NUMERICAL STUDY ON THE BEHAVIOR OF INCLINED MICROPILE

Sepideh Damavandinejad Monfared, Western University, London, Ontario, Canada.

In recognition of the practicality of using inclined micropiles as elements for foundation support to resist static and seismic loading conditions, specifically in retrofitting projects, this study presents an investigation into the behavior of an inclined micropile subjected to simultaneous lateral load and bending moment. Three-dimensional numerical simulations are performed using the finite element method to assess the influence of micropile geometrical parameters such as angle of inclination, length, and diameter on the response of micropile-soil system. The Mohr-Coulomb failure criterion is used to define the behavior of soil and stabilized soil around micropile materials and the micropile, constructed of concrete and steel, is assumed to be elastic. The interaction between soil and micropile is taken into account by defining interaction elements covering both tangential and normal behavior. The study is carried out using nonlinear FEM analyses. The results of these simulations indicate that negative micropiles, in which slip surface deflects downward, have higher lateral load capacity than positive micropiles with slip surface deflecting upward. The conducted research also shows that increasing the diameter and the length of micropile increases the lateral load capacity. Increasing micropile diameter is more effective in increasing lateral load capacity. A relationship is developed from statistical regression analysis of the finite element modeling computations to estimate the

lateral displacement of a micropile inclined at an angle of 30o in silty sands.

Introduction

Micropiles are small diameter (typically less than 300 mm), cast-in-place, drilled, and grouted replacement piles with steel pipes which after being conceived in Italy (Lizzi,1978), were originally developed for underpinning existing structures (Bruce et al.,1990) to arrest and prevent structural movement, upgrade load-bearing capacity of existing structures, repair or replace deteriorating or inadequate foundations or raise settled foundations to their original elevation. Micropiles are subjected to lateral load when they are used in building foundations (earthquake,wind), basement wall foundations, retaining wall foundations (Ueblacker,1996), excavation support, tower and stack foundations, machine foundations or slope stabilization (Lizzi,1982; Pearlman et al.,1992; Palmerton,1984 and Bruce,1988a). Although micropiles are generally considered to have little lateral capacity due to their small diameters compared to conventional driven piles, steel casing provides significant resistance against lateral load. Moreover, they are installed within

tight areas, advancing through difficult formations and obstructions (Pearlman et al., 1993), and can be constructed with different inclination angles. This paper focuses on a single micropile subjected to simultaneous lateral load and bending moment. The purpose is to demonstrate the effect of micropile geometrical parameters, including diameter, length and inclination angle, on micropile-soil system response and to develop a relationship to estimate the lateral displacement of a micropile.

Numerical Model

Analyses were carried out using ABAQUS finite element program driven by SIMULIA's vision of Unified FEA and designed to effectively and efficiently complement existing processes and tools for design, production, and data management. Some of the benefits of ABAQUS include great efficiency in model generation, improved correlation between tests and analysis results, improved data transfer between simulations, easy sharing of models and results, and evolution of legacy methods to a more

sophisticated, real-world approach. Analyses were carried out using a nonlinear analysis. Micropile and soil were modeled using 3D solid elements.

The Mohr-Coulomb failure criterion was used to define the behavior of soil and stabilized soil around micropile materials and the micropile, constructed of concrete and steel, was assumed to be elastic and it maintained within the elastic range for the presented data.

The mechanical properties of the soil, low plasticity silty sand that were given from geotechnical investigations for a hotel in Tabriz, and micropile are summarized in „‟Tables 1‟‟ and „‟Table 2‟‟.

Table 1. Properties of the soil material

°

°φ C

(KPa) ν

E (MPa)

γ (KN/m

3)

3 82 9.28 0.35 89.6 16.67

Table 2. Properties of the micropile material

ν E

(GPa) γ

(KN/m3)

0.2 22

25 concrete

0.3 210 78 Steel case

In order to eliminate the boundary condition effect, the height and diameter of the soil‟s part were defined considering the results of sensitivity analysis, in which one parameter is defined by increasing it up to the value that changing it has no impact on the model‟s results while other parameters are assumed to be constant. In all modelings, a cylindrical part was used as the soil part with 15 m height and 8 m diameter.

The interaction between soil and micropile was taken into account using surface-to-surface contact interaction with finite-sliding formulation and surface-to-surface discretization method which enforces contact conditions in an average sense over regions nearby slave nodes rather than only at individual slave nodes (Node-to-surface contact discretization). Tangential behavior was defined using “Penalty” friction formulation. And, “Hard” contact model was used to define contact pressure-overclosure relationship in normal behavior.

According to the geometry of the model 20-node quadratic hexahedral and 4-node linear tetrahedron elements were used to mesh micropile and soil respectively. The finite element mesh used in numerical simulations for the inclined micropile is depicted in “Figure 1”.

FHWA (2000) recommends lateral displacement of micropiles to be limited to 6.4 mm. Accordingly, the limiting lateral load required to produce this amount of displacement was determined. Numerical simulations were performed for micropiles with different inclination angles, diameters, and lengths, as presented in “Table 3‟‟.

Figure 1. 3D mesh used for the finite element

analysis of the soil-micropile system

Table 3. Range of investigated parameters

NUMERICAL RESULTS

The bending moment to lateral load ratio, determined by geometrical parameters of the structure above the micropile, has a significant effect on the lateral load required to produce recommended lateral displacement. In this study this ratio was assumed to be equal to 3 , as illustrated in “Equation 8” , and the objectives were to achieve the effect of micropile‟s geometrical parameters on the required load to produce recommended lateral displacement for structures subjected to static loads and to develop a relationship to estimate the lateral displacement of micropiles.

100-250 (mm) Micropile‟s Diameter 4-11 (m) Micropile‟s Length

°55 – °5 Micropile‟s inclination angle

Bending moment to lateral load ratio = M/F = 3 (Equation 1)

Where; F = Applied Lateral Load (ton) M = Applied Bending Moment (ton.m)

The Effect of Micropile’s Inclination Angle on Soil-Micropile system response

Battered piles are used to translate lateral loads along the axis of the pile. In order for the translation to occur, additional vertical or opposite battered piles are added to the pile group and, the pile group system response is the primary resistance to lateral loads.

Inclined piles subjected to lateral load are classified into two groups, negative and positive piles, depending on the formation of slip surfaces. Negative piles are the group in which slip surface deflects downward and positive piles are the group with slip surface deflecting upward, as illustrated in „‟Figure 2‟‟.

Figure 2. negative and positive battered piles

To investigate the behavior of inclined micropiles and the effect of inclination angle on the response of soil-micropile system a group of nonlinear static analysis were performed for positive and negative inclined micropiles at different inclination angles to the vertical axis.

Lateral displacement obtained at the ground surface for both negative and positive inclined micropiles are plotted versus lateral load and bending moment in „‟Figure 3‟‟.

The results indicate that a negative micropile has higher lateral load capacity than a positive micropile. Furthermore, increasing the inclination angle in negative micropiles causes to increase lateral load capacity but in positive micropiles increasing the inclination angle up to

30o has contrariwise effect and decreases lateral

load capacity. Increasing the inclination angle

more than 30o

has no notable effect on the micropile-soil system response.

Figure 3. load - displacement response of micropile for negative and positive battered micropiles (Note: L=8m , D=200mm)

The Effect of Micropile’s Diameter and Length on Soil-Micropile System Response

Studying the effect of micropile‟s diameter on soil-micropile system response was conducted by simulating the 8 meter length negative battered micropiles with inclination angle of 35ᵒ to the vertical axis and various diameters, as illustrated in „‟Table 3”.

The results indicate that increasing the diameter of micropile increases the lateral load capacity.

Figure 4. load - displacement response of micropile for negative battered micropiles. (Note: L=8m , inclination angle=30o )

0

3

6

9

12

15

18

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Late

ral

Lao

d (

ton

)

Lateral displacement (mm)

Alpha

Alph0

Series

4

Series

3

Series

2

Series

1

-10

-20

-30

-40

23

Be

nd

ing

Mo

me

nt

(to

n.m

)

0

3

6

9

12

15

18

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Late

ral

Loa

d (

ton

)

Lateral displacement (mm)

D=100

mmD=150

mmD=200

mmD=250

mm

Be

nd

ing

Mo

me

nt

(to

n.m

)

α=50o

α=40o

α=50o

α=20o

α=10o

α=0o

α=10o

α=20o

α=30o

α=40o

α=30o

Negative Micropiles

Positive Micropile

s

The effect of micropile‟s length on its load capacity was investigated by simulating eight negative battered micropiles with 200 millimeter diameter and inclination angle of 30

o and

different lengths in the range of 4-11 m.

“Figure 5” presents the lateral displacement of micropile versus applied lateral load and bending moment.

The results presented in this figure show that micropiles capacity increases with length up to a micropile length of 9 m, after which there is very negligible effect with further increasing the length of micropiles.

In comparison to the diameter, increasing the length of micropile has a significantly less effect on soil-micropile system response. Thus to reach the maximum effect, increasing the diameter is more efficient.

Figure 5. load - displacement response of micropile for negative battered micropiles. (Note:D=200 mm , inclination angle=30

o )

THE PROPOSED EQUATION TO ESTIMATE LATERAL DISPLACEMENT OF A MICROPILE

Micropiles constructed as the foundation of different structures are subjected to different loading conditions. For micropiles subjected to lateral load and bending moment simultaneously, the bending moment to lateral load ratio varies by the geometrical parameters of the structure above the micropile.

Deeming the fact that every single analysis can model one particular loading condition, it is

necessary to adopt an approach to cover all ratios. In order to meet this objective and eliminate the bending moment to lateral load ratio, the results of analyses for one particular micropile (D=200 mm, L=8 m and inclination angle=30

o) subjected to loading with the ratios

equal to 1, 2 and 3 were plotted in a 3D diagram , as illustrated in “Figure 6”.

Next, the equation of the plane going through the Load-Displacement curves was calculated by programming in MATLAB code, “Equation 2” and “Figure 0”. U = 0.0165F

2 + 0.0061M

2 + 0.0011FM + 0.4276F

+ 0.3353M + 0.0181 (Equation 2)

Where; U = Lateral Displacement (mm) F = Applied Lateral Load (ton) M = Applied Bending Moment (ton.m)

Figure 6. load - displacement response of a negative battered micropile. (Note:D=200mm, inclination angle=30

o,

L=8m, loading ratio=1, 2 and 3)

Figure 7. defining the plane which goes through load-displacement curves.

The lateral displacements calculated by the “Equation 2” were in a good agreement with those given from ABAQUS modelings. The average error was 1.8%.

“Equation 2” can be used just to estimate the lateral displacement of negative micropiles with 200 mm diameter, 8 m length, and inclination angle of 30

o to the vertical axis. Considering the

numerous types of micropiles constructed in different projects, it is essential to develop a more inclusive equation. Thus, the diameter and length of the micropile were taken into account during two separate steps, by using the results of 24 and 96 modelings respectively and programming in MATLAB code.

Including the Micropile’s Diameter in the Proposed Equation

In order to include the micropile‟s diameter in the proposed equation, the following multivariable interpolation polynomial was employed:

U = p1D3 + p2F

2 + p3M2 + p4D

2 + p5F + p6M +

p7D + p8D2F + p9D

2M + p10DF + p11DM + p12FM

+ p13DFM + p14

The pi unknown coefficients of the employed equation were obtained using the following algorithm:

Step 1: set { ,

Where, are the variables of the

multivariable interpolation polynomial “U”, is

the magnitude of displacement calculated by

modeling in ABAQUS software, and n is the

number of input data.

Step 2: introduce the multivariable interpolation polynomial “U” with m terms and the unknown

coefficients of , .

Step 3: compute the following summation: ∑ ( )

Step 4: compute the following terms: ,

Step 5: solve the m by m linear system: ,

And calculate Step 6: set the computed in the multivariable interpolation polynomial “U”.

The result of processing ABAQUS outputs by the mentioned algorithm is presented below which can be used for micropiles with inclination angle of 30

o to the vertical axis an 8 m length.

U = (-2.8816×103)D

3 + 0.0155F

2 + 0.0033M2 +

(1.4881×103)D

2 + 2.4026F + 4.8097M +

(-238.7819)D + 48.4873D2F + 90.2667D

2M +

(-20.4271)DF + (-40.9403)DM + 0.2010FM + (-0.8215)DFM + 11.7831

(Equation 3)

Where; U = Lateral Displacement (mm) F = Applied Lateral Load (ton) M = Applied Bending Moment (ton.m) D = Micropile‟s Diameter (mm)

Including the Micropile’s Length in the Proposed Equation

In the next step, in order to include the length of micropile in the proposed equation the results of 96 modelings in the ABAQUS software were processed by programming in MATLAB code using the mentioned algorithm.

The result of processing ABAQUS outputs is presented as “Equation 4” and “Table .”4

∑ {

(Equation 4)

Where: U = Lateral Displacement (mm) F = Applied Lateral Load (ton) M = Applied Bending Moment (ton.m) D = Micropile‟s Diameter (mm) L = Micropile‟s Length (m)

Table 4. Pijk coefficients -

3.0046×103

-265.7225 1.6027×103

-5.4255 -0.1837 5455.0

52.7646 2.9287 0.0178

84.8148 .40333 5455.

-0.7697 -0.0172 1.7089

-6.0664×10-4

548290 -23.2419

13.6886 0.103 -39.4149

0 other 0.0896 -0.0359

The precision of the computation of displacement using “Equation3” and “Equation4” in comparison to those given from ABAQUS was 3.2%. Which confirms there is a good agreement between the displacements calculated using the proposed equations and given from ABAQUS modelings.

Conclusions

This paper presented three-dimensional finite element analyses of single micropile subjected to simultaneous lateral load and bending moment, and the effect of micropile‟s geometrical parameters on soil-micropile system response was investigated.

The results of numerical analyses showed that negative micropiles have higher lateral load capacity than positive micropiles. They also indicated that increasing the inclination angle in negative micropiles increased lateral load capacity but in positive micropiles increasing the inclination angle up to 30

o had contrariwise

effect and decreased lateral load capacity. Increasing the inclination angle more than 30

o in

positive micropiles had no notable effect on the micropile-soil system response.

The results of this study further indicated that increasing the diameter and the length of micropile lead to increased bearing capacity. Increasing the length more than 9 meter

had no

effect on the micropile-soil system response.

Increasing micropile diameter had a significantly larger effect on increasing micropile load-carrying capacity.

A relationship was developed from statistical regression analysis of the finite element modeling computations to estimate the lateral displacement of micropiles inclined at an angle of 30

o in silty sands.

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