New Design Software for Rockfall Simple Drapery Systems

New Design Software for Rockfall Simple Drapery Systems

Author: Grimod Alberto (Maccaferri Canada Ltd.), Giacchetti Giorgio (Officine Maccaferri SpA)

Abstract

Rockfall drapery systems are commonly used all around the word as a simple, fast and cheap measure to avoid rock falls phenomena, which could threat mine sites, people, roads, railways, and inhabited areas. Drapery systems basically consist of a steel mesh that covers the unstable slope, which is held on the top edge with a longitudinal cable and a suitable number of anchors.

The main goal of this kind of intervention is controlling the falls of the rocks, which are driven toward the bottom with slow velocity. It can be used for the protection of any kind of slope. The falling blocks, typically smaller than 0.6 m, pile up into a trench (or into a “pocket of mesh”) at the bottom.

In comparison to other types of rockfall interventions, the simple drapery is cheaper, and its maintenance is easier, but on the other hand it cannot be considered the most effective solution for the slope stabilization, because its main goal is reducing the falling velocity and not to stabilize the slope.

The design of simple draperies require a precise analysis of the main slope features (height, gradient, morphology, type of instability, nature of the ground (or rock), blocks size and presence of vegetation) in order to avoid damages and stresses on the mesh.

Finally the most problematic design-step is the choice of the most suitable mesh, the top longitudinal cable, and the top anchors type. Because of the highly variable nature of rockfall behaviour these structures cannot be standardized, but they have to be analyzed and designed for each case.

In order to supply a practical tool for designers, who has to find out the best solution, Officine Maccaferri S.p.A. has developed a new software (MacRO 2) fit to define the mesh and the related supporting structure composed by up-slope cable and anchors. The software uses the approach proposed by Muhunthan B. et al. (2005), based on the studies carried out by the US Department of Transportation FHA, the catenary theory for the calculation of the longitudinal cable, and the classical geomechanical approach for the calculation of the top anchors. Even if the method seems quite simple and rough, it is effective and let the designer correctly foresee the materials and the geometrical features to be used on the interventions.

The paper analyses the condition for the simple drapery installation, the main steps for the calculations and presents a case history.

Nevertheless, even if the software allows a quick and simple calculation approach, onsite observations are always recommended in order to achieve a good design, with the ultimate goal of protecting property and human lives.

A real case history will be decribe La Lumbrera.

Introduction

The continuous increasing of the number of number roads, railways, buildings, and other public infrastructure in areas which are geologically unstable requires an extended number of interventions act to secure these zones.

Rockfall protection systems are a key element in the design and maintenance of the mentioned structures and have a direct impact on safety in general.

Taking into account their function, they can be divided in 2 categories:

-  Active protection systems: they are applied directly at the instable zone and their goal is to prevent and control the movement of the rock or soil. In this category it is possible to identify:

o  Soil Nailing: it is generally composed by anchors that do not modify the geotechnical characteristics of the soil (passive anchors), and a superficial structural flexible (mesh) or rigid (spritz beton) facing. From a geotechnical point of view this system is classified as passive since no external forces are applied.

o  Secured Drapery System: it is composed by passive anchors and a superficial structural flexible (mesh) or rigid (spritz beton) facing. From a geotechnical point of view it is classified as passive.

o  Pre-stressed and Tie back anchors: it is a geotechnical active system because the soil reinforcement elements (tie back) modify the soil parameters since an external force is applied to the system.

-  Passive protection systems: they do not affect the process of rock fall and are focused to drive the unstable masses to a specific safety zone, or to intercept and contain their falling; they are generally applied far from the detachment area. In this category it is possible to identify:

o  Simple Drapery System: it consists in a rockfall mesh sustained at the top of the slope by anchors and cables and left free along the entire slope.

o  Rockfall or Debris Flow protection Barriers: structures composed by beam, cables, energy dissipaters and an interception structures able to contain the falling. The barrier is composed also by elements able to anchor the different cables and the posts to the ground.

o  Rockfall or Debris Flow protection Embankments: massive structures generally realized by bi-facial reinforced soil structures.

SIMPLE DRAPERY SISTEM

A simple drapery system consists to install a rockfall mesh along a slope. As mentioned before, the drapery is hung as a curtain, suspended by longitudinal ropes and anchors at the crest (Rc) and toe (Rt).

The anchors are positioned in the crest AC) and toe (AT) of the slope and their distance depends on the design and the prevailing instability conditions at the site. They are commonly located in a line and are fitted with suitable terminations (often eye nuts or plates or similar) to accept the crest rope (RC).

Once the crest anchors and the upper longitudinal cable are installed, the mesh can be fixed to them and left free all along the slope.

Mesh installation at the crest

In the end, the mesh has to be fixed at the bottom as well, in order to form a “big pocket” where the debris can be accumulated.

If the space between the toe of the slope and the infrastructure to be protected is enough, the bottom of the mesh can be left opened, in order to reduce the maintenance costs. In this case a trench or an embankment should be built.

Debris accumulation at the toe of the simple drapery system

This system is usually installed on high rocky slope, where it is almost impossible to adopt secured drapery systems (no cost-effective), rockfall barriers (morphology too much irregular) or rockfall embankments (no space), or when the economical availability is limited and/or the intervention time is short.

Reunion Island (Fra) – more than 40,000 sqm of drapery system were installed in a rocky slope higher than 150 m

Macro 2 Design Approach

The design of simple drapery depends of different variables related to the geometry of the slope, the type of the mesh and the hypothetical debris accumulation on the toe of the system. Nowadays, the only researches carried out to give a design guideline for these applications were done by Washington State Department of Transportation (Muhunthan et al. 2005).

Using these studies and the results obtained from several laboratories and field tests which were carried out, Officine Maccaferri S.p.A. has developed a new software (MacRo 2) able to design the type of mesh, the diameter of the up-slope cable and the steel and geometric (diameter and length) characteristic of the up-slope anchors. This tool allows designer to have a quick and easy, but reliable solution to the problem: often a complex numerical analysis has to be done, but this is not practical for every project, especially if the intervention has a modest size and has to be done in a short period of time (emergency protection).

The equations and the procedures at the base of this new formulation are quite simple and rough, but they give reliable and fast results considering the low accuracy level of the input data.

MESH DESIGN

The simple drapery system is a passive system capable to contain the debris at the bottom of the slope. It has to be designed by taking into account all the weights able to transmit a stress on the mesh:

1)  The proper weight of the chosen mesh;

2)  The weight of the debris accumulated at the toe of the mesh;

3)  External weight like the snow accumulation on the drapery.

These three loads may be described by the following formulas, based on the researched of the U.S. Department of Transportation FHA.

First of all, total load due to the mesh (Wm) has to be defined:

[1]

Where:

-  gm = steel mesh unit weight;

-  Hs =total height of the slope;

-  b = inclination of the slope;

-  d = friction angle between mesh and slope.

It is possible to identify the stress transmitted from the debris to the mesh (Wd) as follows:

[2]

Where:

-  gd = debris unit weight;

-  Hd =debris accumulation height;

-  jd = debris friction angle;

-  Bd = debris external inclination value (Muhunthan equation):

[3]

-  Td = debris accumulation width

The last load acting on the mesh is provoked by the snow thickness above the mesh (Ws). It is considered that for slope with an inclination (b) higher than 60 degrees this load is neglected since the snow cannot be accumulated.

[4]

Where:

-  gs = snow unit weight;

-  ts = snow thickness;

-  js = friction angle between soil and snow (generally equal to 35°)

To design the drapery system at the limit equilibrium state, three safety factors have to be introduced in the calculation to increase the acting forces and decrease the resisting forces:

-  Safety factor reducing the resisting forces:

o  gmts = safety coefficient which reduces the tensile strength of the mesh (≥ 1.0; from the in-situ evidences and the in-situ and laboratory test, this factor would not be lower than 2.0)

-  Safety factors increasing the acting forces:

o  gvl = safety coefficient for the variable loads, like the snow thickness and the debris accumulation (≥ 1.0; suggested value according to the Euro Code = 1.5)

o  gpl = safety coefficient for the permanent loads, like the drapery (≥ 1.0; suggested value according to the Euro Code = 1.3)

The acting and resisting forces at the limit equilibrium state can be calculated introducing the partial safety factor coefficients listed above:

Total stress on the revetment (S):

[5]

Serviceability tensile strength of the mesh (Rm):

[6]

Where:

-  Tm = ultimate longitudinal tensile strength of the mesh (defined by laboratory tests)

The design is satisfied if:

Rm – Sw ≥ 0 [7]

The safety coefficient of the mesh is:

FSmesh = Rm / Sw ≥ 1 [7.a]

As shown in the previous pages the transversal tensile resistance of the mesh can be neglected.

CABLE DESIGN

The mesh is secured on the transversal up-slope cable, which is fixed to the up-slope supports (anchors).

Designer must know the maximum load acting on the drapery (defined in the previous paragraph) and the spacing between the up-slope anchors to calculate the deformation and the stress distribution within the rope. This method uses the principle of the catenary to verify if the tensile strength of the cable is sufficient to support the total weight of the system: Wm + Wd + Ws.

The cable is verified if the following equation is satisfied:

Tcbl / gcbl – Fcbl ≥ 0 [8]

Where:

-  Tcbl = ultimate tensile strength of the designed rope (it depends on the steel grade, the type of core and the diameter of the rope);

-  gcbl = safety coefficient decreasing Tcbl (≥ 1.0; Twlc = Tcbl / gcbl = cable working load limit); [9]

-  Fcbl = maximum tensile strength acting on the cable (calculated with the catenary solution).

The safety coefficient of the cable is:

FScable = Tvlc / Fcbl ≥ 1 [8.a]

Moreover, using this theory is possible to define the maximum length of the rope and its maximum arrow between two anchors.

ANCHORS DESIGN

The anchor’s design may be divided in 2 different steps:

1.  The first takes into consideration the sheared load transmitted from the system, composed by the mesh + cable: design of the anchor diameter;

2.  The second is the definition of the minimum anchor length, which depends on the soil characteristics.

Evaluation of the anchor diameter:

With the catenary theory is possible to determinate the maximum force acting on the intermediate and lateral anchors.

These two forces have to be related to the working shear resistance of the designed anchors;

Sbar(j) – N(j) ≥ 1 [10]

Where:

-  Sbar(j) = working shear resistance of the anchor j:

[11]

-  Ybar(j) = yield load of the steel bar j = ESS(j) sadm(j); [12]

-  ESS = effective area of the steel bar j = p / 4 {[fe(j) – 2 fc(j)]2 – fi2}; [13]

-  fe(j) = external diameter of the steel bar;

-  fc(j) = thickness of corrosion on the external crown;

-  fi(j) = minor diameter of the steel bar;

-  gst = safety coefficient for the steel strength of the bar (> 1.0);

-  N(j) = force that the cable and the mesh develop on the anchor j (calculated with the catenary solution);

-  j = position of the anchor: intermediate or lateral.

The safety coefficient of the different cable may be calculated as follows:

FSanchor(j) = Sbar(j) / N(j) ≥ 1 [10.a]

Evaluation of the anchors length

The evaluation of nail length takes into account the following:

a)  The nail plays an important role because it has to support the entire system. Its length must be deep enough to reach the stable section.