## 1 Introduction  
In concrete and cement based structures, the early stage of hydration and the conditions at which curing occurs, influence the quality and the durability of the final products. For instance, as a result of the chemical reactions between water and the cement during hydration, the mixture progressively develops mechanical properties. Final set for the mixture is defined as the time that the fresh concrete transforms from plastic into a rigid state. At final set, measurable mechanical properties start to develop in concrete and continue to grow progressively. The durability and the strength of concrete may deviate from design conditions as a result of accidental factors. Some of these factors are water-to-cement (\(w/c\)) ratio not controlled well and rainfall that permeates the fresh concrete or dampens the forms prior to casting. As such, the development of nondestructive evaluation (NDE) methods able to determine anomalous concrete conditions is very much needed, and has been a long-standing challenge in the area of material characterization. To date, many NDE methods for concrete exist, and some of them resulted in commercial products. The interested reader is referred to the excellent monograph [1] to gain a holistic knowledge of such methods. The most common technique is probably the one based on the propagation of bulk ultrasonic waves through concrete. This approach measures the speed of the waves propagating through the thickness of the test object to determine the elastic modulus using an empirical formula [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. This approach is usually referred to as the ultrasonic pulse velocity (UPV) method. If the access to the back wall of the sample is impractical, the ultrasonic testing is conducted in the pulse-echo mode. A popular commercial system is the Schmidt hammer [11; 12; 13; 14], which consists of a spring-driven steel hammer that hits the specimen with a defined energy. Part of the impact energy is transmitted to the specimen and absorbed by the plastic deformation of the specimen and the remaining impact energy is rebounded. The rebound distance depends on the hardness of the specimen and the condition of the surface. The harder the surface, the shorter the penetration time (or depth) and therefore the higher is the rebound. Despite decades of research and developments, much research is still ongoing [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28] and many interesting works covering a wide spectrum of NDE techniques are being investigated. In this paper, we propose an NDE method based on the propagation of highly nonlinear solitary waves (HNSWs) along a 1D chain of spherical particles placed in contact with the concrete to be tested. These waves are compact mechanical waves that can form and travel in highly nonlinear systems, such as a chain of elastically interacting spheres. The interaction between two adjacent beads is governed by the [PERSON]'s law [29; 30]\(F=A\delta^{3/2}\), where \(F\) is the compression force between the granules and \(\delta\) is the closest approach of their centers. The coefficient \(A\) is equal to \(E\cdot d^{1/2}/[3\cdot(1-v^{2})]\) where \(E\), \(d\), and \(v\) are the modulus of elasticity, diameter, and Poisson's ratio of the spheres, respectively. The most common way to induce a solitary pulse, hereinafter indicated as the incident solitary wave (ISW), is by tapping the first particle of the chain with a particle striker having at least the same mass of the individual beads forming the chain. Some researchers have demonstrated that a piezo-actuator [31; 32] or even laser pulses [33] can be used as well. When the ISW reaches the interface with the material to be tested, the pulse is partially reflected giving rise to the primary reflected solitary wave (PSW). Both ISW and PSW can be sensed either by a force sensor located at the opposite end of the chain or by embedding a sensor bead along the chain. For a detailed description of the underlying basis of HNSWs, see ref. [34; 35; 36; 37].