Dipanjan Basu

Analytical solutions for consolidation aided by vertical drains

Soil disturbance caused during the installation of vertical drains reduces the in situ hydraulic conductivity of soft deposits in the immediate vicinity of the drains, resulting in a slower rate of consolidation than would be expected in the absence of disturbance. Experimental investigations have revealed the existence of two distinct zones, a smear zone and a transition zone, within the disturbed zone around the vertical drain. The degree of change in the hydraulic conductivity in the smear and transition zones is difficult to assess without performing of laboratory tests. Based on the available literature, four different profiles of hydraulic conductivity versus distance from the vertical drain were identified. Closed-form solutions for the rate of consolidation for each of these four hydraulic conductivity profiles were developed. It is found that different variations of the hydraulic conductivity profiles in the disturbed zone result in different rates of consolidation.

Elastic analysis of laterally loaded pile in multi-layered soil

An analysis is developed to determine the response of laterally loaded piles in layered elastic media. The differential equations governing pile deflections in different layers due to a concentrated static force and/or moment acting at the pile head are obtained using the principle of minimum potential energy and calculus of variations. The differential equations are solved analytically using the method of initial parameters. Pile deflection, slope of the deformed axis of the pile, bending moment and shear force can be reliably obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. It is observed that soil layering has a definite impact on pile response and must be taken into account for proper analysis and design. The analysis forms the basis for future formulations that can consider stress–strain nonlinearity.

Elastic Solutions for Laterally Loaded Piles

AbstractLaterally loaded piles are analyzed using the Fourier FEM. The analysis is performed for piles embedded in single-layer elastic soil with constant and linearly varying modulus and in two-layer elastic soil with constant modulus within each layer. The pile responses were observed to be functions of the relative stiffness of pile and soil, and of the pile slenderness ratio. Based on the analysis, equations describing pile head deflection, rotation, and maximum bending moment are proposed for flexible long piles and stubby rigid piles. These design equations are developed after plotting the pile responses as functions of pile-soil stiffness ratio and pile slenderness ratio. These plots can also be used as design charts. Design examples illustrating the use of the analysis are provided.

Drilled Displacement Piles – Current Practice and Design

Abstract Drilled displacement piles are being increasingly used as foundation elements, particularly in projects requiring fast construction. Different types of drilled displacement (DD) piles are available in practice. DD piles are classified according to the drilling tool design and installation method. The capacity of a DD pile, depending on its type, is between the capacities of geometrically similar nondisplacement and full-displacement piles installed in the same soil profile. This paper provides an overview of the different types of DD piles and their installation techniques and describes three design methods used in practice. It also compares DD pile capacities obtained with these design methods for two different sites.

Load and Resistance Factor Design of Drilled Shafts in Sand

AbstractResistance factors are developed for drilled shafts for a design method based on soil variables. The uncertainties associated with the design variables and equations were systematically quantified, and Monte-Carlo simulations were performed to obtain the distributions of the shaft and base capacities. Both the base and shaft capacities were found to follow normal distributions, and the applied dead and live loads were assumed to follow normal and lognormal distributions, respectively. Reliability analysis was then performed to obtain the limit state and nominal resistances and loads for a variety of soil profiles and pile dimensions. The optimal dead- and live-load factors were subsequently obtained from the analysis. The optimal resistance factors were then adjusted for use with the load factors recommended by the Federal Highway Administration.

Analysis of Laterally Loaded Piles in Multilayered Soil Deposits

This report focuses on the development of a new method of analysis of laterally loaded piles embedded in a multi-layered soil deposit treated as a three-dimensional continuum. Assuming that soil behaves as a linear elastic material, the governing differential equations for the deflection of laterally loaded piles were obtained using energy principles and calculus of variations. The differential equations were solved using both the method of initial parameters and numerical techniques. Soil resistance, pile deflection, slope of the deflected pile, bending moment and shear force can be easily obtained at any depth along the entire pile length. The results of the analysis were in very good agreement with three-dimensional finite element analysis results. The analysis was further extended to account for soil nonlinearity. A few simple constitutive relationships that allow for modulus degradation with increasing strain were incorporated into the analysis. The interaction of piles in groups was also studied.

Closure to “Load and Resistance Factor Design of Drilled Shafts in Sand” by D. Basu and Rodrigo Salgado

The main points in the discussion by Bengt H. Fellenius seem to be related to the following: 1. Choice of the load at 10% relative settlement as the ultimate pile load capacity; 2. Existence of the limit pile base resistance; and 3. The shaft capacity equation and the variables involved in that equation. Each of the previous points are addressed, but in a different sequence. Point 2 will be addressed first, followed by points 1 and 3.

Response of Laterally Loaded Rectangular and Circular Piles in Soils with Properties Varying with Depth

Continuum-based analyses for laterally loaded piles with rectangular and circular cross sections are presented using solutions that can be obtained quickly without requiring any elaborate inputs for the geometry and numerical mesh. The analysis is developed by solving the differential equations governing the displacements of the pile-soil system derived using the variational principles of mechanics. Parametric studies are performed to investigate the influence of the pile cross-sectional shape, soil layering, pile slenderness ratio, and pile-soil modulus ratio on the response of laterally loaded piles in heterogeneous soil in which the soil shear modulus varies continuously or discretely with depth. The results show that piles with the same second moment of inertia have similar lateral-load response. The lateral responses of piles in two-layer systems were mainly affected by the thickness and stiffness of the top soil layer. Soil layering also influences the lateral response of piles in three-layer soil deposits consisting of two thin layers overlying the third layer. Algebraic equations for estimating the pile-head deflection and maximum bending moment are proposed that can be readily used in design. A user-friendly spreadsheet program is developed as a tool to perform calculations of pile response using the analysis. Numerical examples demonstrating the use of the analysis are provided.

Study on laterally loaded piles with rectangular and circular cross sections

The conventional approach in the design of laterally loaded piles with rectangular cross section involves the simplification of converting the rectangular cross section of the pile to an equivalent circular cross section. An analysis to determine the response of laterally loaded rectangular or circular piles in elastic soil is presented in which this simplification is not required. The analysis is based on the solution of differential equations governing the displacements of the pile–soil system derived using energy principles. The pile geometry and the elastic constants of the soil and pile are the input parameters to the analysis. Using this analysis, comparisons are made between the response of rectangular and circular piles in elastic soil. Based on the proposed solution scheme, a user-friendly spreadsheet program (LATPAXL) was developed that can be used to perform the analysis. In addition, simple equations obtained by regression analysis of the pile head deflection and bending moment profiles are proposed. Examples illustrate the use of the analysis.

Resistance Factors for Laterally Loaded Piles in Clay

Sustainable engineering requires that engineering products are not only socially acceptable, economically feasible, and environmentally friendly, but also safe against all possible serviceability and ultimate limit states. Laterally loaded piles are mostly designed against the serviceability limit state of excessive lateral deflection. This study takes into account the uncertainties associated with the response of laterally loaded piles and focuses on their load and resistance factor design based on the serviceability limit state of excessive lateral deflection. Resistance factors are obtained for laterally loaded piles embedded in clay deposits in which the soil properties are assumed to be random variables. Pile capacities are determined based on a specified allowable lateral deflection at the pile head. The pile load-displacement curves are generated using the p-y method. Model uncertainties and bias factors are incorporated in the analysis. The uncertainties associated with the lateral capacity, for a specified lateral head deflection, are quantified, and the probability distribution of the lateral capacity is determined using Monte Carlo simulations. The applied dead and live loads are assumed to follow normal and lognormal distributions, respectively. First order reliability analysis is then performed using the distributions of loads and capacity to determine the load and resistance factors.