In many application areas such as pavement engineering, the phenomena are complex, and as a result, we do not have first-principle models describing the corresponding dependencies. Luckily, in many such areas, there is a lot of empirical data and, based on this data, many useful empirical dependencies have been found. The problem is that since many of these dependencies do not have a theoretical explanation, practitioners are often hesitant to use them: there have been many cases when an empirical formula stops being valid when circumstances change. To make the corresponding empirical formulas more reliable, it is therefore desirable to look for theoretical foundations of these formulas. In this paper, we show that many of such dependencies can be naturally explained by using invariances. We illustrate this approach on the example of pavement engineering, but the approach is very general, and can be applied to other systems as well.

在路面工程等许多应用领域，现象复杂，因此我们没有描述相应依赖关系的第一性原理模型。幸运的是，在许多这样的领域中，有大量的经验数据，并且基于这些数据，已经发现了许多有用的经验相关性。问题在于，由于许多这些依赖关系没有理论解释，从业者往往对使用它们犹豫不决：在很多情况下，经验公式在环境变化时不再有效。为了使相应的经验公式更可靠，因此需要寻找这些公式的理论基础。在本文中，我们展示了许多这样的依赖关系可以通过使用不变性来自然地解释。