some sites have ever used the jet grouting method to improve the soil. as you have mentioned, there is medium sand at formation level. it may be a good idea to jet grout below the formation level before excavation, or deep mixing method to form the water-tight wall along the excavation trench. but in this method the hydraulic heaving should be checked in case the grouted slab is spoiled by uplifting force. =;Q:z^S
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I have ever seen the combination of recharge well and relief well. the premise is water should be cut off with sheetpile/diaphram wall/ or soldier pile wall before the wells start to work.
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generally the relief well is useful in soft clay rather than in sand.