Capítulo 3: 3.1 PRODUCCIÓN VEGETAL
1.0 Manejo del suelo
Figure 2.5 Trend for the berm erosion for the 4 input values of gradation found by Hall and Kao (1991)
In summary, Hall and Kao recognize contrasting effects of the grading on the stability which can find a physical explanation. The stabilizing role of the big stones, if the ratio D85/D15 is sufficiently high, is probably due to the enhanced segregation phenomenon which increases locally the grain-size and the resistance to the wave action. If the grading is narrow, instead, the high porosity (and permeability) of the structure provides a more efficient wave energy dissipation, which means again more stability. As a result, within the investigated range of D85/D15, a value of about 3 gives the least stability.
The above consideration about the narrow grading is in accordance with the general meaning of the results by Van der Meer (1988), who considered values of grading up to 2.5 and included a parameter P ( notional permeability) in his formula for static stability. No analytical insight is provided on the phenomenon, and P has to be assessed by engineering judgement through comparison with some reference cases. However, the proportionality between the stability of a stone and the permeability of the underlying material is confirmed by the outcome of his tests.
2.2.3 Further research and findings of Tørum et al.
More recent investigations of the effect of grading, although limited to a smaller range of values, by means of physical models were carried out by Mansard et al. (1996), van der Meer et al. (1996), Juhl and Sloth (1998) and Tørum et al. (2003), with the latter providing a new empirical formula to describe berm recession (see Par. 2.4).
Mansard et al. (1996) performed laboratory tests to reproduce the stability of riprap exposed to the wave action of a reservoir. The stone-size gradation, expressed in terms of
Stability of wide-graded rubble mounds Chapter 2
ratio between the maximum and minimum mass of the stones, varied between 1 and 10, which correspond roughly to D85/D15 = 1-2. They derived from the measurements that a positive effect on stability is given by a narrow gradation, although for higher values of such parameter the trend of a lower stability is less clear. A similar trend is found by Van der Meer et al. (1996), who investigated gradations up to 2.5 and found for this value a faster damage development with the wave load (but only for a low wave steepness).
In both the test series, the damage parameter assumed was S, defined as the ratio between the eroded cross sectional area and Dn502. This approach is typical for investigations on armour layers, where the number of displaced elements is usually relatively low: the maximum value of S was < 10 in the tests by Mansard et al. and < 20 in the tests by van der Meer et al.
The tests carried out by Juhl and Sloth (1998) at the Danish Hydraulic Institute aimed at analyzing different armour layer solutions for berm breakwaters. Specific tests were intended to study the effect of stone gradation (D85/D15 equal to 1.4 or 1.8) and reduced permeability, the latter being obtained adding fine material in the berm. Such a condition may be representative of the outcome of deficient design or construction, or simply the consequence of a temporary construction road on the berm which was not removed.
In Fig. 2.6 the outcome of the investigation on the permeability is shown in terms of recession of the berm (y-axis) against significant wave height (x-axis).
Figure 2.6 Relation between berm recession and significant wave height found by Juhl and Sloth (1998) for varied permeability
Juhl and Sloth found that the wider gradation and the lower permeability produce similar effects. They deduced that the increase of D85/D15 actually consists of a permeability reduction, resulting in a decrease of the energy dissipation in the berm. In such
Stability of wide-graded rubble mounds Chapter 2
conditions, besides the increase of instability, a significantly larger wave run-up and overtopping was found, with direct influence on the damage of both crest and rear side.
Considering the investigated values of grading (1.4 and 1.8), this conclusion is in accordance with the findings of Hall and Kao.
In order to study specifically the recession of the berm of breakwaters, Tørum (1998) collected the data relative to many recent laboratory test series, including the ones from Juhl and Sloth (1998), and carried out additional tests at SINTEF (the Norwegian Foundation for Scientific and Industrial Research). He found a considerable scatter in the test results, probably because the ways different laboratories carry out tests are not consistent and/or that some relevant parameters are overlooked (Tørum et al, 2003).
Despite of this, Tørum was able to derive a 2nd degree polynomial fit (Eq. 2.3) which related the recession to the stone diameter, the significant wave height and the mean period, to be used as a design equation at least in a conceptual design phase.
2 representation of the intensity of the wave attack for dynamic stability, is defined as:
0 0 polynomial fit, was modified with the introduction of terms accounting for stone-size gradation and water depth: in particular, the importance of D85/D15 was suggested by the earlier findings by Hall and Kao (1991) and Mansard et al. (1996). The term involving the gradation was obtained as a 2nd degree polynomial fit, based on some of the SINTEF tests by Tørum and some of the DHI tests by Juhl and Sloth (1998).
The resulting formula is given in Par. 2.4 (Eq. 2.8). Only the quadratic term which takes into account the grading is reported here:
2 Eq. 2.5), being equal all the other parameters.
Stability of wide-graded rubble mounds Chapter 2