Stop Gridsplitter stretching content beyond window

Given the below XAML, how do I have the gridsplitter respect the MinHeight given to the 3rd row and have the content remain inside my window?

<Grid>
    <Grid.RowDefinitions>
        <RowDefinition Height="Auto" />
        <RowDefinition Height="Auto" />
        <RowDefinition MinHeight="40" />
    </Grid.RowDefinitions>
    <Expander Grid.Row="0" ExpandDirection="Down" VerticalAlignment="Top">
        <Grid>
            <Grid.RowDefinitions>
                <RowDefinition Height="Auto" MinHeight="40" />
                <RowDefinition Height="*" />
            </Grid.RowDefinitions>
            <Border Grid.Row="0" MinHeight="100" Background="Black" />
            <GridSplitter Grid.Row="1" Height="5" HorizontalAlignment="Stretch" VerticalAlignment="Bottom" Background="LightBlue" ResizeBehavior="PreviousAndCurrent" />
        </Grid>
    </Expander>
    <Expander Grid.Row="1" ExpandDirection="Down" VerticalAlignment="Top">
        <Grid>
            <Grid.RowDefinitions>
                <RowDefinition Height="Auto" MinHeight="40" />
                <RowDefinition Height="*" />
            </Grid.RowDefinitions>
            <Border Grid.Row="0" MinHeight="100" Background="Black" />
            <GridSplitter Grid.Row="1" Height="5" HorizontalAlignment="Stretch" VerticalAlignment="Bottom" Background="LightBlue" ResizeBehavior="PreviousAndCurrent" />
        </Grid>
    </Expander>
    <Border DockPanel.Dock="Bottom"  Grid.Row="2" Background="Lime" MinHeight="30" >
        <TextBlock Text="{Binding RelativeSource={RelativeSource Mode=FindAncestor,AncestorType=DockPanel},Path=ActualHeight,StringFormat={}{0:f0}}" />
    </Border>
</Grid>