Soil Nailing with Flexible Structural Facing: Design and Experiences

Abstract

Officine Maccaferri has developed BIOS, a simplified as well as realistic design approach for the calculation of the flexible structural facing of soil nailing. The approach shows that the most important property of this kind of application is membrane stiffness of the mesh. With the procedure of BIOS is possible to reduce the timing of design and get a cost effective intervention. Anyway the designer judgment is required for a better evaluation of the critical factors like the slope morphology, the admissible displacement and settlement, the presence of water and erosion processes.

Appendix: Stability and Displacement of the Mesh

Officine Maccaferri has developed the software BIOS for the automatic computation of the mesh capacity which uses the “two wedge method” for the calculation of the instable soil mass, in the hypothesis that the two wedges lye within the space delimitated by two adjacent nails; in order to maximize the driving force, the software automatically searches the worst wedges combination. It is assumed that the debris develops distributed load on the facing, so that the total force acting shall be (Fig. 6):

$$ {{T}_{{tot}}} = {{T}_1} + {{T}_2} $$

(1)

where:

$$ {{T}_1} = \frac{{\left[ {\left( {{{W}_1} + {{Q}_1}} \right)\cdot \left( {{\rm tan}{{\theta}_1} - {\rm tan}{\rm{phi}} {{^{\prime}}_1}} \right) + \left( {{{U}_1}\cdot {\rm tan} {\upphi} {{^{\prime}}_1} - {{K}_1}} \right)/{\rm cos}{{\theta}_1}} \right]}}{{\left( {1 + {\rm tan}{{\theta}_1}\cdot {\rm tan}{\upphi} {{^{\prime}}_1}} \right)}} $$

(2)

$$ {{T}_2} = \frac{{\left[ {\left( {{{W}_2} + {{Q}_2}} \right)\cdot \left( {{\rm tan}{{\theta}_2} - {{\lambda}_s}\cdot {\rm tan}\phi {{^{\prime}}_2}} \right) + {{\lambda}_s}\cdot \left( {{{U}_2}\cdot {\rm tan}\phi {{^{\prime}}_2} - {{K}_2}} \right)/{\rm cos}{{\theta}_2}} \right]}}{{\left( {1 + {{\lambda}_s}\cdot {\rm tan}{{\theta}_2}\cdot {\rm tan}\phi {{^{\prime}}_2}} \right)}} $$

(3)

where:

• W1 (kN) Weight of wedge 1;

• W2 (kN) Weight of wedge 2;

• Q1 (kN) Overload acting on wedge 1;

• Q2 (kN) Overload acting on wedge 2;

• θ₁ (°) Angle at the base of wedge 1;

• θ₂ (°) Angle at the base of wedge 2;

• U₁ (kN) Resultant of the pressure of the water acting at the base of wedge 1;

• U₂ (kN) Resultant of the pressure of the water acting at the base of wedge 2;

• K₁ (kN) Cohesion force acting at the base of wedge 1;

• K₂ (kN) Cohesion force acting at the base of wedge 2;

• λ_s Slip factor at the base.

Fig. 6

Geotechnical model with wedges

The safety factor is calculated with:

$$ FS = \frac{{{{K}_1} + {{K}_2} + \left( {{{W}_1}\cdot \cos \left( {{{\theta}_1}} \right) - {{U}_1}} \right)\cdot \tan {\upphi} {{^{\prime}}_1} + \left( {{{W}_2}\cdot \cos \left( {{{\theta}_2}} \right) - {{U}_2}} \right)\cdot \tan {\upphi} {{^{\prime}}_2}}}{{{{W}_1}\cdot sen{{\theta}_1} + {{W}_2}\cdot sen{{\theta}_2}}} $$

(4)

In order to calculate ultimate limit state deformation of the mesh, the following initial assumptions apply:

• The deformed shape is divided into three sections (Fig. 5): the first limb, rectilinear, with length X inclined with an angle α with respect to the slope, the angle of which is indicated by β; the second limb, curved, with length (π + α) r that characterises the sack shape of the soil; the third limb, rectilinear, lies on the slope, with the same inclination and a length X − L;

• The second stretched limb is tangential to both the first and third limbs of the mesh;

• The mesh, completely stretched, deforms and reaches a maximum length at the failure limit of not more than:

  $$ {{L}_{{tot}}} = L + \varepsilon \cdot L $$

  (5)

  where:

  • $\varepsilon$ percentage deformation under failure conditions obtained from large scale puncturing tests and tension;

  • L distance of the mesh between two nails in a direction parallel to the slope.

• The area of the section corresponding to the sack is equal to that of the circular sector with an angle at the centre equal to (π + α) and radius r (Fig. 7);

Fig. 7

Geotechnical model with instable soil divided in elemental areas

The area 1 is obtained by resolving the following system of equations:

$$ L + \varepsilon \cdot L = X + \left( {\Pi + \alpha } \right)\cdot r + \left( {X - L} \right) $$

(6)

$$ r = X\cdot tg\left( {\frac{\alpha }{2}} \right) $$

(7)

$$ P = {{T}_{{amm}}}\cdot \frac{{\left( {1 + {\rm cos}\alpha } \right)}}{{sen\beta - {\rm cos}\beta \cdot {\rm tan}\delta }} $$

(8)

$$ P = \gamma \cdot V $$

(9)

$$ AREA1 = \frac{{\left( {\Pi + \alpha } \right)\cdot {{r}^2}}}{2} + X\cdot r - \sqrt {{per\cdot \left( {per - A} \right)\cdot \left( {per - B} \right)\cdot \left( {per - C} \right)}} $$

(10)

with:

$$ per = (A + B + C)/2 $$

(11)

$$ A = \frac{X}{{sen\left( {180 - \beta } \right)}}\cdot sen\left( {\beta - \alpha } \right) $$

(12)

$$ B = \frac{X}{{sen\left( {180 - \beta } \right)}}\cdot sen\alpha $$

(13)

$$ C = X $$

(14)

where:

L (m)	Length of the mesh;
γ (kN/m3)	Unit weight of soil;
β (°)	Angle of inclination of the slope;
ϕ’a (°)	Friction angle of the soil;
δ (°)	Friction angle of the soil-slope interface;
EA (kN)	Axial stiffness of the mesh;
Tmax (kN/m)	Maximum tensile strength of the mesh;
Fsmesh	Factor of safety of the mesh;
Tamm (kN/m)	Permissible tensile strength of the mesh;
ε	Maximum percentage deformation of the mesh.

Area 2 is determined by:

$$ AREA2 = \frac{{{{A}^2}\cdot sen(\theta_1 - \beta )\cdot sen(\beta - \phi ^{\prime})}}{{2\cdot sen(180 - \theta_1 + \phi ^{\prime})}} $$

(15)

Area 3 is the difference between the volume of long-term unstable soil and area 2. The total volume thereby obtained must be compared with the unstable volume under the long-term conditions; if the unstable volume is greater than that necessary for failure of the mesh, the flexible facing will be put at risk.