Analytical Solution for Consolidation of Soft Soil with Partially Penetrated Stiffened Deep-Mixed Columns under an Embankment
Publication: International Journal of Geomechanics
Volume 24, Issue 6
Abstract
Stiffened deep-mixed columns (SDM columns) have increasingly been used to reinforce soft soils. When an embankment is constructed on a thick saturated soft clay, partially penetrated SDM columns are usually adopted. However, limited studies have been carried out to investigate the consolidation characteristics of thick soft soil with partially penetrated SDM columns. This paper conducted a theoretical analysis of the consolidation problem in soft soil with partially penetrated SDM columns under an embankment load. Two types of SDM columns were considered. The length of the outer deep-mixed (DM) column is equal to the length of the core pile or longer than the core pile length. After the load share effect of the core pile was considered under one-dimensional (1D) consolidation, the complex two-dimensional (2D) consolidation problem was transformed into a simplified layered consolidation problem, where equivalent consolidation coefficients were utilized. The effectiveness of the developed solution was confirmed by comparing it with the outcomes from a three-dimensional (3D) finite-element analysis. A systematic investigation was conducted to analyze the consolidation properties of this composite ground, which led to practical recommendations for its application. To validate the proposed solution further, it was implemented in a centrifugal model test that involved an embankment that was supported by partially penetrated SDM columns. The predictions made by the solution aligned well with the actual measurements, which indicated a high level of agreement.
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Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors appreciate the financial support provided by the National Natural Science Foundation of China (Grant No. 42372317), the Shanghai Sailing Program (Grant No. 23YF1418400), and the Shanghai Science and Technology Development Funds (Grant Nos. 22ZR1466600 and 22ZR1447100).
Notation
The following symbols are used in this paper:
- Ac, Ap, As, A
- cross section area of DM column, core pile, surrounding soil, and influence zone;
- Am, Bm, Cm, Dm, Xm, Ym, Zm
- polynomial;
- Cvk, Cv2
- equivalent consolidation coefficients of Region k;
- Esk, Ec
- constrained modulus of soil in Region k and DM column;
- h1, h2, h3
- thickness of the three regions;
- kvk, khk
- soil permeability in vertical and horizontal directions in Region k;
- nk, mk, ak, bk, ck, Yk, θk, ξk
- ratio used in derivation;
- R(t)
- function used in derivation;
- rc, rp, re
- radius of DM column, core pile, and influence zone;
- SCR
- stress concentration ratio of core pile;
- overall average consolidation degree of soil in terms of excess pore water pressure;
- average excess pore water pressures of the soil in Region k;
- αp, αc
- area replacement ratio of core pile and DM column;
- γw
- unit weight of water;
- vertical strain;
- λm
- eigenvalues;
- average stress on the composite soil of DM column and surrounding soil, average stress on the core pile, and total applied stress;
- average vertical stress within the soil in Region k and column;
- ultimate load on the composite soil; and
- initial excess pore water pressure at a depth z.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 6 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jun 1, 2023
Accepted: Nov 20, 2023
Published online: Mar 18, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 18, 2024
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