In 3 Nephi 8 we read about the destruction that occurred when Jesus died which included earthquakes, broken cities and darkness.
Interestingly, there are traditions recorded by Mariano Veytia (only recently translated into English) from native Mexicans which fit this description in the exact same year as Christ dying:
These natives indicate another singular event in their histories with great exactness, which later served them as a fixed era for their chronological calculations. They say that 166 years after the correction of their calendar, at the beginning of the year that was indicated with the hieroglyph of the House in the number ten, being a full moon, the sun was eclipsed at midday, the solar body being totally covered, such that the earth became darkened so much that the stars appeared and it seemed like night, and at the same time an earthquake was felt as horrible as they had ever experienced, because the stones crashing against one another were broken into pieces, and the earth opened up in many parts. Confused and bewildered, they believed that the end of the third age of the world had already arrived, which, according to the predictions of their wise men in Huehuetlapallan, should end in strong earthquakes, in whose violence many living people would perish, and mankind would suffer the third calamity; but the earthquake ceasing entirely and the sun once again being uncovered perfectly, everyone was found to be whole, without any living persons having perished, and this caused them such great wonder that they noted it in their histories with singular care.
Following these calculations, and adjusted to the comparison of the tables, this event should be placed in the year 4066 of the world, which was indicated with this character as can be seen in the tables, and precisely 166 years after the adjustment of the calendar; and because of the circumstances surrounding this eclipse and earthquake, it was impossible for it to be any other than that which was observed at the death of Jesus Christ Our Lord, having suffered it in the thirty-third year of his age, and so it seems that the incarnation of the Word should be placed in the year 4034 of the world, which the Indians indicated with the same hieroglyph of the House in the number 4, and I have noted it that way in the tables, and with this calculation following the chronological order that they observed, counting the years from one memorable event to another with the assignment of the hieroglyph of the year in which they fell, I have been able to coordinate it perfectly with our years in the year 1519, in which Cortez landed at Veracruz, as will be seen in the discourse of this history– Ancient America Rediscovered, translated by Ronda Cunningham, compiled by Donald W. Hemingway and W. David Hemingway (Springville, Utah: Bonneville Books, 2000).
What are the odds there would be traditions of such destruction in the year Jesus died?