Upload
jared-bruce
View
12
Download
0
Embed Size (px)
Citation preview
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.
References
ALSALEH, H. and SHAHROUR,I. (2009). Influence of plasticity on the seismic soil-micropiles-structure interaction. J. Soil Dynamics and Earthquake Engineering (29): 574– 578.
BRUCE,D.A., 1988a. Developments in geotechnical construction processes for urban engineering, Civil Engineering Practice, Vol. 3, No. 1, Spring, pp. 49-97.
BRUCE,D.A., PEARLMAN, S. L., and CLARK, J. H. (1990). Foundation Rehabilitation of the Pocomoke River Bridge, Maryland, Using High Capacity Preloaded Pinpiles. Proceedings of the 7
th Annual International Bridge Conference,
Pittsburgh, Pennsylvania, June 18-20, Paper IBC-90-42.
FHWA., 2000. Micropile design and construction guidelines-implementation manual, Rep. No. FHWA-SA-97-070, Federal Highway Administration, U.S. Dept. of Transportation, McLean, Va.
HAN, J. and YE, S.L., 2006. A field study on the behavior of micropiles in clay under compression or tension. Canadian Geotech. Journal. Vol. 43, pp. 30–42.
LIZZI, F., 1978. Reticulated Root Piles to Correct Land Slides, Proceedings of the ASCE Conference., Chicago, IL, Oct. 16-20.
LIZZI, F., 1982. The Pali Radice (Root Piles), Symposium on Soil and Rock Improvement Techniques including Geotextiles, Reinforced Earth and Modern Piling Methods, Bangkok, December, Paper Dl.
MASASHI, I., TOSHINOBU, K., SEIICHI, O. and TAKESHI, O., 2002. Centrifuge model test on pile group effect of pile foundation reinforced by
micropile. Proceedings of the 5th International
Workshop on Micropiles.
MISRA ,A., CHEN, C.H., OBERIO, R. and KEIBER, A., 2004. Simplified analysis method for micropile pullout behavior. Journal of Geotechnical and Geoenvironmental Engineering. Vol. 130, pp. 1024-1033.
PALMERTON, J. B., 1984. Stabilization of moving land masses by cast-in-place piles, Geotech Lab, USACOE, WES, Vicksburg, Mississippi, Final Report GL-84-4, 134 pages.
PEARLMAN, S. L., CAMPBELL, B. D., and WITHIAM, J. L., 1992. Slope stabilization using in-situ earth reinforcements, ASCE Specialty Conference on Stability and Performance of Slopes and Embankments-II, June 29-July 1, Berkeley, California, 16 p.
PEARLMAN, S. L., WOLOSICK, J. R. and GRONEK, P. B., 1993. Pin piles for seismic rehabilitation of bridges, Proceedings of the 10
th
International Bridge Conference, Pittsburgh, PA, June 15-17.
THOMPSON. M. J., 2005. Lateral load tests on small-diameter piles for slope remediation. Proceedings of the 2005 Mid-Continent Transportation Research Symposium, Ames, Iowa, August. Iowa State University4
UEBALCKER, G., 1996. Portland Westside Lightrail Corridor Project Micropile Retaining Wall, Foundation Drilling, November, pp. 8-12
Zamri, H.Ch., Jasim, M.A., Mohd, R.T., Qassun S.M.Sh. (2009). Lateral Behavior of Single Pile in Cohesionless Soil Subjected to Both Vertical and Horizontal Loads. European J of Scientific Research, ISSN 1450-216X Vol.29 No.2, pp.194-205.