**Non-Deterministic Assessment of Surface Roughness as Bond Strength Parameters between Concrete Layers Cast at Di** ff**erent Ages**

### **Janusz Kozubal 1, Roman Wróblewski 1,\*, Zbigniew Muszy ´nski 2, Marek Wyjadłowski 1 and Joanna Strózyk ˙ 1**


Received: 15 May 2020; Accepted: 30 May 2020; Published: 3 June 2020

**Abstract:** The importance of surface roughness and its non-destructive examination has often been emphasised in structural rehabilitation. The presented innovative procedure enables the estimation of concrete-to-concrete strength based on a combination of low-cost, area-limited tests and geostatistical methods. The new method removes the shortcomings of the existing one, i.e., it is neither qualitative nor subjective. The interface strength factors, cohesion and friction, can be estimated accurately based on the collected data on a surface texture. The data acquisition needed to create digital models of the concrete surface can be performed by terrestrial close-range photogrammetry or other methods. In the presented procedure, limitations to the availability of concrete surfaces are overcome by the generation of subsequential Gaussian random fields (via height profiles) based on the semivariograms fitted to the digital surface models. In this way, the randomness of the surface texture is reproduced. The selected roughness parameters, such as mean valley depth and, most importantly, the geostatistical semivariogram parameter sill, were transformed into contact bond strength parameters based on the available strength tests. The proposed procedure estimates the interface bond strength based on the geostatistical methods applied to the numerical surface model and can be used in practical and theoretical applications.

**Keywords:** concrete; roughness; texture; close-range photogrammetry; bond strength; random field generation; semivariograms
