The decay of the proton-rich nucleus $^{22}$Si was studied by a silicon array coupled with germanium clover detectors. Nine charged-particle groups are observed and most of them are recognized as $beta$-delayed proton emission. A charged-particle group at 5600 keV is identified experimentally as $beta$-delayed two-proton emission from the isobaric analog state of $^{22}$Al. Another charged-particle emission without any $beta$ particle at the low energy less than 300 keV is observed. The half-life of $^{22}$Si is determined as 27.5 (18) ms. The experimental results of $beta$-decay of $^{22}$Si are compared and in nice agreement with shell-model calculations. The mass excess of the ground state of $^{22}$Si deduced from the experimental data shows that three-nucleon (3N) forces with repulsive contributions have significant effects on nuclei near the proton drip line.
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