The Gemara in Masechet Shabbat (73-74) discusses the concept of "Mit'aseik" as it applies to Shabbat, meaning, situations where one inadvertently commits a forbidden act on Shabbat while intending to perform a permissible act. The example addressed in the Gemara concerns an individual who had intended to cut something that had been detached from the ground – which does not constitute a Shabbat violation – and inadvertently cuts grain that was still attached, which is forbidden on Shabbat. The Gemara records Rava's ruling exempting such a person from a sin-offering, because he had not intended at all to perform the forbidden action.
An interesting modern-day application of this Halacha is the question of walking in a public domain on Shabbat with shoes. It very often occurs as one walks that pebbles or sand make their way into his shoes, such that he carries the pebbles or sand as he walks. Of course, one may not carry pebbles or sand in a public domain on Shabbat. Should we then require a person who walks in a public domain on Shabbat to stop from time to time to clean his shoes and rid them of the pebbles or sand that has collected?
Chacham Ovadia Yosef, in his work Yehaave Da'at, Helek 5:23, addresses this issue tangentially amidst his discussion as to whether Halacha obligates one to designate a special pair of shoes on Shabbat. (He rules that one is not required to designate a pair of shoes for Shabbat, but should polish his shoes in honor of Shabbat.) In this context, he cites a comment by Rabbi Chayim Vital (Israel, 1542-1620) who recorded an incident he heard from his mentor, the Arizal (famed Kabbalist, Israel, 1534-1572). The Arizal told that a certain person passed on, and each year he would stand judgment before the Heavenly Tribunal as his soul was considered for elevation in the afterlife. His judgment became progressively stricter from year to year, and among the misdeeds for which he was held accountable was his failure to remove his shoes when walking in the public domain on Shabbat. This clearly suggests that one must, indeed, make a point to clean his shoes from any pebbles and sand as he walks in the public domain on Shabbat. In fact, Chacham Ovadia cites the work "Yafeh La'lev" as recording a practice not to wear shoes while walking in a public domain on Shabbat, due to this concern.
Chacham Ovadia himself, however, disagrees. Firstly, he writes, it is difficult to imagine that there was a custom to walk barefoot on Shabbat. As for the concern that one will carry pebbles and sand in his shoes, Chacham Ovadia presents three arguments for why this would not entail a Shabbat violation. For one thing, walking with pebbles and sand in one's shoes would be classified as "Dvar She’en Mitkaven" – not having intention to transgress. The individual intends to walk, which is, of course, permissible on Shabbat, and has no intention to collect pebbles and sand in his shoes. If pebbles and sand do collect in his shoes, carrying them would constitute "Dvar She’en Mitkaven", which, as we saw, is not considered a Shabbat violation from the Torah. Secondly, carrying pebbles and sand in one's shoes does not represent the standard manner of carrying these objects, and this would therefore fall under the category of "Ke'le'achar Yad" – carrying in an unusual manner. Finally, in virtually all cases, the sand or pebbles that collects in one's shoe does not amount to the minimum quantity required to transgress the prohibition against carrying on Shabbat. Hence, Chacham Ovadia rules that one may walk in a public domain in Shabbat with shoes, and one need not remove his shoes to clean them as he walks.
Summary: It is permissible to walk in a public domain on Shabbat with shoes, even if pebbles and sand collect in one's shoes, and it is not necessary to remove and clean one's shoes regularly as he walks.
