Infiltration rate indicate the needed time by different soils to infiltrate an amount of water within a precised area Rainfall is the source of water for naturlation infiltration. so the relation is in  between amount of  rainfall water and the amount of  infiltrated water in aprecised soil type, within time

Dear Evangelos, there is not direct relation between infiltration and rainfall intensity. As mentioned above, the rainfall is a source of water for infiltration. Thus, it can limit the infiltration when there is not enough water for ponding. The infiltration itself is directly related to soil properties, both actual (soil moisture content) and long-term (porosity, texture, pore distribution). I don't think that there is much sense for consideration of crusting during rainfalls of high intensities. The reason is that fine particles are usually run off during storm rainfalls and thus are not available for sealing. We did a lot of rainfall experiments with constant precipitation intensity and the results show that runoff gets stable after some time which means that there is no considerable decrease of infiltration. 

Dear Imadeddin and Vavlav, 

Thank you for your contributions. Let me set the question in a more suitable way: What is the effect of rainfall intensity to groundwater recherge, assuming that the rest vadose zone layers have no impact and we only focus on topsoil? 

Dear Evangelos, the problem is that topsoil is not usually limiting infiltration due to its higher hydraulic conductivity which is caused by higher porosity, root systems etc. Lower layers have usually lower hydraulic conductivities. It all of course depends on conditions in your area of interest.

Infiltration is a soil property. Rainfall intensity is a meteorological parameter. They should not have a direct relationship. However, infiltration is known to be a function of soil moisture content. Since rainfall supplies water to raise soil moisture, there is an indirect relationship. At the beginning when the soil is dry, the infiltration is low. After a rainfall event, the low infiltration starts to increase soil moisture, which leads to a further increase in infiltration. When the soil moisture reaches saturation, the infiltration reaches a maximum. Such process is simulated in the watershed model like WARMF.

There are - ideed - few relationships between rainfal intensity and the infiltration rate. That because infiltration rate is dependent on soil properties as the foregoing repondents underlined. An other important factor is soil cover. In the case of bare soils the splash generated by rain drops energy close the pores and obstruct in this way the absortion capacity of soil, even if its moisture content is very low.  In the case of a covered soil by any type of vegetation, between the soil itself and the reception area is interposed, on the one hand, a layer of litter which absorbs the raindrop energy and generates a "bucket"and, on the other hand, the vegetation cover itself which redistributes and delays also the feeding rate of rainfall. So, soil absortion can be at its higher level, decreased only by soil water content.

This is the starting point of infiltration process. Further, into the soil profile is applied Darcy's law, if you want.

At a watershed scale, the single direct relationship between rainfall intensity and infiltration rate that I know is that of Armand, D.L. (1961) (Fiziko-geograficheskiye osnovy proyektirovaniya seti polezashchitnykh lesnykh polos).   

At a small forested watersheds (under 50 kmp), based on a long period of research in pilot catchments, you can find a relationship between infiltration amount and some other factors in our paper "Research on runoff and sediment transport in small torrential catchments restaurated as part" published in my profile. There, at pages 17, 23, 27, 30 you can see the [4] equation where: F = infiltration amount (mm), h = the precipitation amount (mm), Z = the precipitation retained by vegetation cover (mm), h20 = 20 min amount of precipitation (practically the higher rainfall intensity core) (mm), I15 = antecedent precipitation index (15 days), t = actual duration of the h precipitation. If you need a translation, contact me.

Concerning your supplement to the base question, if you are thinking the rainfall intensity and infiltration rate in terms of speed, you'll see that Vinfiltration

Hi see this paper: 

http://ac.els-cdn.com/S1002007108002141/1-s2.0-S1002007108002141-main.pdf?_tid=7a292fd2-9cfd-11e6-9610-00000aacb362&acdnat=1477652497_73f4f61307a2a889fff2745e3860935f

infiltration  depends on mostly soil factors; type of soil, dry or wet which is attributed to moisture content.

It is a very nice string of discussion. See infiltration is the most dominating link while transformation of rainfall takes place into runoff. Unfortunately it is still very poorly accommodated in so called hydrological modleing. As discussed in above expressions , to the my way of thinking rainfall intensity certainly have ample net effects on soil infiltration. From physical process point of view, it could be expressed as a two fold effect (1) higher intensive rains easily loosen and disturb the soil structure and their particle arrangement which greatly influence entry of rain in soil i..e. instant higher infiltration and so on with consecutive effects (2) higher intensive rains generates higher ponding depths and it again drastically change the ongoing infiltration rate suddenly and may be for a while when intensity is high..