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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 66-80
Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium
Arash SEKHAVATIAN, Asskar Janalizadeh CHOOBBASTI()
Department of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran
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The design of high-rise buildings often necessitates ground excavation, where buildings are in close proximity to the construction, thus there is a potential for damage to these structures. This paper studies an efficient user-friendly framework for dealing with uncertainties in a deep excavation in layers of cemented coarse grained soil located in Tehran, Iran by non-deterministic Random Set (RS) method. In order to enhance the acceptability of the method among engineers, a pertinent code was written in FISH language of FLAC2D software which enables the designers to run all simulations simultaneously, without cumbersome procedure of changing input variables in every individual analysis. This could drastically decrease the computational effort and cost imposed to the project, which is of great importance especially to the owners. The results are presented in terms of probability of occurrence and most likely values of the horizontal displacement at top of the wall at every stage of construction. Moreover, a methodology for assessing the credibility of the uncertainty model is presented using a quality indicator. It was concluded that performing RS analysis before the beginning of every stage could cause great economical savings, while improving the safety of the project.

Keywords uncertainty      reliability analysis      deep excavations      random set method      finite difference method     
Corresponding Authors: Asskar Janalizadeh CHOOBBASTI   
Online First Date: 26 February 2018    Issue Date: 04 January 2019
 Cite this article:   
Arash SEKHAVATIAN,Asskar Janalizadeh CHOOBBASTI. Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium[J]. Front. Struct. Civ. Eng., 2019, 13(1): 66-80.
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Asskar Janalizadeh CHOOBBASTI
Fig.1  Upper bound (Pl) and lower bound (Bel) on ‘precise’ probability (Pro) [18]
Fig.2  Random set. (a) Construction of random set, (b) upper and lower discrete cumulative distribution functions [18]
Fig.3  Upper and lower discrete cumulative distribution function considering spatial correlation [18]
Fig.4  Soil model at Soheil commercial complex project
No. elevation nail/strand inclination wrt horizontal (°) bonded length (m) unbonded length (m) No. of strands prestressing force (Ton)
1 ?2.00 Nail 15 12 ? ? ?
2 ?5.00 Strands 15 8 16 4 60
3 ?8.00 Strands 15 8 14 4 60
4 ?11.0 Strands 15 8 12 4 60
5 ?14.00 Strands 15 8 10 4 60
6 ?17.00 Strands 15 8 9 4 60
7 ?20.00 Strands 15 8 7 4 60
Tab.1  Geometric configuration of Soheil commercial complex excavated wall
parameter value
vertical height of the wall (m) 21.0
face batter (°) 0.0
backslope angle (°) 0.0
yield strength of reinforcement fy (MPa) 400
elasticity modulus of reinforcement En (GPa) 200
elasticity modulus of grout (concrete) Eg (GPa) 21
diameter of steel bar d (mm) 28
diameter of strands (mm) 15
drill hole diameter DDH (mm) 110
spacing Sh× Sv (m × m) for nails 1.5 × 3.0
spacing Sh× Sv (m × m) for strands 3.0 × 3.0
facing thickness (mm) 15
Tab.2  Some detailed information on Soheil complex excavated wall
Fig.5  Definition of We, Be, and Db [36]
Fig.6  An illustration of target functions with different sensitivities with respect to input variable x (after [18])
Fig.7  Relative sensitivity for the deep excavation problem
Soil Information source c, kN/m2 F', o K
Fill materials Geotechnical report 0?4 24?27 10?70
Expert knowledge 2?5 26?29 30?100
Clayey sand with gravel (SC) Geotechnical report 30?45 32?36 50?150
Expert knowledge 40?55 34?37 100?250
Clayey gravel with sand (GC) Geotechnical report 35?50 36?40 150?250
Expert knowledge 40?60 37?42 200?300
Tab.3  Basic variables for material parameters (input values)
Fig.8  Random sets of input parameter: (a) friction angle of the first layer; (b) modulus factor of the middle layer; (c) cohesion of the middle layer and d) friction of the third layer
Run number 1 2 3 4 5 6 7 8
Run Mass prob. Var. Set No. LLLa LLU LUL LUU UUU ULU ULL UUL
1?8 0.5 C2b 1 33.4 33.4 33.4 33.4 48.4 48.4 48.4 48.4
0.5 K2 2 67 67 184 184 184 67 67 184
0.5 K3 1 182 282 182 282 282 282 182 182
Tab.4  Inputs relating to (C21, K22, K31) variables used in deterministic finite difference calculations
Row No. First part Second part
1 1 1 2 1 2 1
64 1 2 1 1 1 1
Tab.5  Permutation matrix of RS-FDM analysis
Fig.9  Range of horizontal displacement of point A (in Fig. 5) in different construction stages. (a) Stage 3 (H=9 m); (b) Stage 4 (H=12 m); (c) Stage 5 (H=15 m); (d) Stage 6 (H=18 m); (e) Stage 7 (H=21 m)
Construction stage Depth of excavation (m) Allowable Ux,A (cm) Pf(min) Pf(max)
3 9 1.8 0 0
4 12 2.4 0 0
5 15 3.0 0 0
6 18 3.6 0 0
7 21 4.2 0 0.21
Tab.6  Pf(min) and Pf(max) for different phases of construction
Expected performance level Probability of unsatisfactory performance
Hazardous 0.16
Unsatisfactory 0.07
Poor 0.023
Below average 0.006
Above average 0.001
Good 0.00003
High 0.0000003
Tab.7  Expected performance level (US Army Corps of Engineers 1997)
Fig.10  Range of most likely values and spread of distribution
Results Horizontal displacement at top of the excavated wall, Ux-A (mm)
Stage 3 Stage 4 Stage 5 Stage 6 Stage 7
Interval of true mean values (Eq. (24)) ?8.4 ↔ 2.0 ?7.0 ↔ 10.6 ?3.1 ↔ 20.2 2.5 ↔ 25.1 9.6 ↔ 33.0
Interval of most likely values ?8.4 ↔ 1.65 ?6.9 ↔ 10.15 ?3.2 ↔ 19.9 2.1 ↔ 23.8 9.6 ↔ 32.7
Tab.8  Lower and upper mean values of true system response
Fig.11  Horizontal displacements of the top of the wall (most likely values and spread of distributions)
Fig.12  Normalized maximum lateral wall movement vs. excavation depth (after [48])
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