal consolidated state, K nc o . The interpretation of some of the parameters in Eqs. (2)–(4) are illustrated in Fig. 6. Fig. 7. Plan view of the DCM the arrangement of the CDM columns and crosssection of a 6 m height embankment.

2.2. Assumed other cases The following numerically.

factors/variables

have

been

investigated

(1) Geometrical variables (a) Embankment height: 4, 6 and 8 m (the top width and slope angle were fixed).

(b) Thickness of soft clay layer (Hs): 6, 8, 10, 14 and 20 m. (c) Area improvement ratio (a) by the CDM column: 10%, 15%, 20%, 25% and 30%. As illustrated in Fig. 7, reducing the value of a increased the spacing between the columns.

173

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178 2

su (kN/m )

0

0

10

20

30

40

2m

-1

basic case as kb, the k/kb ratios considered were k/kb = 0.25, 0.5 and 1.0. All cases investigated are summarized in Table 2. 2.3. Numerical results

sumin The results presented are focused on the maximum bending moment in the CDM column under the toe of the embankment, which is the critical location for the bending failure of the CDM column. The bending moment in the column was calculated using the simulated distribution of stresses in the column.

-2 2m

Depth (m)

-3

Zone for calculating suavg

-4

(1) Effect of undrained shear strength (su)

-5

For a natural clayey deposit, the values of su vary with the depth. It is desirable to define a representative value of su to propose a design method that considers the tensile failure of the CDM columns. Although two possible options can be considered, (1) the average value and (2) the minimum value, as illustrated in Fig. 9, the two profiles may have the same average value (suavg) but different minimum values (sumin). It is considered that neither suavg nor sumin can serve as a representative value. Therefore, a parameter (sua) that represents both the effects of the average and the minimum value of su is introduced and designated the representative value of su as:

-6 -7 Soft Clay

-8 -9

c' c' c' c'

= 0 kN/m2 = 5 kN/m2 2 = 10 kN/m = 15 kN/m2

-10

sua ¼ ðsuav g  sumin Þ0:5

Fig. 8. Simulated value of su of the model ground.

(d) Diameter of CDM column: 0.6, 0.8, 1.0 and 1.2 m. (2) Soil properties (a) Undrained shear strength (su) of the soft clay layer: Variations in su was simulated by varying the effective cohesion (c0 ) in Eq. (4). The simulated cases are c0 = 0, 5, 10, and 15 kN/m2. Using the parameters of the basic case, for c0 = 0–15 kN/m2, the SSM simulated variations of su with respect to the depth are depicted in Fig. 8. (b) Compressibility of the soft clay: The values of k were varied to investigate the effect of the compressibility of soft soil layer. Designated the values of k for the

ð5Þ

Then, to calculate suavg, the applicable range must be considered. Considering that for many natural deposits, the thickness of the crust layer is 1–2 m and the minimum value of su occurs below the crust layer, it is proposed to use the average values of a zone (range) from 2 m above to 2 m below the minimum value of su as illustrated in Fig. 8. For the distributions of su in Fig. 8, the estimated values of sua are summarized in Table 3, which were used to analyse the results of the finite element analysis (FEA). Using the other conditions of the basic case, but varying the value of c0 for the soft clay from 0 to 15 kN/m2 (sua = 9.6–19.4 kN/m2), the effect of sua on the maximum bending moment (Mmax) in the CDM columns under the toe of the assumed embankment is compared in Fig. 10. It can be seen that increasing sua significantly reduced the values of Mmax. Increasing sua from 9.6 to 19.4 kN/m2 reduced Mmax from approximately 31.6 to approximately 7.5 kN-m in the column.

Table 2 Cases investigated. No.

Height of embankment (m)

Thickness of soft soil, Hs (m)

Area improvement ratio, a (%)

k/kb (kb from Table 1)

Diameter of the column, D (m)

c0 (kN/m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4 6 8 4 6 8 4 6 8 6 6 6 6 6 6 6 6 6 6 6

10 10 10 10 10 10 10 10 10 10 10 10 10 6 8 14 20 10 10 10

30 30 30 30 30 30 30 30 30 25 20 15 10 30 30 30 30 30 30 30

1.0 1.0 1.0 0.5 0.5 0.5 0.25 0.25 0.25 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.0 0.8 0.6

0, 5, 10, 15 0, 5, 10, 15 0, 5, 10, 15 0, 5, 10 0, 5, 10, 15 0, 5, 10, 15 0, 5 0, 5, 10, 15 0, 5, 10, 15 5 5 5 5 5 5 5 5 5 5 5

174

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178 2

su (kN/m )

0

20

60

40

60

80 50

Mmax (kN-m)

Profile 1 Profile 2

Depth (m)

-10

H = 6 m, b = 1.0 2 sua = 12.7 kN/m

40

D = 1.2 m

30

y = 7.1x-0.82 20 10 0

-20

0

0.1

0.2 Area improvement ratio (

0.3

0.4

Fig. 11. Mmax - a relationship.

-30

Stiffness index (I r )

Fig. 9. Illustration of the su distribution patterns.

0

Table 3 Summary of the representative values of the undrained shear strength (sua).

-1

sua (kN/m2)

0 5 10 15

9.6 12.7 16.0 19.4

50

100

150

200

-2 Depth (m)

c0 (kN/m2)

0

250

300

350

400

sua = 9.6 kN/m2 b b b

-3

= 1.0 = 0.5 = 0.25

-4 Bending moment (kN-m)

0

0

10

20

30

40

-5 Fig. 12. Distributions of the stiffness index with depth.

-2

Mmax ¼ 7:1 a0:82 ðM max in kN  mÞ

ð6Þ

Depth (m)

(3) Effect of stiffness index of soft subsoils (Ir) -4

-6 H = 6 m, D = 1.2 m /

-8

sua sua sua sua

b

= 1.0 2

= 9.6 kN/m = 12.7 kN/m2 2 = 16.0 kN/m = 19.4 kN/m2

-10 Fig. 10. Effect of the ground sua on the bending moment in the column.

(2) Effect of area improvement ratio (a) Using the basic case conditions but varying a from 10% to 30%, the maximum bending moments (Mmax) in the column versus the value of a is depicted in Fig. 11. The relationship can be expressed by a power equation as:

Both the stiffness of the soft ground and the CDM column will influence the Mmax in the CDM column. Since the stiffness of the CDM columns is normally much higher than that of soft clays, the Mmax is more sensitive to the stiffness of soft clay layers. The stiffness index (Ir) is used to represent the effect of the stiffness of the soft soil. The expression for Ir is as follows:

Ir ¼

G su

ð7Þ

G¼

E50 2ð1 þ mÞ

ð8Þ

where G is the shear modulus of the soil, E50 is the secant modulus of the soil corresponding to 50% of the shear strength, and m is Poisson’s ratio of the soil. The value of Ir of the assumed ground was determined from the results of the numerical triaxial tests by Plaxis 3D. Several researchers have justified the effectiveness of the numerical simulation of triaxial tests to study the stress-strain behaviour of the soft clay and the cement treated clay [30,31]. Values of E50 and su were calculated from the simulated stress-strain curves. Fig. 12

175

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178 Table 4 Summary of the representative values of the stiffness index (Ira).

20 Ira

1.0 0.5 0.25

9.6–19.4 9.6–19.4 9.6–19.4

65 130 255

shows the variations of Ir with depth for the assumed 10 m thick soft clay layer. The sua value was 9.6 kN/m2 but with different compression indexes, i.e., k/kb = 0.25, 0.5 and 1.0. Similar to su, the representative value of the stiffness index (Ira) is defined as:

Ira ¼ ðIrav g  Irmin Þ0:5

H = 6 m,

b=

1.0

sua = 12.7 kN/m2,

4

sua (kN/m2)

Mmax / D

k/kb

10

ð9Þ

where the subscript ‘‘min” means minimum and ‘‘avg” means average. The value of Iravg was calculated from a range of 2.0 m from the location of Irmin. For all the analysed cases, the values of the representative stiffness index are summarized in Table 4. Fig. 13 shows the effect of Ir on the simulated bending moment in the column under the toe of the assumed embankment. The higher the Ir, the lower the Mmax was in the column.

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Diameter (D) Fig. 14. Effect of the column diameter on the ratio of Mmax/D4.

Bending moment (kN-m)

0

10

20

30

(4) Effect of diameter (D) of the column In the moment-area theory for a beam, the bending equation is expressed as:

M E ¼ I R

-5

where R is the radius of curvature, I is the moment of inertia of the cross-sectional area, E is the Young’s modulus, and M is the bending moment on the beam. Eq. (10) indicates that for two beams formed by a given material, if the ratio of M/I is the same, the curvature of the beams will be the same. Then, for a cylinder column, I / D4, and M/I / M/D4. The numerical results indicate that for a given value of a, the diameter of the columns does not significantly influence the curvature (R) of the deformed column under the toe of the embankment. Therefore, Mmax/D4 was used in the analysis. Fig. 14 shows the

Depth (m)

ð10Þ

-10

-15

H = 6 m, b= 1.0 sua = 12.7 kN/m2, D = 1.2 m Hs=6m Hs=8m H s = 10 m H s = 14 m H s = 20 m

Bending moment (kN-m)

0

0

10

20

30

-20 Fig. 15. Effect of the thickness of soft deposits (length of end bearing columns) on the bending moment in the column.

-2

relationship of Mmax/D4 versus D. It can be seen that the value of Mmax/D4 is nearly a constant for the cases investigated.

Depth (m)

(5) Effect of thickness of soft deposit (Hs)

-4

-6

-8

sua = 12.7 kN/m2, H = 6 m, D = 1.2 m b= b= b=

1.0 0.5 0.25

-10 Fig. 13. Effect of stiffness on the bending moment in the column.

To investigate the effect of the thickness (Hs) of a soft subsoil layer, the Hs was varied from 6.0 m to 20.0 m. In the cases where Hs was less than 10.0 m, the corresponding soft clay layer(s) was changed to sand layer(s). In the cases when Hs was more than 10.0 m, clay layers were added by changing the corresponding sand layer(s) to clay layer(s). Considering the fact that for most thick clayey deposits, the compressibility of the clay layers gradually reduces with depth, the added clay layers used a value of k of 0.282 and 0.217 for the depths of 10.0–14.0 m and 14.0–20.0 m, respectively, while the values of the other parameters were set to be the same as the values of the clay layer from 9.0 to 10.0 m depth (Table 1). Fig. 15 compares the simulated distributions of the bending moment in the CDM columns under the toe of a 6.0 m high embankment. It can be observed that the thickness of soft deposit

176

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

does not have a significant effect on the Mmax for the assumed conditions, i.e., the stiffness increased with depth.

3.3. Proposed design chart With a few trials, it was found that the numerical results can be summarized in Pn  Mn relationships with Ir as an independent parameter, as shown in Fig. 16, which is the proposed design chart. The chart is applicable only for the following ranges of parameters:

3. Proposed design method 3.1. Main influencing factors From the numerical results presented in the above, the factors that influence the maximum bending moment (Mmax) in CDM columns under the toe of an embankment are: (1) the embankment load (pem), (2) undrained shear strength (su) and rigidity index (Ir) of the subsoil, (3) area improvement ratio (a) by the CDM columns, and (4) the diameter (D) of the CDM column. To propose a design methodology, all these factors must be considered.

(1) (2) (3) (4)

Load/strength ratio, Pn: 4–16; Area improvement ratio, a: 10–30%; Diameter of the column, D: 0.6–1.2 m; Stiffness index, Ir: 65–255.

3.4. Design procedure The main steps to use the proposed design chart are as follows:

3.2. Key parameters Two new dimensionless key parameters are introduced, the load/strength ratio (Pn) and the normalized maximum bending moment in the CDM column (Mn), with their definitions explained in below. (1) Load/strength ratio (Pn) Since the effects of the maximum embankment load (pem) and undrained shear strength (su) of the soft subsoil are relevant factors, a parameter, the load/strength ratio, is defined as:

Pn ¼

pem su

ð11Þ

Generally, the larger the Pn, the larger the bending moment in the CDM column will be. (2) Normalized maximum bending moment (Mn) From the numerical results, the effect of the main influencing factors on the maximum bending moment (Mmax): (1) the load/ strength ratio, Pn = pem/su, (2) the area improvement ratio (a) of the columns, and (3) the diameter (D) of the columns, have been quantified. Then, assuming the effects of these parameters are independent, a normalized maximum bending moment (Mn) is defined as:

Mn ¼

M max a0:82 Do

ð12Þ

Pn D4 pa

where pa is the atmospheric pressure and Do is a constant of 1.0 m. The Do and pa are included to non-dimensionalize Mn.

(1) Step 1: Calculate pem. With the known height of an embankment (H) and the unit weight of the fill (ct), the maximum embankment load (pem) is calculated as

pem ¼ ct  H

ð13Þ

(2) Step 2: Calculate Pn. Estimate the representative value of the undrained shear strength (sua) of a deposit with Eq. (5) using the su profile and computing Pn as pem/sua. (3) Step 3: Estimate Ira using Eq. (9). (4) Step 4: Obtain Mn. With known values of Pn and Ira, Mn can be obtained from the design charts of Pn – Mn. Then, calculate Mmax:

Mmax ¼

M n Pn D4 pa Do a0:82

ð14Þ

(5) Step 5: Calculate the maximum tensile stress in the CDM column, rtmax. Finally, evaluate the possibility of bending failure of the CDM column.

rtmax ¼

M max D  r0a 2I

ð15Þ

where r0 a is the effective axial stress in the column at the location where the maximum bending moment occurred. To be practical it is proposed to use the initial vertical effective stress at the middle of the column under the toe of an embankment. If rtmax is greater than the tensile strength of the CDM column, the CDM column will fail by bending. For example, if the CDM columns have a compressive strength of 1000 kN/m2, then the tensile strength will be approximately 100 kN/m2 (1/10 of the compressive strength) [29,32]. If rtmax > 100 kN/m2, bending failure occurs. 4. Verification of the proposed design method

Normalized maximum bending moment (Mn )

0.006 0.005

Ir = 65 Ir = 130

0.004

Ir = 255

0.003 0.002

Ir = 65.0 Ir = 130.0 Ir = 255.0

0.001 0

0

2

4

6

8

10

12

14

Ratio of load to undrained shear strength (Pn )

Fig. 16. Pn – Mn relationships.

16

18

In the literature, the results of two centrifuge model test with the bending failure of the model soil-cement columns have been collected. For these two cases, the columns were installed only under the toe and the slope of the model embankments, which is different from the assumed full improvement condition adopted in the numerical investigation. The full improvement aims to increase the stability of the embankment and control settlement. While partial improvement is mainly focused on increasing the factor of safety of an embankment system. Shrestha et al. [22] reported results of a 3D finite element simulation of embankments on a CDM column improved soft subsoil and noted that increasing the size of the CDM column improved zone under the embankment, which can reduce the maximum bending moment in the column. However, when the zone under the toe and the slope of an embankment was improved, further increasing the size of the improved zone has only marginal effects on the maximum bending

177

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

moment of the column under the toe of the embankment. Therefore, the results of these two model tests can be used to validate the proposed design method.

of the soil-cement columns (qu) of 219–302 kN/m2 was reported. Then, the estimated tensile strength is approximately 21.9– 30.2 kPa (approximately 1/10 of the value of qu). The centrifuge gravity adopted was 50g.

4.1. Brief descriptions of each test

(2) Model test by Kitazume and Maruyama (2006; 2007) (M-2)

(1) Model test by Inagaki et al. (2002) (M-1) The geometry of the centrifuge model test reported by Inagaki et al. [11] (Case 2 in their paper) and particular physical and mechanical properties of the model ground are shown in Fig. 17. The value of the representative sua was approximately 18 kN/m2, and the representative Ira was chosen as 65, the lowest value in the design chart (Fig. 16). The unconfined compressive strength

One of the centrifuge model tests reported by Kitazume and Maruyama [9,10] (Case 8 in their paper) is analysed here. The geometry of the model test is shown in Fig. 18(a). The undrained shear strength of the model ground was measured at two depths, as shown in Fig. 18(b). Here, the measured smaller value of the su of 4.4 kN/m2 is chosen as the representative value. The model ground was very weak, and an Ira of 65 was assumed; however, the actual value of Ira might be lower than 65 (lower boundary of the proposed design chart). As a result, the predicted maximum tensile stress may be lower. It will be explained later that even using Ira = 65, the bending failure was predicted. The reported unconfined compression strength (qu) of the soilcement column was 409 kN/m2, and the reported tensile strength (rt) was 132 kN/m2. Because a small carbon rod with a diameter of 2 mm (dimension in centrifuge scale) was inserted inside the 20 mm diameter model soil-cement column. However, it appears that the value of rt was evaluated by simply adding the bending strength of the soil-cement column and the carbon rod. For this kind of composited column, the failure process will be a progressive manner, i.e., the two materials may not fail simultaneously. The tensile strength of the soil-cement column is 1/10 of its compression strength, which is approximately 40.9 kPa. The rt of the composited column can be in the range of 40.9–132 kPa. The centrifuge gravity adopted was also 50g. 4.2. Predicted rtmax and FS

Fig. 17. Cross–section of the embankment and soil profile for the model test by Inagaki et al.

Using the available parameters of the model tests, from the proposed design method, Mmax was calculated for the two cases using Eq. (14). Then, the value of rtmax was obtained using Eq. (15). The conditions and the analysed results of pem, sua, Ira, Pn and rtmax for the two model tests are summarized in Table 5. For the two model tests, the predicted maximum tensile stresses (rtmax) in the soil-cement columns were nearly equal to or larger than the values of the tensile strength (rt f) of the columns. It had been reported that for Case M-1, cracks on the columns were observed, and for Case M-2, the columns failed through bending. Therefore, the predictions agree with the observed results. 5. Conclusions

(a)

The bending failure mechanism and maximum bending moment in cement deep mixing (CDM) formed column under an embankment load was investigated by a series three-dimensional (3D) finite element analyses (FEA). Based on the results of the FEA, the following findings/conclusions can be obtained.

(b)

(1) The main factors influencing the value of the maximum bending moment in CDM columns are as follows: (a) magnitude of an embankment load (pem), (b) undrained shear

Fig. 18. (a) Cross–section of the embankment and soil profile for the model test by Kitazume and Maruyama [9,10] and (b) the measured su profile of the model ground.

Table 5 Predicted results of the centrifuge model tests. Cases

pem (kN/m2)

a (%)

D (m)

sua (kN/m2)

Ira

Pn

Predicted maximum tensile stress rtmax (kN/m2)

Tensile strength rtf (kN/m2)

FS Predicted

Observed

M-1 M-2

110.5 50

20 28

1 1

18 4.4

65 65

6.14 11.4

26 123

21.9–30.2 (26.1) 40.9–132.0 (81.5)

1.0 Fail

Cracks Fail

178

J.-c. Chai et al. / Computers and Geotechnics 91 (2017) 169–178

strength (su) and rigidity index (Ir) of the soft deposit, (c) the area improvement ratio by the CDM column (a), and (d) the diameter (D) of the column. The effect of each factor was evaluated quantitatively. (2) A design method to consider the bending failure of CDM columns under an embankment load is proposed. The method considers all the main influencing factors on the maximum bending moment in the CDM column, which are summarized into three dimensionless parameters, namely, the load to shear strength ratio, (Pn = pem/su), Ir, and the normalized maximum bending moment in the CDM column. Using this method, with known values of pem, a, D and su and Ir, the factor of safety of the CDM column against bending (tensile) failure can be predicted. (3) Using the results of two centrifuge model tests of embankments on cement mixing formed model columns improved soft subsoils reported in the literature, the usefulness of the proposed method was verified. For the two cases considered, tensile cracks or failure of the model columns were reported, and the predicted results agree with the test results.

References [1] Kamon M, Bergado DT. Ground improvement techniques. Proc 9th Asian regional conf on soil mech found eng, Bangkok, vol. 2. p. 526–46. [2] Bergado DT, Anderson LR, Miura N, Balasubramaniam AS. Soft ground improvement in lowland and other environments. ASCE; 1996. p. 427. [3] Broms BB. Lime and lime/cement columns. In: Moseley MP, Kirsch K, editors. Ground improvement. Spon Press; 2004. p. 252–330. [4] Chai J-C, Carter JP, Miura N, Zhu H-H. Improved prediction of lateral deformations due to installation of soil-cement columns. J Geotech Geoenviron Eng ASCE 2009;135(12):1836–45. [5] Wang Z-F, Shen S-L, Ho C-E, Kim YH. Investigation of field-installation effects of horizontal twin-jet grouting in Shanghai soft soil deposits. Canad Geotech J 2013;50(3):288–97. [6] Shen S-L, Wang Z-F, Yang J, Ho C-E. Generalized approach for prediction of jet grout column diameter. J. Geotech Geoenviron Eng, ASCE 2013;139 (12):2060–9. [7] Shen S-L, Wang Z-F, Cheng W-C. Estimation of lateral displacement induced by jet grouting in clayey soils. Geotechnique 2017;67(7):621–30. [8] Inagaki M, Abe T, Yamamoto M, Nozu M, Yanagawa Y, Li L. Behavior of cement deep mixing columns under road embankment. In: Proc int conf on physical modelling in geotechnics. p. 967–72. [9] Kitazume M, Maruyama K. External stability of group column type deep mixing improved ground under embankment loading. Soils Found 2006;46 (3):323–400. [10] Kitazume M, Maruyama K. Internal stability of group column type deep mixing improved ground under embankment loading. Soils Found 2007;47 (3):437–55.

[11] Zheng G, Diao Y, Li S, Han J. Stability failure modes of rigid column-supported embankments. In: Proc geo-congress. ASCE; 2013. p. 1814–7. [12] Nguyen B, Takeyama M, Kitazume M. Internal failure of deep mixing columns reinforced by a shallow mixing beneath an embankment. Int J Geosynth Ground Eng 2016;2(4):30. [13] Yapage NNS, Liyanapathirana DS, Leo CJ. Failure modes for geosynthetic reinforced column supported (GRCS) embankments. In: Proc 18th int conf soil mech and geotech eng, Paris. p. 849–52. [14] Yapage NNS, Liyanapathirana DS, Poulos HG, Kelly RB, Leo CJ. Analytical solutions to evaluate bending failure of column supported embankments. IACSIT, Int J Eng Tech 2013;5(4):502–6. [15] Zhang Z, Han J, Ye G. Numerical analysis of failure modes of deep mixed column-supported embankments on soft soils. In: Proc ground improvement and geosynthetics, GSP 238. ASCE; 2014. p. 78–87. [16] Chen J-F, Li L-Y, Xue J-F. Failure mechanism of geosynthetic-encased stone columns in soft soils under embankment. J Geotext Geomembr 2015;43 (5):424–31. [17] Shrestha S, Chai J-C, Kamo Y. 3D numerical simulation of a centrifuge model test of embankment on column improved clayey soil. In: Proc. young geotechnical engineer’s symposium on finite element methods, May 17–18, IIT, Mumbai; 2015, Paper no. FEM022. [18] Goh ATC, Teh CI, Wong KS. Analysis of piles subjected to embankment induced lateral soil movements. J Geotech Geoenviron Eng ASCE 1997;123(9):792–801. [19] Chai J-C, Carter JP. Deformation analysis in soft ground improvement. Springer; 2011. p. 247. [20] Neher HP, Wehnert M, Bonnier PG. An evaluation of soft soil models based on trial embankments. In: Proc 10th int conf on computer methods and advances in geomech, Tucson, Arizona, USA. CRC Press; 2001. p. 373. [21] Chai J-C, Shrestha S, Hino T, Ding W-Q, Kamo Y, Carter JP. 2D and 3D analyses of an embankment on clay improved by soil-cement column. Comput Geotech 2015;68:28–37. [22] Shrestha S, Chai J-C, Bergado DT, Hino T, Kamo Y. 3D FEM investigation on bending failure mechanism of column inclusion under embankment load. Lowland Technol Int 2015;17(3):157–66. [23] Miura N, Chai J-C, Hino T, Shimoyama S. Depositional environment and geotechnical properties of Ariake clay. Ind Geotech J 1998;28(2):121–46. [24] Chai J-C, Hino T, Shen S-L. Characteristics of clay deposits in Saga Plain, Japan. Geotechnical Engineering. In: Proc the Institution of Civil Engineers; 2017. http://dx.doi.org/10.1680/jgeen.16.00197. [25] Chai J-C, Igaya Y, Hino T, Carter JP. Finite element simulation of an embankment on soft clay-case study. Comput Geotech 2012;48:117–26. [26] Taylor DW. Fundamentals of soil mechanics. New York, NY: Wiley; 1948. [27] Tavenas F, Jean P, Leblond P, Leroueil S. The permeability of natural soft clays. Part II: permeability characteristics. Canad Geotech J 1983;20(4):645–60. [28] Porbaha A, Shibuya S, Kishida T. State of the art in deep mixing technology. Part III: geomaterial characterization. Proc Inst Civil Eng-Ground Improve 2000;4(3):91–110. [29] Igaya Y, Hino T, Chai J-C. Laboratory and field strength of cement slurry treated Ariake clay. In: Proc 8th Int symposium on lowland technology, Bali, Indonesia. p. 40–5. [30] Surarak C, Likitlersuang S, Wanatowski D, Balasubramaniam A, Oh E, Guan H. Stiffness and strength parameters for hardening soil model of soft and stiff Bangkok clays. Soils Found 2012;52(4):682–97. [31] Suebsuk J, Horpibulsuk S, Liu MD. Finite element analysis of the non-uniform behavior of structured clay under shear. KSCE J Civil Eng 2016;20(4):1300–13. [32] Ito M, Kamo K, Okouchi Y. Investigation on the tensile strength of cement treated soils. In: Proc 71th annual meeting of Japanese Civil Eng Society, VI. p. 653–4.