一维水平非饱和水动力参数的测定原理

Ei?Gi?1/2?Di?1/2kk?1/2k?1/2r?k?1/2k?t2?x2

k?1/2Hi??Aici?1?Fici?1(?zqi?1?Dk?1/2i?1/2k?Di?1/2?Gi?1/2kik?1/2?Gk?1/2i?1/2??i

r)c土壤含水率除满足溶质运移基本方程外，还满足非饱和土壤水分运动基本方程：

??c?t???x(D??????x)??k???x?

方程中，k(?)是土壤水扩散率，D(?)是土壤水导水率，实验表明k(?)、

D(?)均与含水率?近似成指数关系，故采用D(?)?a?，k(?)?c?，

Dsh?e?fbd，a,b,c,d,e,f是由土样试验确定的参数，显然，

?k(?)?k?(?xk(?)k(?),??,D,?()?),??,D?(?)?D?x?D(?)?x,k1,k2使得是有界的，即存在常数?k2

()k1?k(?),?k(?)??,?k(?)?x,D(?),?D(?)??q??D(?)(ck?1i???xki

Dlhi?1(ci?1?ci2?k?1i?c?)kik?1k?1k?1?t?)?Dlhi?1(ci2k?1k?1?ci?1)k?1?x?Dik?12k?1(cik?1?ci?1)(?i?x2k?1k?1??i?1)k?12k?1

k?1?ci[Di?1(?i?1??i2k?1k?1k?1)?Di?1(?i2??i?1)]k?1?xk?12ci?ik?1k?1?ci?i?ci?1r[Dlhi?1?Di?1(?i2kkk?1k?1k?1??i?1)]??i?1)?(Dlhi?1?Dlhi?1)?Di?1(?i?1??i222k?1?cir[(Dik?1k?1k?1?Di?1)(?i2k?1k?1k?1k?1k?1k?1k?1k?1)]?ci?1rDlhi?1?ci?1r[Dlhi?1?Di?1(?i22k?12k?1k?1k?1k?1??i?1)]k?12k?1?ci{?ik?1k?1k?1?r[(Dik2k?1?Di?1)(?ik?1??i?1)?(Dlhi?1?Dlhi?1)?Di?1(?i?1??i222k?1k?1k?1k?1k?1k?1)]}?ci?1rDlhi?1?ci?ik?1k令

ai??r[Dlhi?1?Di?1(?i22k?1k?1k?1??i?1)]k?1k?1bi??ik?1?r[(Dik?12k?1?Di?1)(?i2k?1??i?1)?(Dlhi?1?Dlhi?1)?Di?1(?i?1??i222k?1k?1k?1k?1k?1k?1)]ei?rDlhi?1hi?ci?ik?1kk则上式可写成

aici?1?bicik?1?eici?1?hi

k?1最后写成?A???ici?

k?1??H?矩阵形式