Uktena cistern — water weight & hydrostatic pressure on masonry walls

The build: the Uktena catchment — a masonry-built cistern in the garage, on the slab, holding collected rainwater. (The Ogua hot tub is its own separate chapter.) The problem: two checks — what the slab under it carries (same method as Ch. 9), and what the water does to the walls (new).

Assumed (replace with real dimensions): interior 4×4 ft, water depth 4 ft, 8" block walls, masonry weight ≈ 4,500 lb (hollow-block estimate; grouted and reinforced runs heavier; cast geopolymer blocks may differ).

Concepts pulled in — new, fluid pressure: hydrostatic pressure. Water pushes sideways like the gravel backfill in Ch. 4, but harder, because it has no internal friction to hold itself up. Pressure = 62.4 pcf × depth, triangular: zero at the surface, maximum at the base.

Check 1 — weight on the slab

Water: 4 × 4 × 4 = 64 cu ft × 62.4 pcf ≈ 4,000 lb (≈ 480 gal at 8.34 lb/gal). Water + masonry ≈ 8,500 lb over the outer footprint (≈ 5.3 × 5.3 ft = 28 sq ft) ≈ 300 psf. Against the 1,500 psf default allowable soil bearing that's about 20%, lighter than the Snawfus (417 psf). Passes, and the Ch. 9 rule still applies: a reinforced pad under it, not a thin residential slab.

Check 2 — water pushing on the walls (the real governing check)

• Pressure at base: 62.4 × 4 ≈ 250 psf
• Thrust per ft of wall: ½ × 250 × 4 ≈ 500 lb/ft, acting 1.33 ft above the base
• Compare Ch. 4: the 2 ft gravel-backfilled gabion wall saw 67.5 lb/ft. Water at 4 ft pushes about 7× as hard — twice the depth (4× the force) and water pushes about 1.85× harder than gravel at the same depth (62.4 vs. roughly 34 pcf equivalent)
• Base moment per ft of wall, worst case with the wall acting as a cantilever off its base: 500 × 1.33 ≈ 665 lb-ft ≈ 8,000 lb-in
• Section modulus of 8" block (7.625" actual) per ft: 12 × 7.625² ÷ 6 ≈ 116 in³
• Bending tension = 8,000 ÷ 116 ≈ 69 psi

Answer

Unreinforced masonry only takes tens of psi in tension (roughly 25–70 psi depending on grout and mortar type; representative order-of-magnitude values, and cast geopolymer blocks need real test numbers). 69 psi sits at or above that ceiling, so the walls can't rely on the masonry alone. Masonry is strong pressed and weak pulled, and water loads it the weak way. Standard answer: grouted cells with vertical rebar plus a horizontal bond beam at the top, sized by a pro. A 4 ft square tank's walls also span sideways between corners, which helps, so the cantilever number is the conservative case, but only if the corners are tied together.

Rules of thumb that fall out: water pushes about 1.85× harder than gravel at the same depth, and doubling the depth quadruples the thrust.

Honest flag — when to call a pro: this is a small cistern. A failure releases about 4,000 lb of water inside the garage, which is the reason to lean conservative. Bigger or deeper cisterns go to an engineer, since thrust grows with depth squared.

Build clarification (Zach)

The Uktena is built from cast moon-eye geopolymer bricks with integrated rebar channels, mortared together. That means the reinforced-masonry answer above is already part of the block design rather than something added later. Three details decide whether it actually works as reinforced masonry:

• Channels filled solid. Rebar only carries tension once it's bonded to the wall, so the channels need to be grouted full, not just have bars dropped in.
• Bars tied into the base. The vertical bars should be doweled into the reinforced pad so the wall base has a real tension path. That base is exactly where the ~69 psi cantilever tension peaks.
• Top and corners tied. A bond beam or continuous horizontal bar at the top, with the corners tied, since the walls also rely on spanning sideways between corners.

Reinforcement check (brick details from Zach)

The brick is about cinder-block size and locks together Lego-style, with mortar as extra securement and channels that take either 3/8" or 1/2" rebar. That's close enough to the 8" block stand-in that the ~69 psi figure holds, so here is the steel it takes.

• Base moment from Check 2: about 8,000 lb-in per ft of wall
• Assumptions: bars centered in the wall (d ≈ 3.8"), lever arm ≈ 0.9d, and steel stress held to 20,000 psi, the TMS 402 allowable stress for Grade 40 or 50 bars (Grade 60 bars are allowed 32,000 psi), which is the right choice for rebar of unknown grade, and a low steel stress also keeps cracks narrow, which a tank wall needs so it doesn't weep
• Required steel: As = M ÷ (fs × 0.9 × d) = 8,000 ÷ (20,000 × 0.9 × 3.8) ≈ 0.12 in² per ft of wall
• 3/8" bar (0.11 in² each): every 8" gives 0.165 in²/ft, passes. Every 12" gives 0.11 in²/ft, borderline.
• 1/2" bar (0.20 in² each): every 16" gives 0.15 in²/ft, passes. Every 12" gives 0.20 in²/ft, comfortable margin.
• Either bar size works. What decides it is how far apart the channels sit in the brick.

Base connection: the wall's own weight gives only about 120 lb/ft of friction (≈ 240 lb per ft of wall × 0.5) against about 500 lb/ft of thrust at the base, so the doweled bars do real work resisting sliding, not just tension. That's the conservative cantilever picture; walls tied together at the corners also carry some of the load as a ring.

Still needed to close the check: the actual channel spacing and brick wall thickness, real strength numbers for the geopolymer brick and mortar, and a pro's sign-off before it holds water.

Open items for a later pass

Actual dimensions, real strength numbers for the geopolymer blocks, an overflow so it can never over-fill, and waterproofing/sealing (not structural, but it affects how the walls perform over time).