Behavior of Granular Pile and Granular Piled Raft

Elastic–perfectly plastic response (Mohr–Coulomb criterion) is used to model both the granular pile and the soft clay. Critical length of granular pile is also suggested for the cases considered in the study.

Overview

Objectives of the study

The study related to the buckling behavior of granular pile is aimed at studying the effects of different properties of granular material and soft clay on buckling depth, maximum buckling and corresponding depth. To study the critical GP length and how it affects the failure mode of a granular pile.

Organization of the study

To conduct a parametric study to quantify the effects of different properties of clay and granular piles on the bulging behavior and load settlement behavior of granular piles and granular pile rafts.

Introduction

History and applications of granular pile

They are cost-effective, use little energy (environmentally responsible), are technically feasible and can be built in the shortest possible time. Although granular pile construction is a very effective method for various applications, the behavior of GP is not yet fully understood.

Methods of construction of granular piles

Vibro-compaction method
Vibro-replacement method
Vibro-displacement method
Vibro-composer method
Cased borehole method

But it is not suitable for sensitive soils due to their reduction in strength during the installation of granular pile. But this method can only be used when the hole formed can withstand without collapsing during the extraction of the probe.

Figure 2.1: Vibro-compaction method [10]

Failure mechanisms

In this study, we focus on the swelling behavior of single isolated floating granular pile. 2011) [15] observed that the maximum swelling occurs at a depth of 1.2 times the column diameter in the case of crushed aggregate used to improve clay deposition and the swelling diameter is equal to 1.24 times the diameter of the pile.

Methods to predict the ultimate load carrying capacity of granular pile

If the soil is treated as an ideal elasto-plastic material, the ultimate lateral stress (σ3) of the crushed aggregate is given by Gibson and Anderson as. Wrapping with geosynthetics or geogrids provides additional confinement to the aggregate, thus reducing swelling of the aggregate [17, 24].

Introduction

PLAXIS 2D- Finite element program

Model
Element type
Interface elements
Meshing
Loads and boundary conditions
Modeling soil behavior

By selecting default fixity, PLAXIS automatically imposes a set of general boundary conditions on the geometry model. Vertical geometry lines for which the x-coordinate is equal to the lowest or highest x-coordinate in the model achieve a horizontal fixity (ux=0). Horizontal geometry lines for which the y-coordinate is equal to the lowest y-coordinate in the model achieve full fixity (ux=uy=0).

Plates extending to the boundary of the geometry model achieve a fixed rotation at the point at the boundary (Фz=0) if at least one of the displacement directions for this point is fixed.

Figure 3.2: Mohr-Coulomb failure criterion

Mohr-Coulomb Model

Deformation modulus
Poisson’s ratio
Cohesion (c)
Friction angle
Dilatancy angle (ψ)

However, if exact effective parameters are not available, it is possible to perform a total stress analysis using stiffness parameters (undrained deformation modulus Eu and an undrained Poisson's ratio µu) and strength parameters (undrained shear strength cu and φu=0). For undrained behavior, an effective value of Poisson's ratio is strongly recommended if Undrained behavior is selected for material behavior. PLAXIS will automatically add bulk stiffness for pore water based on implicit undrained Poisson's ratio of 0.495.

To avoid numerical problems, it is advisable to set a small value (c of the order of 0.2 kPa).

Introduction

Problem Definition

Validation of the model

Validation with Madhav et al

For each type of mesh, load corresponding to 13 mm prescribed displacement is calculated against the center of grain pile. It is observed that load taken by GP converges as the mesh configuration is varied from coarse mesh to very fine mesh. Medium mesh with further refinement and very fine mesh with further refinement give the same results.

Therefore, medium mesh is used for the entire domain and further refinement is done within and near the GP.

Figure 4.2: Model of granular pile and soil with the insert showing the enlarged view near the pile top

Validation with Ambily and Gandhi

The fine meshes generated using 15-node triangular elements and the boundary conditions for both cases are shown in Figure 4.6. In the case of column alone loading, buckling occurs with the maximum buckling at a depth of 0.5 times the grain pile diameter as found in the study by Ambily and Gandhi [3]. No bulges were observed in the case of whole area loading and similar behavior was reported in their analysis.

Based on the axial stress developing at the pile top and the settlement behavior, it can be observed for the case of grain piles loaded only that GP reaches a failure stage.

Table 4.3: Details of material properties

Validation with Hughes et al

In this section, the load-settlement response of the isolated granular pile given by Hughes et al. The crushed aggregate material is considered a purely frictionally dilatant material, while the soft soil is considered to have a purely undrained shear strength. The average grid is used for the entire domain and the granular cluster is further refined as shown in Figure 4.12.

The deformation modulus of granular pile which is calculated back from the elastic part of the load-settlement curve and is taken as 50 000 kN/m2.

Figure 4.10: Deformed shape of granular pile after testing [22]

Non-linear analysis of isolated floating granular pile

Bulging behavior of single floating granular pile

Effect of angle of shearing resistance of granular material
Effect of dilatancy angle of granular material
Effect of undrained shear strength of clay deposit
Effect of loading
Effect of deformation moduli of granular pile and clay
Effect of diameter of granular pile

The influence of the shear resistance angle of granular material, φp, on the bulging behavior is studied by varying φp from 30o to 50o. Instead of applying load, an incremental prescribed displacement (up to 10 cm) is applied to the top of the granular pile. The maximum bulge is not affected by variation in the diameter of the granular pile, as shown in Figure 4.23.

According to Braun's equation [Eq. 4.1)], hump depth varies linearly with the diameter of grain stack.

Figure 4.17: Influence of angle of shear resistance of granular pile on lateral displacements of GP

Load-settlement behavior of granular pile

Influence of angle of shearing resistance of granular material
Influence of dilatancy angle of granular pile
Influence of modular ratio
Effect of E c /c u ratio
Influence of L/d ratio

Numerical analysis is performed to evaluate the effect of shear resistance angle, dilation angle and stiffness (in terms of modular ratio) of GP on the loading behavior of GP settlement. The effect of the dilation angle on the loading behavior of GP is not significant compared to the effect of the shear resistance angle. The range of the modular ratio is varied from K = 10 to K = 25 to observe its effect on the load settlement behavior of the GP.

From this study, it can be observed that the bearing capacity of GP increases for L/d = 2 to L/d = 3 as shown in Figure 4.29.

Figure 4.24: Growth of yielded zones in soil and GP

Comparison of ultimate load carrying capacity of GP with existing

The model is validated in the finite element program software PLAXIS V9 with the linear tension loading and elastic-perfectly plastic analysis (including field tests) of granular pile. Elastic–perfectly plastic analysis of granular pile (unit cell concept) in PLAXIS shows good agreement with experimental result reported by Ambily and Gandhi (2007). The buckling and load-settlement behavior of a single floating granular pile in semi-infinite medium of clay is studied.

For a given value of d and Ec/cu, a well-compacted (higher value of φp) granular pile with a high dilation angle acts stiffer and can absorb a larger portion of the applied load.

Introduction

Problem Definition

Linear elastic analysis of granular piled raft (GPR)

Non-linear analysis of granular piled raft

Comparison between GP and GPR

Bulging behavior

Load-settlement behavior

Critical length

In Figure 5.10, it can be observed that plastic points are developed at the bottom of the GP for L. According to Vidyaranya et al, if the grain pile failure depends on the buckling mode, the ultimate bearing capacity of the GP will be independent of the L/d ratio as shown in Figure 5.11 . Beyond the critical length of the GP, there is no further improvement in the carrying capacity of the GP.

By providing the float on top of GP (GPR), the critical length of grain stack can be increased.

Figure 5.10: Development of plastic zone with respect to length of granular pile Using cavity expansion theory [19] and Hughes and Withers (1974) [21] study, critical length of GP is calculated as 3.25 m and 2.29 m, respectively

Load settlement behavior of single floating granular piled raft

Influence of angle of shearing resistance of granular material
Influence of dilatancy angle of granular pile
Influence of E c /c u ratio of clay
Influence of modular ratio
Influence of d r /d ratio of granular pile
Influence of L/d ratio

It can be verified by analyzing the load-settlement behavior of the GPR for different L/d ratios as shown in Figure 5.13. By increasing the value of Ec/cu, the load carrying capacity of GP increases up to about 21 % and 29 % only for GP (Figure 4.28) and GPR, respectively. For this range of values, it is found that there is no significant influence of the modular ratio on the load-settlement behavior of the GPR as shown in Figure 5.17.

By increasing the dr/d ratio, the load carrying capacity of the GPR increases as shown in Figure 5.18.

Figure 5.14: Influence of angle of shear resistance of granular material on load- load-settlement behavior of GPR

Conclusions

The increases in bearing capacity are not significant for L/d ratios greater than or equal to 5. This is because the buckling failure mode controls the behavior of the GPR as discussed earlier in Section 5.5.3. Angle of shear resistance of granular material, dr/d and Ec/cu of clay have been found to have significant influence on the load setting behavior of GPR for the length of the pile greater than or equal to critical length.

In this study, the behavior of a single floating granular pile and a pile raft embedded in a semi-infinite clay deposit medium is analyzed using the finite element method using the PLAXIS 2D software package.

Single floating granular pile

Among the possible failure mechanisms of the granular pile, buckling failure has been considered as it is the common failure criterion for long granular pile. It is observed that the PLAXIS analysis is able to predict the response of a single liquefied granular pile if the material properties and geometry of the GP are well defined from field tests. The ultimate load carrying capacity of a single floating granular pile is compared with available theories based on buckling failure mode.

For a given value of d and Ec/cu, the ultimate load of a single pile is proportional to the angle of shear strength of the granular material.

Single floating granular piled raft

The shear resistance angle of the granular material, the diameter of the GP and the amount of load at the top of the pile were found to have a significant effect on the buckling behavior of the GP. The Brauns equation is not suitable for calculating the depth of bulge, as the equation does not take into account the top load. For a given value of d and Ec/cu, it is found that the angle of shear resistance (φp) and the dr/d ratio of the granular material have a significant influence on the GPR behavior under load settlement with a pile length greater than or equal to the critical length.

Therefore, for low-rise buildings based on clay deposits, granular piles can be used as an effective reinforcement method to increase bearing capacity and prevent bulging, as a single floating granulate pile is not sufficient to reduce bulging due to less confinement near the top of granular pile.