study on the effectiveness of … of micropiles are also very frequent and variable. carried out as...

1. INTRODUCTION

In Slovakia, soil nailing is in current use to reinforce and to stabilise excavations, road cuts or natural slopes. In the majority of cases, soil nails are made as grouted steel bars, installed under 10° – 20° from horizontal. They are considered to work in tension, especially. Applications of micropiles are also very frequent and variable. Carried out as grouted steel tubes, for example, they can be used to underpin foundations, stabilise a road cut or in a form of retaining micropile wall. Depending of the use, they can be working in tension, shear, or coupled tension-shear and bending (Hulla et al., 2002).Available Czech computer programme GEO 4, commonly used by Slovak engineers, is based on a German design practice of soil nailed walls and any additional forces in nails are taken into account but tensile ones. French computer code Talren, developed by the company Terrasol, is based on a French theory of soil nailing

(Schlosser et al., 1994). Tensile and shear forces are calculated in nail intersection points with a failure surface and then included into equations of the stability analysis. Amount of mobilised shear forces depends on different factors, of which the inclination angle and moment of inertia of the bar are the most important ones.Based on a simple case, a parameter study on the influence of effectiveness of introduced reinforcing elements on the global safety factor is presented in the paper. The aim is to study, using the code Talren, how the reinforcements of different types are working when installed in different positions.

2. DEFINITION OF SLOPE AND SOIL DESIGN PARAMETERS

As shown in Figure 1, the original slope is 10 m high and 20 m long without any reinforcing elements. Ground conditions are

M. MATEJČEKOVÁ

STUDY ON THE EFFECTIVENESS OF REINFORCING ELEMENTS BY TALREN

KEY WORDS

• soil mechanics, • foundation engineering, • soil nailing

ABSTRACT

An example case of reinforced slope is presented. Two types of reinforcement are considered – soil nails and micropiles. Both types of reinforcements consist of grouted boreholes with inserted steel elements. Attention is paid on how the slope global safety factor Гmin changes in function of the inclination of the reinforcing element and of its moment of inertia varying. Stability analyses are provided by the French computer code Talren.

Miroslava Matejčeková, Ing., lecturerResearch field: Geotechnics, stability analysis Dept. of GeotechnicsFaculty of Civil Engineering of the Slovak University of Technology in BratislavaRadlinského 11, 813 68 Bratislava, SlovakiaE-mail: [email protected]

2007/2 PAGES 13 – 19 RECEIVED 16. 1. 2007 ACCEPTED 4. 6. 2007

2007 SLOVAK UNIVERSITY OF TECHNOLOGY 13

matejcekova_01.indd 13 26. 6. 2007 14:10:30

14 STUDY ON THE EFFECTIVENESS OF REINFORCING ELEMENTS BY TALREN

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homogeneous, consisting of sandy soil of some cohesion. There is no groundwater, so the stability will be considered in dry soil conditions.Design parameters of the soil which are required for Talren calculation are given in Table 1.Limit lateral pressure allowed for the soil is given by pressuremeter limit plim. Modulus of soil reaction ES which is necessary to analyse soil/structure interaction is calculated by Ménard’s formula recommended in Talren manual. The formula (1) is based on the soil/structure interaction theory for structural elements of diameter

less than 60 cm (Frank, 1995) and both soil nail and micropile satisfy this condition.

(1)

where EM is the Ménard’s pressuremeter modulus of the soil = 5,9 MPa;

α is the Ménard’s rheological coefficient = 1/3 for this type of soil and the given set of measured pressuremeter parameters.

3. STABILITY OF UNREINFORCED SLOPE

The stability of unreinforced slope was evaluated by Talren using Bishop’s simplified method. In the first step, the slope background surface was considered as free, without any surface loading. Corresponding minimum of the global factor of safety Гmin was of 1,56. In the second step, a surface loading of 30 kPa was applied at the slope crest. Thus the minimal safety factor dropped slightly down to 1,47. In both presented states, condition of stability will be satisfied.Results of the two calculations are shown in Figure 2.

3. STABILITY ANALYSIS OF REINFORCED SLOPE

Although the safety factor was found being high enough, it would be interesting to investigate the effect of the reinforcement on global

Tab. 1 Design parameters of the sand

ParameterUnit

weight

Angle of internal friction

CohesionLimit lateral

pressure

Modulus of soil

reactionSymbol γ φ c plim ES

Unit kN.m-3 ° kPa kPa kPaValue 19 30 4 860 16320

Fig. 1 Geometry of the slope

b

Fig. 2 Results of stability analyses: a – unloaded slope, b – slope with the surface loading.

a


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15STUDY ON THE EFFECTIVENESS OF REINFORCING ELEMENTS BY TALREN

stability of the slope. Hence in the following steps, stability has been studied when different types of reinforcing elements are installed: soil nails as the first solution, and micropiles as the second. Whereas the borehole diameters may be kept of the same size in each case, the moment of inertia of a tubular micropile bar is bigger than that of a nail bar with a circular cross-section. The same number of input data required by Talren should be defined for the two solutions. They are presented as follows:

a) Tensile yield strength TR (kN):

(2)

where fy is the yield stress of the steel (kPa), Asteel is the cross-sectional area of the bar (m2).

b) Horizontal spacing of the reinforcement ESP (m);c) Coordinates at the head of the reinforcement [X ;Y];d) Total length of each reinforcement LL (m);e) Angle with respect to the horizontal axis (positive counter

clockwise) ANG (°);f) Width of the base of diffusion for the forces at the point of

application LB (m);g) Diffusion angle for the forces ALB (°);Input data from e) to g) are illustrated in the following figure.h) Equivalent radius (giving the external perimeter of the grout

or the borehole radius (parameter used to calculate the soil/reinforcement friction) RE (m);

i) Rule that indicates how to estimate the forces IND: = 1 : the tensile force is computed and the shear force is imposed,

independent of the tensile force, = 2 : zero tensile force and the shear force is computed, = 3 : the tensile and shear forces are computed as a function of the

critical angle (ANGC); j) Imposed shear force RCIS taken as 0 kN when reinforcing

element is supposed to work in traction only;

k) Minimal length of the nail beyond the failure surface so that the shear force is taken into account;

l) Maximal moment of the reinforcement MMAX (kNm); Here the user can choose how to calculate the maximal bending moment allowable for the reinforcements, and whether plastic or elastic approach will be used in design. Then the moment MMAX can be taken either as the maximal elastic moment Me (only the first fibre is plasticized), or as the maximal plastic moment Mp (plastic state is attained in the whole cross-section). Corresponding stress states are illustrated in Figure 4.

Maximal elastic moment is calculated by

(3)

where I is the moment of inertia of the steel section (m4); grouted part of the section usually is neglected because its quality may be doubtful,

zmax is the maximal distance in the neutral axis in the cross-section = bar radius (m).

Maximal plastic moment Mp, however, is often considered as an idealization. In practice, it can never be fully reached because of the previous rupture of the most tensioned/compressed fibre. In addition, the multicriteria used to evaluate the work of a soil nail according to the French design theory often are dominated rather by the failure in the soil than by the failure of the steel section. In result the plastic moment is given as follows:

(4)

where A is the cross-sectional area (m2), z is the transversal coordinate in the cross-section (m),

Fig. 3 Illustration of selected input data: AZ – active zone, PZ – passive zone

possible failure surface

reinforcement inclination angle

PZAZ force diffusion base

force diffusion angle

Fig. 4 Illustration of possible stress states in a steel bar, d – diameter of a steel bar



2007/2 PAGES 13 — 19

SA/2 is the static moment of the half of section related to the mean axis of the full section (m3).

Related formulas for both circular and tubular cross-section are given in Table 2.m) Rigidity of the inclusion EI (kN.m2);n) Critical angle for soil/nail interaction ANGC (°) which usually is

comprised between 0° and 5° for the current sections (Schlosser, 1994);

o) Interaction of the reinforcement head IENC:(If IND = 1 or 3) = 0 or 1: pull-out force computed on the portion of the

reinforcement outside the active zone, = 2 or 3: the pull-out force is the minimum between the forces

mobilized in the portion of the reinforcing element inside and outside the active zone,

(If IND = 2 or 3) = 1 or 3: the shear force is computed on the portion outside the

active zone, = 0 or 2: the shear force is the minimum between the forces

mobilized in the portion of the reinforcement inside and outside the active zone;

p) Limit of the unit skin friction QS (kPa) resulting from the soil/element interaction.

The two individual parameter studies presented here after contain, in the first step, a solution that copies the usual practice (soil nails inclined by 15° from the horizontal and micropiles installed on the vertical). In the second step, the own parameter studies are presented getting varied the inclination angle of the reinforcing element.

3.1 Reinforcing of the slope by soil nails

The first solution is made by reinforcing the slope by soil nails. In this case the surface load was kept in place for the study. Three rows of nails with 10 cm in borehole diameter are arranged with horizontal spacing of 2 m. Total length of each nail is 10 m, and diameter of steel bar is d = 30 mm (circular cross-section). In the first calculation the nails are inclined by 15° from horizontal as shown in Figure 5. As a basic arrangement, this presents a current value of nail inclination used in practice (10° ~ 20°). Set of other input data necessary for the calculation is given here after:• TR = 350 kN (fy = 500MPa);• RE = 0,05 m;• ANG = 15°;• LB = 0,2 m;• ALB = 20°;• MMAX = Mp = 2,25 kNm;• IND = 3 and IENC = 1;• EI = 8,35 kN.m2 ;• QS = 75 kPa.

Method after Bishop was used in the stability analysis. Resulting minimum of the global safety factor was found Гmin = 1,79. In the next step, calculations were pointed at the investigation of influence of different input data on the stability result Гmin:

Tab. 2 Characteristics of the circular (nail) and tubular (micropile) cross-section

Type of section

CIRCULAR TUBULAR

Scheme

Extreme coordinate

Moment of inertia

Static moment of the half-section

Elastic moment

Plastic moment

Fig. 5 Basic arrangement of soil nails


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• nail inclination angle with respect to the horizontal ANG = ‹ 0°, 60°›,

• variable combination of design hypotheses IND and IENC :- T-ex and C-zero: Tensile (pull-out) force is computed on the

portion of the nail outside the active zone and the shear force is defined by 0 kN (soil nails are working is tension only).

- T-ex and C-ex: Tensile (pull-out) force is computed on the portion of the nail outside the active zone and the shear force is taken as mobilised in the portion of the nail and outside the active zone.

- T-min and C-ex: Tensile force is the minimum between the forces mobilised in the portion of the nail inside and outside the active zone, and the shear force is taken as mobilised in the portion of the nail and outside the active zone. This option is only suitable when nail heads are not fixed to the shotcrete facing of the soil nail wall.

- T-zero and C-min: Tensile force is defined as 0 kPa and the shear force is the minimum between the forces mobilised in the portion of the nail inside and outside the active zone (nails are working in shear only).

The Figure 6 shows how the global safety factor of the slope Гmin depends on the given nail inclination angle. Red line presents the initial state of unreinforced slope loaded at the crest that gave Гmin = 1,47 in part 3 (Figure 2b).We can see that the use of design hypotheses {T-ex ; C-0} and {T-ex ; C-ex} gives the highest values of safety factor. The contribution of mobilised tensile forces to the stability was the most important for ANG = 20° to 50°, in particular. This was of 1,88 which means that the stability has increased by nearly 28 % from the initial state. The third one of design hypotheses {T-min; C-ex} leads to

almost the same value of safety factor as the previous options when ANG is from the interval ‹ 5°, 35°›. This means that there is not any important difference between the uses of these three design hypothesis for the inclination angle currently applied in soil nailing practice. On the other hand, for ANG = ‹ 0°, 5°› and ‹ 35°, 60°› calculations employing this type of the theory result in lower Гmin. This may be related to variation of the critical failure surface resulting in a different value of the minimal pull-out force accounted in the calculation. When the fourth design option {T-0; C-min} is used, no tensile forces help stabilise the slope. In this way, amount of benefit from the shear forces can be directly examined. Moment of bar inertia plays an important role when reinforcements are subjected to shear and bending. Circular bars of 30 mm in diameter used for soil nails have rather small moment of inertia. Resulting shear forces get the maximal Гmin of 1,53 when ANG = 60°. Maximal calculated shear force is 9,15 kN per nail. Regarding the initial state, the overall benefit from shear forces does not exceed 4 % and can be neglected in the majority of current soil nailing projects. Such a tendency has already been found in previous comparative studies using the French design approach (Matejčeková, 2003; 2005).

3.2 Reinforcing of the slope by micropiles

The actual solution has been slightly modified from the previous one. Soil nails are replaced by micropiles of tubular cross-section and thus higher moment of inertia. Tubular cross-section 108/16 mm has 108 mm in external diameter, 76 mm in internal diameter and the thickness of 16 mm. The total length and spacing of reinforcing elements has not been changed.In the first step (basic arrangement) which copies the current real solution, the inclination angle was taken by 90° which makes the micropiles act as soil dowels. Moreover the surface loading was removed in this case, and so the initial state is that with Гmin = 1,56

Fig. 6 Dependence of the minimal safety factor on the inclination angle through different design hypotheses.

Fig. 7 Solution with micropiles 108/16 – basic arrangement.

{T-ex; C-0}{T-ex; C-ex}

{T-min; C-ex}

{T-0; C-min}

initial Гmin

Min

imal

fact

or o

f saf

ety

Г min

Nail inclination angle ANG (°)



2007/2 PAGES 13 — 19

(Figure 2a). The basic arrangement is illustrated in Figure 7. It leads to the safety factor of 1,98, so the stability increase of 27 % due to the existing micropiles. Set of other input data necessary for the calculation is given here after:• TR = 2310 kN (fy = 500MPa);• RE = 0,075 m;• ANG = 90°;• LB = 0,2 m;• ALB = 20°;• MMAX = Mp = 68 kNm;• IND = 3 and IENC = 1;• EI = 1059 kN.m2 ;• QS = 75 kPa.

In the second step, the main interest was paid on the dependency of the global safety factor on the reinforcement inclination angle ANG again. This has been varying from 60°to 90° with regards to horizontal. Results obtained using different options (combinations of IND and IENC criteria) are presented in Figure 8.Results presented graphically indicate that more the inclination angle is bigger, less the tensile force mobilisation helps stabilise the slope. Tensile forces are helpful up to the ANG = 80°, further they can be neglected due to the zero value. For ANG = ‹ 80°, 90°› the micropiles are working essentially in shear. Whereas the moment of inertia of the micropile is rather high (the flexural rigidity EI is 127 times higher than the rigidity of the soil nails presented above), we can see that the mobilised shear forces play an important role to increase the stability of the slope. For the micropile inclination angle of 60° and the third design option {T-0; C-min} the increment of safety factor ΔГmin makes 23 %. For 90°,

this improvement rises up to 27 % and the corresponding shear force mobilised in the reinforcing element is 61,38 kN.

3.3 Comparison of the two solutions in identical conditions

In order to compare the two cases, both soil nailing and micropile solution have been recalculated using the {T-ex; C-ex}-option (tensile forces are computed on the portion of the nail outside the active zone and the shear forces are taken as mobilised in the portion of the nail and outside the active zone). Inclination angle has been varying from 0° to 90° with regard to horizontal. There was no surface loading on the slope crest, so the safety factor of reference was 1,56 in both two cases. Calculated in this way, the cases are different each from another only by the strength parameters of the reinforcement, e.g., yield strength, maximal plastic moment and flexural rigidity. Positive contribution of reinforcing elements to the slope stability in function of the inclination angle is illustrated in Figure 9.We can see that the solution by micropiles is more effective than the solution by soil nailing. This tendency is evident for the inclination angle more than 20°, in particular. Maximum of the minimal global safety factor Гmin was achieved when ANG ~ 35° (soil nails) and ANG ~ 50° (micropiles). This arrangement corresponds to the highest values of mobilised tensile forces due to skin friction in reinforcing elements which are determined by their external diameters. When the inclination angle further increases, mobilised tensile forces decrease down to zero (ANG = 80°). In nearly vertical or vertical nails and micropiles, respectively, no tensile forces are mobilised and reinforcing elements are working in shear only. Shear forces taken into account were 9,15 kN per soil nail and 61,38 kN per micropile.

Fig. 8 Dependency of the minimal safety factor on the inclination angle through different design hypotheses.

Fig. 9 Dependency of the minimal safety factor on the inclination angle of different reinforcing elements.

{T-ex; C-min}{T-min; C-min}{T-0; C-min}initial Гmin

Min

imal

fact

or o

f saf

ety

Г min

Micropile inclination angle ANG (°)

soil nail dbar = 30 mm

micropile 108/16

initial Гmin of unreinforced slope

Nail/micropile inclination angle ANG (°)

Min

imal

fact

or o

f saf

ety

Г min


2007/2 PAGES 13 — 19


4. CONCLUSIONS

Through the parameter study, we can see how differently various types of reinforcing elements act to stabilise the slope. Allowable forces depend not only on the soil and structure strength, but also on the mutual arrangement of structural elements and the ground which is determining for soil/structure interaction. Mobilisation of tensile and shear forces is strongly influenced by the rigidity of cross-section and the inclination angle of reinforcing element.In current design situation, in our geotechnical practice, contribution of shear forces in soil nails is neglected. The study has confirmed that there may be a small reserve in the behaviour of reinforced slope which is not usually taken into account in the design, but can explain some real cases where the slope did not failed under an additional loading. In the actual case example, dependency of slope safety factor on the reinforcement inclination was shown. Presented results illustrate,

however, only one theoretical case and are valid in conditions mentioned in the article.In real cases soil nailing often is applied as a solution for steep slopes and so the shear force contribution ratio might be different. As, in this case, the best nail ”work” is observed when this last is inclined by 30° ~ 40° from the horizontal, it can be attained near 10°~ 20° in steeper slopes. This may confirm the usual solutions adopted in our current practice.

ACKNOWLEDGEMENT

The author thank the Grant Agency of the Slovak Republic, VEGA (Grant No. 1/0320/03) for supporting this work as well as ARCADIS ESG France to supply the computer code Talren for purpose of this comparative study.

REFERENCES

• Frank, R. (1995) Fondations profondes, Extrait de collection – Construction C 248, Technique de língénieur, Paris, 46 p.

• Hulla, J. – Turček, P. – Baliak, F. – Klepsatel, F. (2002) Predpoklady a skutočnosť v geotechnickom inžinierstve, Jaga, Bratislava, pp. 185-191.

• Matejčeková, M. (2003) Porovnanie metód posúdenia klincovaného svahu (Comparison between design methods for nailed wall), Diploma thesis, Slovak University of Technology in Bratislava, Department of Geotechnics, 99 p.

• Matejčeková, M. (2006) Design of soil nailed walls, Dissertation thesis, Slovak University of Technology in Bratislava, Department of Geotechnics, 164 p.

• Schlosser, F. et al. (1994) Recommandations Clouterre 1991 pour la conception, le calcul, léxécution et le contrôle des soutčnements réalisés par clouage des sols, Paris, Presses de lÉNPC 1994, 268 p.

• TERRASOL: Le Manuel Talren 97. Online version, Url: http://www.terrasol.com, Logiciels.


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