Seismic analysis of soil nail performance in deep excavation
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Abstract
Deep excavation is a common part of development to utilize underground space in densely populated areas. Protection of contiguous building and properties is a primary design concern space. Soil nailing is one such technique to exchange conventional retaining system for deep excavation. It will also donate to significant saving in cost and time of construction compared to conventional retaining systems. In this study an attempt has been made to have a deep vertical excavation on ground of 10 m height using soil nail wall. Also studied the enactment of soil nail wall under different nail inclination to horizontal i.e., Ѳ = 0° and Ѳ = 15° with water table. The finite element analysis of soil nail wall was carried to study the behavior of maximum horizontal wall displacement, maximum horizontal nail displacement, base heave, maximum axial force in nail, maximum shear force in nail, maximum bending moment in nail under both static and seismic conditions using PLAXIS 2D. The process of construction is carried out in stages and a value of Global factor of safety (FS_{G}) is maintained above 1.5 to make sure its stability. The length of nail has a major impact on the behavior of soil nail wall system; increase in nail length will increase the FS_{G}. Results of the numerical analysis direct that the use of soil nail wall is desirable to impart stability to retaining systems.
Keywords
Soil nail Horizontal wall displacement Base heave Axial force in nail Shear force Bending momentBackground
Soil nailing is a method in which soil slopes, excavations or retaining wall are passively reinforced by the insertion of relatively slender elementsnormally steel reinforcing bars [1]. Such structural element which offers load transfer to the ground in excavation reinforcement application is called nail. The fundamental concept of soil nailing relies upon two possible mechanisms, both of which donating to improve stability of soil mass: the transfer of tensile forces generated in the nails through frictional interaction between the ground and the soil nail, and the development of shear stress and bending stiffness in the nails as a result of deformation of soil mass [2]. In the accumulation to the aforementioned mechanisms, the soil structure interaction between the facing and the soil helps to restrain displacement, limit decompression during and after excavation, and produce nail head load at the connection between the nail and the facing necessary to develop the force along the nail. The long term performance of soil nailed excavations is a major unknown to those designing the soil nail systems because there are very few over 20 years old [3].
Modeling and analysis

Change in geometry (excavation, fill placement)

Change in soil properties (fill replacement).
Material parameters
The material parameters considered for the analysis of the soil are tabulated in Table 1 [4].
Calculation of axial stiffness (EA) and bending stiffness (EI)
Parameters used for numerical simulation [8]
Parameters  Values 

Soil  
Vertical height of wall H (m)  10 
Nail type  Grouted 
Simulation model  Plane strain 
Element type  15 node 
Insitu soil  
Material model  Mohr–coulomb 
Cohesion c (Kpa)  4 
Internal friction angle Ø{deg}  31.5° 
Unit weight γ [KN/m^{3}]  17 
Elastic modulus E_{s} [Mpa]  20 
Poison’s ratio of soil ν_{s}  0.3 
Grouted nails and facing  
Yield strength F_{y} [Mpa]  415 
Elastic modulus E_{n} [Gpa]  200 
Elastic modulus of grout (concrete) E_{g} [Gpa]  20 
Diameter d [mm]  20 
Drill hole diameter D_{DH} [mm]  100 
Length of nail L [m]  7, 10, 13, 15 
Declination with respect to horizontal Ѳ [degree]  0° and 15° 
Spacing S_{h} × S_{v} [m]  1 × 1 
Facing thickness t [mm]  200 
Material properties for grouted nail
Pameters  Name  Value  Unit 

Material type  –  Elastic  – 
Axial stiffness  EA  228.707 × 10^{3}  kN/m 
Bending stiffness  EI  142.9419  kNm^{2}/m 
Material properties for facing
Parameters  Name  Value  Unit 

Material type  –  Elastic  – 
Axial stiffness  EA  4.4 × 10^{6}  kN/m 
Bending stiffness  EI  1466.74  kNm^{2}/m 
Case studies carried out
The following two cases are considered for Finite Element Analysis of the soil nail wall without water table are as shown below. Soil nails are placed horizontally i.e. Ѳ = 0° and at an inclination of Ѳ = 15° and the construction is carried out in stages at every increment of 20 %. Initially 2 m excavation is carried and followed by insertion of nails and facing, if stability is less, then the nail length is increased to achieve the factor of safety more than 1.5. Further another 2 m excavation is carried and the process is repeated until a depth of 10 m.
Case 1: soil without water table (WOW) having Ѳ = 0°
Global FoS with construction stages
Depth of excavation in meters  Construction stage %  No. of nails  Global factor of safety  

Length of nail  
7 m  10 m  
2  20  2  3.595  – 
4  40  2  2.353  – 
6  60  2  1.844  – 
8  80  2  1.56  – 
10  100  2  1.37  1.529 
Case 2: soil without water table (WOW) having Ѳ = 15°
Global FoS with construction stages
Depth of excavation in meters  Construction stage %  No. of nails  Global factor of safety 

Nail length 7 m  
2  20  2  4.115 
4  40  2  2.714 
6  60  2  2.122 
8  80  2  1.76 
10  100  2  1.52 
Results and discussions
Static analysis: This work is carried out to find the impact of angle of nail inclination for the construction of soil nail wall using “PLAXIS version 8.2” is twodimensional finite element code is used to conduct analysis of deformation and stability.
For dynamic analysis: once the excavation is complete up to 10 m using soil nail wall a dynamic analysis is also carried by applying strong motion record of Upland earthquake (occurred during 20th Feb 1990 at 3.44 pm in South California)
Maximum shear force in nail
It is perceived that the maximum shear force for Ѳ = 0° inclination is less for WOW, whereas it is maximum for Ѳ = 15°. In WOW condition the maximum shear force value for Ѳ = 0° inclination is higher than Ѳ = 15° for 20 % construction stage and later it decrease by from 40 to 100 % construction stage.
Maximum bending moment in nail
The movement of soil mass and the soil mass subjects the soil nails to bending moment and shear force in addition to axial forces.
Static and dynamic analysis comparison
Maximum horizontal displacement in nails
Maximum axial force in nails
Conclusions
 1.
The length of nail has a major impact on the behavior of soil nail wall system.
 2.
Increase in nail length will increase the Global factor of safety (FS_{G}) to certain degree.
 3.
As the depth of excavation increases the displacement of soil nail wall too increases.
 4.
It can be seen that the displacement of wall for nail inclination at Ѳ = 0° is less than Ѳ = 15° up to a depth of 4 m.
 5.
The displacement increases for Ѳ = 0° from 4 to 10 m when compared to nails at Ѳ = 15°. Hence soil nails inclined at Ѳ = 0° is suitable for shallow depths.
 6.
It can be seen that the maximum displacement of the soil without water table condition should have lesser displacement.
 7.
It is also seen that there is not much different in the displacement since the nail length is increased to achieve the global factor of safety above 1.5.
 8.
The maximum displacement of wall is found at the top in both static and seismic circumstances.
References
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