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You need a resistor in parallel with the piezo, or alternatively from pin 1 of the op amp to ground. See my previous email. Without this, the circuit won't work at all, the output will go to +5v after a short while and stay there. Your simulation is incorrect because you have simulated the piezo as a voltage source, instead of a voltage source in series with a capacitor.
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The output of the op amp is saturating in a positive direction when the input is negative because you are simulating with a very large input signal, much larger than you are likely to get from the piezo unless you hit it.