How to explain this unit root process?

I have a time series $X_t$ (shown below) with a structure break. The stationary test kpss.test() says it has a unit root. How to explain this? Why does $X_t$ have a unit root? Sure it is not constant in mean, so it is non-stationary. But I can not relate its non-stationarity to the concept of unit-root.

x=c(rnorm(1000,0,1),rnorm(1000,10,1))
kpss.test(x)

The $p$-value of the test is 0.01, so we reject the null hypothesis of a stationary process.

For example, a random walk has a unit root but it is constant in mean. So any relationship between unit root and constant-in-mean? Any comments about this? • Note that a random walk does not have a constant mean; its first difference does. Nov 21 '13 at 9:41

• Thanks for you answer. When I use PP.test to this time series. It gives me $p=0.01$, which means a wrong assumption of unit root. If I use 'adf.test', it gives $p>0.1$, so we don't have enough evidence to reject the null hypothesis of unit root. A little bit confusing here. Do you have any comments please? Nov 22 '13 at 4:09