Mixing sand into clay soil improves its drainage.
Don't add sand to clay to "loosen" it. In the amounts anyone actually adds, the clay fills the gaps and you get a denser, worse-draining mix. Work in compost and mulch instead; organic matter is what builds the structure that drains.
What is actually known
A modest amount of sand in clay does the opposite of what is intended. The fine clay fills the gaps between the sand grains, giving a dense, poorly-draining mix closer to concrete than to loam. To actually shift the texture you would need sand in huge volumes (over half by volume), which is impractical for a bed. What does open clay is organic matter. Compost and mulch build aggregate structure and the pore space that drains. (Whether a gravel layer helps a container drain is a separate and more equivocal case; here the mechanism, clay filling the pore space between the sand grains, is well established.)
The evidence
Evidence: checked against 1 source in the research-based literature.
The source
If you mix sand into clay, the clay particles will fill in all the open spaces between the sand particles and often the clay will act as a glue sticking all particles together, ultimately resulting in a more dense soil
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Milpa Gardens. “Mixing sand into clay soil improves its drainage.” Evidence grade: Refuted. https://milpa.garden/beliefs/sand-clay-soil-improve-clay-drainage/
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