Analytical solution of soil deformation caused by vertical pipe jacking construction considering grouting pressure.

As the distance from the centre axis of the pipe ( y = 0) increases, the value of the horizontal displacement also increases; with increasing depth, the value of the horizontal displacement shows a decreasing trend, reaching its minimum at z = 8 m.

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Within this range, as the burial depth of the horizontal utility tunnel rises, the resulting vertical surface displacement generally exhibits an increasing trend.

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