Based on provincial panel data of water footprint and grey water footprint, and with the help of data envelopment analysis model considering and without considering the undesirable output, this paper estimates the water resources utilization efficiency in China from 1997 to 2011. The spatial weighting matrix based on economy-spatial distance function is established to discuss spatial autocorrelation of water resources utilization efficiency. With the help of absolute β-convergence model, this paper concludes that there exists β-convergence in the water resources utilization efficiency. Under the conditions of considering and without considering the undesirable output, it takes about 52.6 and 5.6 years respectively to achieve the extent of half of convergence. By mean of the spatial Durbin econometric model, this paper studies spatial spillover effects of the provincial water resources utilization efficiency in China. The results are as follows. 1) With considering and without considering the undesirable output, there is significant spatial correlation in provincial water resource efficiency in China. 2) Under the two cases, the spatial autoregressive coefficients (ρ) are 0.278 and 0.507 respectively, at 1% significance level. There exist the spatial spillover effects of provincial water resources utilization efficiency. 3) With considering the undesirable output, these factors of the education funds, the transportation infrastructure, and the industrial and agricultural water consumption proportion have positive impacts. These factors of foreign direct investment, the industry value-added water consumption per ten thousand yuan, per capita water consumption, and the total precipitation have negative impacts. 4) Without considering the undesirable output, the factor of GDP per laborer has a greater positive significant influence on the water resources utilization efficiency. However the facts of industry value-added water consumption in ten thousand yuan and the transportation infrastructure have no significant influence. 5) Regardless of undesirable output of water resources utilization efficiency, the assessment of the present real water resources utilization in China will be distorted and policy-making will be misled. The water efficiency measure considering environmental factors (such as gray water footprint) is more reasonable.

The stability of a slope with reinforcing piles in anisotropic and nonhomogeneous soils is analyzed using the kinematic approach of limit analysis combined with a strength reduction technique. A slope without piles is considered first and the limit state equation is obtained to determine both the safety factor and the critical sliding surface for a given anisotropic and nonhomogeneous slope. The solutions are compared with published data to verify the practicality of the approach. A slope stabilized by a row of piles is then analyzed. Next, mathematical optimization is used to derive analytical expressions for determining the lateral force provided by piles (this is required to increase the slope safety factor to an expected value). Numerical examples are then applied. The optimal location of piles within a slope and the effects of nonhomogeneity and anisotropy of the soil strength on the dimensionless limit stabilizing force are also studied. Finally, a simplified procedure is proposed for a structural design that stabilizes the piles against landslide.

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