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To avoid serious clogging and loss of drainage capacity, which puts the underground structure at risk of anti-floating failure, the buried drainage filter must be equipped with a nonwoven geotextile layer. In this scenario, nonwoven geotextiles are subjected to normal compressive stress, which can cause changes in geotextile porosity and structure, affecting the filtration behavior of the geotextile filter. In this paper, in order to evaluate the filtration compatibility of the soil–geotextile system, gradient ratio (GR) tests were performed under a hydraulic gradient of 1.0 using a specially designed gradient ratio filtration device capable of applying normal stress. In total four nonwoven geotextiles and two types of soil were used. The results of the gradient ratio filtration tests were discussed in terms of GR values, the permeability of the soil–geotextile system, and the amount of fines retained in geotextiles. It was shown that under a larger normal compressive stress, the GR value would also increase, while the permeability coefficient of the soil–geotextile system decreased. The filtration responses to various soil–geotextile combinations differed under normal compressive stress. A thick nonwoven geotextile with a small filtration opening size exhibited poor filtration performance while benefiting soil retention. Fines retention was influenced by geotextile thickness, soil type, and normal compressive stress magnitude. In addition, for nonwoven geotextiles filter fine-grained soil under normal compressive stress, the test results indicated that anticlogging design criteria should be improved.