# Determination of Concrete Formwork Removal Time Based on Ultrasound Reflection
## 2 Ultrasound  
Ultrasound has proven very effective in monitoring the hardening of concrete [9, 10, 11]. The transit time between the pulser and the receiver can be easily measured leading to the ultrasonic pulse velocity and eventually to the elastic modulus, even allowing projections to the final compressive strength [12,13]. This is usually conducted in a special mold, where a relatively thin specimen of concrete is cast (a few cm maximum). However, one serious limitation is the attenuation of the fresh material that does not allow the measurement to be applied in thick members. Therefore, reflection measurements have also been utilized [14, 15, 16]. In this case, a pulser introduces an elastic wave into a buffer material that is in contact with concrete. The wave propagates until the interface between the buffer and the concrete. Then, one part of the energy is reflected, and it is captured by the receiver, while another part is transmitted into fresh concrete (see Figure 1a). The ratio between the transmitted and the reflected amplitude depends on the \"reflection coefficient, R\" [17]. R is defined by the mismatch of acoustic impedances \(Z_{1}\) and \(Z_{2}\) of the two media (buffer and concrete respectively), as seen in Equation (1):  
\[R=\frac{Z_{2}-Z_{1}}{Z_{2}+Z_{1}}, \tag{1}\]  
where the impedance, Z for any material is given by  
\[Z_{i}=\rho_{i}\cdot C_{i}, \tag{2}\]  
In Equation (2), \(\rho\) is the density and C is the wave velocity of each material. When concrete is fresh, its impedance is low because of the low pulse velocity, in the order of 500 m/s or less [9,10]. Therefore, initially a quite strong reflection coefficient is expected. Gradually, as concrete hardens and the pulse velocity increases (the final could overpass 4000 m/s), concrete impedance rises towards the one of the buffer material or even higher, depending also on the impedance of the buffer itself. This change in impedance is monitored by the change of the reflected wave that is acquired by the receiver. A typical reflection setup for monitoring of concrete curing can be seen in Figure 1a. This technique has been used in literature producing adequate results for monitoring of hardening. In most cases, the reflection coefficient development resembles the actual S-shaped hydration curve as seen in Figure 1b and is well correlated to the development of strength [18]. The choice of the buffer material is of paramount importance as pointed out in literature [14; 19]. If a very stiff buffer is used, then its impedance would always be much higher than the one of concrete (even hardened) limiting the sensitivity of characterization. Setting time of cement pastes and concretes has been determined by high-sensitive, low-impedance buffers such as polymethyl methacrylate (PMMA) [20] and high impact polystyrene (HIPS) [14]. While an S-shaped reflection curve such as Figure 1b allows the global monitoring of the hydration, it does not provide an unambiguous point of reference when the demolding should be conducted. To highlight the adequate moment, in this work the buffer material was suitably \"engineered\" and, specifically, it was designed so that its mechanical impedance matches the necessary impedance of concrete for safe demolding. This allows demolding when the reflection, as monitored by the receiver, drops to zero or a minimum point. When the impedances of the two media are similar, in theory, no reflection is expected (\(R=0\)) and the transmission coefficient should be equal to 1. Practically, this means that the reflected wave amplitude will undergo a minimum at that point, see Figure 2. As the concrete continues to harden, its impedance will overpass the one of the buffer, and the reflection coefficient will start rising again in absolute value. This way the characteristic minimum point in the reflection amplitude vs. monitoring time curve, will allow easier determination of the safe time for demolding.