Word for "partially buried"?

Solution 1:

Settle

To cause to sink, become compact, or come to rest; to move downward; sink or descend, especially gradually. (The American Heritage® Dictionary of the English Language)

They can also nestle into the sand. Nestle implies partially obscuring, or settling into (similar to) a nest.

Ensconced:

To settle (oneself) securely or comfortably. (AHDEL)

Solution 2:

When it comes to partial burial, there can be no more obvious Germanic choice than half-buried, with learnèd Latinate alternatives semi-interred, semi-inhumed, and semi-intumulated available for those faint not of heart nor pen.

All would be grave terms indeed, especially the Latinate ones, and at risk for tenebrous overtones anywhere this side of the lich-gate — and surety of such on its far side.

Solution 3:

Sunk, the past participle of sink.

From Macmillan

2. move to lower level
3. fall/sit/lie down

For example

They sat on the lower part of the beach, sunk in the sand.

Solution 4:

It's not technical, but 'planted' in the sand is the visual I get from your description.