Shear resistance of unreinforced concrete-to-concrete interfaces in codes

The Dutch and European code on precast concrete products and floor plates for floor systems, ([4]

NEN-EN 13747+A2, 2011) states: “The design shear stress at the interface should satisfy 6.2.5 of EN 1992-1-1:2004” ([4], para. D.1 General).

([5] NEN-EN 1992-1-1+C2, 2011) art. 6.2.5 describes the shear resistance of an unreinforced concrete-to-concrete interface as follows:

𝑣_𝑅𝑑𝑖 = 𝑐 ∙ 𝑓_𝑐𝑡𝑑 + 𝜇 ∙ 𝜎_𝑛 ≤ 0,5 𝜈 ∙ 𝑓_𝑐𝑑 Eq. 2.1 Where:

𝑐 is the cohesion factor of the interface

𝑓_𝑐𝑡𝑑 is the design tensile strength of the weakest concrete 𝜇 is the shear friction coefficient of the interface

𝜎_𝑛 is the normal force present perpendicular to the interface ν is a strength reduction factor

𝑓_𝑐𝑑 is the design compressive strength of the weakest concrete

Eurocode 2 (2011) defines the two coefficients, 𝑐 and 𝜇, for different types of surfaces. Four types of surfaces are considered; very smooth, smooth, rough, and profiled.

Table 2.1: Design expressions for interface parameters proposed by EC2, 2011

Surface type cohesion factor (𝒄) shear friction coefficient (𝝁)

Very smooth 0,025 ≤ 𝑐 ≤ 0,10 𝜇 = 0,5

Smooth 𝑐 = 0,20 𝜇 = 0,6

Rough 𝑐 = 0,40 𝜇 = 0,7

Profiled 𝑐 = 0,50 𝜇 = 0,9

The very smooth surface is described as a surface cast against a formwork made of steel, plastic or wood that is specially prepared. The smooth surface is described as being formed by a sliding formwork, formed by extrusion, or a free surface untreated after vibration. The rough surface is described as a surface with a roughness elements of at least 3mm with a spacing of about 40mm. The profiled surface requires cast indentations described in [5] fig. 6.9.

2.1.2 Fédération Internationale du Béton, FIB Model Code, 2010

The FIB Model Code 2010 describes the individual mechanisms that contribute to the shear

resistance of an unreinforced concrete-to-concrete interfaces, namely ([6] fédération internationale du béton, 2010):

- Mechanical interlocking and adhesive bonding

- Friction due to external compression forces perpendicular to the interface

The main parameters decisive for shear resistance of an unreinforced concrete-to-concrete interface that the FIB Model Code 2010 describes are:

- Interface Roughness - Cleanliness of surface

- Concrete strength and concrete quality - Eccentricity of shear force

- State of bond (pre-cracked or not) 2.1.2.1 Interface roughness characteristics

[6] Chapter 6.3.2 describes two interface roughness parameters, the average roughness deviation (Ra) and the mean peak-to-valley height (Rz(DIN)). The average roughness deviation is the most commonly used parameter and represents the average profile deviation from the mean line. While the average roughness deviation is an average along a measurement interval, maximum peak-to-valley height is averaged within a certain number of assessment lengths. [6] formulates the Ra and Rz(DIN) as follows:

𝑅_𝑎= 1

𝑙_𝑚∙ ∫ 𝑦(𝑥) ∙ 𝑑𝑥

𝑙_𝑚

0

≈1 𝑛∑ 𝑦_𝑖

𝑛

𝑖−1

Eq. 2.2

𝑅_{𝑧(𝐷𝐼𝑁)}= 1 𝑚∙ ∑ 𝑧_𝑖

𝑚

𝑖−1

Eq. 2.3

Where:

𝑙_𝑚 is the measurement interval

𝑦_𝑖 is the subsequent height between peaks and valleys 𝑛 is the amount of amplitudes

𝑚 is the amount of assessment lengths (usually one fifth of the measurement interval) 𝑧_𝑖 is the maximum peak to valley height

[6] describes four categories of roughness:

Table 2.2: Roughness category expressions described in FIB Model Code 2010

Category Ra (mm)

Very smooth (e.g. cast against steel formwork) Not measurable Smooth (e.g. untreated, cast against wooden formwork) <1,5 mm Rough (e.g. sand blasted, high pressure water blasted etc.) ≥1,5 mm Very rough (e.g. high pressure water jetting, indented) ≥3 mm

Santos ([8] Santos, P.M.D., 2009) illustrates the average roughness parameter Ra (fig 2.1) and the mean peak-to-valley height Rz(DIN) (fig 2.2).

Figure 2.1: Average roughness deviation of a 2D profile ([8] Fig. III.22)

Figure 2.2: Mean peak-to-valley height of a 2D profile ([8] Fig. III.25) 2.1.2.2 Adhesion

FIB Model Code 2010 describes the interface adhesion (𝜏𝑐) as being reliant on a multitude of parameters. Adhesion only plays part in the interface shear resistance if slip is minimal and the interface is not fully pre-cracked. If the surface roughness is high, a mechanical interlocking effect may occur. This effect decreases with an increase of slip. Note that for smooth surfaces, the adhesion equals zero. The adhesive strength of an interface [7] can be given by:

𝜏_𝑐 = 0,09 ∙ 𝑘_𝑐∙ 𝑓_𝑐^{1 3⁄ Eq. 2.4}

Where:

𝑘_𝑐 is a coefficient for interface roughness, dependent on Ra 𝑓_𝑐 is the cylinder compressive strength of concrete

2.1.2.3 Friction

The interface friction is dependent on compression forces perpendicular to the interface, these compression forces are caused by an external compression force, or clamping forces due to

(activated) reinforcement crossing the interface. [6] Refers to the same friction coefficient 𝜇 as EC2.

[6] Formulates the friction mechanism of the interface shear resistance as:

𝜏𝑓 = 𝜇 ∙ 𝜎𝑛 Eq. 2.5

Where:

𝜇 is the friction coefficient of the interface surface

𝜎_𝑛 is the external compression force perpendicular to the interface 2.1.2.4 Total shear resistance

FIB Model Code 2010 [6] describes the ultimate shear resistance of an unreinforced concrete-to-concrete interface, combining the two mechanisms, as:

𝜏_𝑢= 0,09 ∙ 𝑘_𝑐∙ 𝑓_𝑐^{1 3⁄} + 𝜇 ∙ 𝜎_𝑛≤ 𝛽 ∙ 𝑣 ∙ 𝑓_𝑐 ^{Eq. 2.6} Where:

𝑘_𝑐 is a coefficient for interface roughness, dependent on Ra 𝑓_𝑐 is the cylinder compressive strength of concrete

𝜇 is the friction coefficient of the interface surface

𝜎_𝑛 is the external compression force perpendicular to the interface 𝛽 is a coefficient related to concrete compression struts forming

𝑣 is a reduction factor for the strength of the concrete compression struts

In table 2.3 some collected values for coefficients for the FIB Model Code 2010 design expression (Eq.

3.7) are given [6][7].

Table 2.3: Design expressions for interface parameters proposed by FIB Model Code 2010

Surface preparation Ra kc µ β

fck ≥ 20 MPa fck ≥ 35 MPa

High-pressure water-blasting ≥0.5 2.3 0.8 1.1 0.5

Sand-blasting ≥0.5 0.0 0.7 0.7 0.4

Smooth n/a 0.0 0.5 0.5 0.4

2.1.3 Conclusions

Eurocode 2 (2011) as well as FIB Model Code 2010, describe the shear resistance of an unreinforced concrete-to-concrete interface as a linear function with a constant (depending on a cohesion parameter and the concrete strength), one independent variable (stress perpendicular to the interface), and a slope dependent on a friction parameter (dependent on the interface surface preparation).

To be able to compare these code predictions to experimental research, these three components of the linear function are to be expressed by the experimental research. To be able to re-evaluate the influence of interface surface preparation, a surface roughness quantification method is needed.

Different expressions to describe the shear resistance of a concrete-to-concrete interface are proposed, these propositions are based on experimental research. Shear tests, material tests and roughness quantification methods are required to be able to assess the influence of the material parameters on the shear behavior of a concrete-to-concrete interface.

In document Eindhoven University of Technology MASTER Behavior of unreinforced concrete-to-concrete interfaces under shear loading Croes, L. (pagina 8-12)