Muddy water dripping from an urban planter box usually means excess water is escaping through the drainage holes and carrying fine soil with it. The fix is part drainage improvement and part soil control.
First, check the drainage holes. They should be open, but not so large that soil washes out. Cover them with a piece of geotextile fabric, landscape fabric, or fine mesh. This lets water through while holding most of the soil in place. Avoid using only loose gravel over large holes; fine soil can still wash down into the gaps.
Second, add a catch system. Place a sturdy drip tray, saucer, or shallow basin under the planter. Choose one with raised edges and empty it after rain or watering so it does not become a mosquito-breeding puddle. If the box is on a balcony, raise it slightly on pot feet or battens so air can circulate and you can slide the tray out.
Third, improve the soil mix. Heavy, fine soil compacts and sends muddy water out quickly. Use a coarse, free-draining potting mix blended with bark, perlite, or coarse compost. Top the soil with mulch or a thin gravel layer to stop rain and watering from splashing fine particles into the drainage path.
Water more slowly and less often. Apply water until it just begins to drain, then stop. For balcony planters, a small watering can or drip irrigation is easier to control than a fast hose. After heavy rain, check the tray and drainage holes.
If the planter is built in, line it with a waterproof membrane that slopes toward a drain, and use a filter fabric over the drain. For simple boxes, a false bottom with a drainage outlet and filter fabric can keep muddy water contained. With clear holes, filter fabric, a drip tray, and better watering habits, your urban planter should stop leaving muddy stains everywhere.